(Technology Infrastructure Series)

In case you’re taking seriously guarantees about uptime, reliability, or backups advertised by website hosting companies, you should know that most guarantees of service are an idealized concept, especially if you use a low-cost web hosting service. Now, this doesn’t mean you should avoid low-cost web hosts. What you should do [...]]]>

(Technology Infrastructure Series)

In case you’re taking seriously guarantees about uptime, reliability, or backups advertised by website hosting companies, you should know that most guarantees of service are an idealized concept, especially if you use a low-cost web hosting service. Now, this doesn’t mean you should avoid low-cost web hosts. What you should do is give a little thought to the “what if’s” that may arise, and what you can do before they arise to minimize the pain when they do.

In this article, I’ll go through a few situations you might want to consider, and some options you can use to reduce your risk.

In case you’re taking seriously guarantees about uptime, reliability, or backups advertised by website hosting companies, you should know that most guarantees of service are an idealized concept, especially if you use a low-cost web hosting service. Now, this doesn’t mean you should avoid low-cost web hosts.¹ What you should do is give a little thought to the “what-if’s” that may arise, and what you can do before they arise to minimize the pain when they do.

Prepare for Data Vaporization

The first thing is to accept that, even with top-dollar sites, “Life happens”. No amount of post-disaster frustration will bring back your data if it has vaporized, and the compensation — typically the waiver of a month’s hosting fees at most — is usually meaningless when compared to the time it has taken to configure your site and enter your data. So, no how much you pay, nor how good the “guarantee” seems, you should always take care to maintain your own set of backups of crucial content, databases, and software configurations.

Some sites make backups easy by providing administration dashboards such as cPanel. If they do, you should take advantage of the user-friendly interface, and schedule periodic backups.

But even if you use these services, you should also go in through an FTP client and physically create a local tarball (assuming your webserver is a Linux machine) of your entire home directory and download this onto your own computer — Windows or Linux, either is fine. This is the only way to ensure that you have everything, including server logs, configuration settings, etc., stored elsewhere.

Handling Backups

Date your backups. Keep at least the last two. And retain at least one snapshot from every 6-12 month period, going back indefinitely. That way, if you don’t notice something has gone missing for some time, you’ll still have a reference to go back to. If this sounds prohibitive, remember: storage space is cheap. You can now buy a terabyte drive in an external enclosure for under US$75 (55 GBP).

Plan for Mid-Stream Disruption

Once your site is up and running, every connectivity hassle with your hosting company will be magnified a thousand-fold as you imagine frustrated users unable to connect and giving up on your site. To give yourself the greatest flexibility in finding a speedy resolution, I’d recommend studiously avoiding the “bundled” domain + hosting offers that are so common and heavily advertised.

Buy your domain name registrations separately from your hosting service contract, being sure to keep the two companies separate as well. The key is flexibility as an operating principle.² In the event of repeated problems with your hosting company, it is often simpler and cheaper (and less damaging to your users) to simply take your site-hosting business elsewhere.

If you’ve registered your domain name with a different company than your webhost, you can simply open an independent hosting account with a third company offering similar features and a similar software stack. While the original site is still configured, migrate your content and those critical configurations from one site to the other, testing as you go. Once the new site is ready, simply redirect your domain name traffic from the host with the problems to the site with the newly selected host, and you’re ready to roll again.

Since domain name redirection happens with the company you registered the domain with, you can see why it is important to keep this an independent third company. That way there is no conflict of interest, and minimum likelihood of additional complications. Once your web traffic situation is taken care of, you are free to continue to pursue a resolution with the previous company, or just cut your losses (chalk it up to “cost of doing business”).

The Concept of a “Warm Site”

If you’re truly in the mindset of disaster prevention, or if your website represents a critical operating asset that you simply cannot afford to have go down, then consider taking these precautions one step further.

To combine low monthly costs with seamless service for your users, consider opening that second hosting account before the problem happens and keeping it configured and current, ready for disruption. In this way, you’ll have a reasonably low cost duplicate server that serves as a “warm site” — ready to go at any time. In the event of disruption, simply redirect your domain name to the warm site, and your users will be slid over to the prepared backup while you resolve the issues with the primary site. You should know, however, that it takes a while for domain redirections to propagate through the system. For a level of redundancy that provides “flick of a switch” transitions, you’ll need true mirrored servers, i.e. an enterprise level hosting service.

An Ounce of Prevention…

If you’ve ever had the unenviable task of migrating hosting services under pressure, you’ll know that in the data business, a pound of cure would be a bargain — real life remedies can get much more costly. So, start those backups, consider those what if’s, and start taking steps toward regular, sustainable disaster management of your data.

Footnotes

Statistics and Data Mining Series, Part 1 of 3

For a variety of reasons, meaningful website visitation and behavior statistics are an elusive data set to generate. In this series of articles, I’ll describe an approach using free, open source tools and basic statistical and data mining techniques to dig into your site’s traffic patterns, [...]]]>

Statistics and Data Mining Series, Part 1 of 3

For a variety of reasons, meaningful website visitation and behavior statistics are an elusive data set to generate. In this series of articles, I’ll describe an approach using free, open source tools and basic statistical and data mining techniques to dig into your site’s traffic patterns, find and then filter out spurious traffic data, and gain insight into visitor profiles and characteristics.

Along the way, we’ll encounter the “Good News Cheap, Bad News Expensive” Paradox of Data Mining — or, why raw information is often used “as-is”.

What are Visitor Statistics?

Every site with online articles deals with a fundamental question: who’s the audience? And the more fine-grained the answer, the better. For example, one might like to know what kinds of readers are reading (academic?, individuals?, commercial?, military?, government?), from where they are reading (by country?, city?, browser?, from a desktop or mobile platform?), whether they are new visitors to the site or returning visitors, how often they visit, how many pages were read on each visit and which ones. And if a reasonable gauge of interest or engagement level could be had, that would be swell!

Why is it so difficult to get meaningful results? The answer lies in where website visitation information (the raw data) comes from and how it is generated.

Where the Information comes from: Server-Side vs. Client-Side Statistics

There are two fundamentally different ways in which one obtains web traffic statistics: at the server side, generated by the webserver itself, or at the client side, generated by client-side code that executes within the user’s browser whenever a page is loaded that has this tracking code in it. Each method has its own pros and cons, and its own biases.

Client-side statistics require information to be sent to a traffic-recording server directly from the user’s browser, typically bypassing your own webserver. To do this, client-side statistics require that you add special code to each page of content that you want analyzed. When the page is loaded by a user, the embedded code on the page executes and makes a connection with a traffic-recording server, which updates its tally. (If the client-side code is prevented from running (for example, if JavaScript — a typical implementation language — is blocked, you get nothing.)

For client-side statistics, fast traffic-recording servers with high uptime are crucial in order to minimize the overhead that the user experiences due to the additional roundtrip time caused by the execution of the client-side code. For this reason, client-side statistics were typically a paid-for service. You paid for two things: the uptime and fast response time of the traffic-recording server, and for the analytical methods — sometimes transparent, sometimes proprietary — that were used to generate the statistics that were then made available to you as reports. But the client-side statistics game is changing, thanks to Google Analytics, a free client-side statistics package. Wikipedia review here.

By contrast, Server-side statistics are typically generated from information that resides in the logs that your own webserver and its various modules maintain by default. Thus server side statistics do not affect the user’s browing experience.

From the processing standpoint, server-side statistics are typically free, courtesy of some excellent open source web analysis packages. But perhaps more significantly, with server-side statistics you have complete control over how the entire history of your web-site’s traffic data is analyzed. The advantage is that you know exactly what processing methods you’re using to obtain your visitation numbers, and thus what kinds of biases are involved. You can analyze, re-analyze, and set up heuristic filters of your own, re-processing the entire history at will. This means that you can evolve custom heuristic filters suited to the nature of your site’s particular traffic patterns. As these algorithms evolve, the entire history can be re-processed using the same algorithm, thus keeping your time-series data ready for direct comparisons.

Fortunately, these two methods are not mutually exclusive. And as with any estimation problem with elusive quantities, you should ideally use more than one estimator, exploiting the particular characteristics of each to improve the joint estimate.

With this as background, let’s look at the headlined question:

Why is it Difficult to Obtaining Meaningful WebSite Visit Statistics?

For most content generating sites, “meaningful” means interested humans reading the material. Robots and Web Crawlers don’t count. Casual glances (i.e. the “gone in 60 seconds” visitors) don’t count. The driving desire is to understand one’s audience through its online behavior, as opposed to using survey techniques.

With the advance in web based technologies and platforms, one might think that it would be reasonably straight-forward to get meaningful traffic-based statistics. But if you’re looking for counts and histograms that are ready to be interpreted as “interested human visitors”, you are likely to come away less than satisfied.

Below are seven reasons why the interpretation that one would like, is difficult to get:

1. Ubiquitous Autobot Traffic (Autonomous Web Crawlers).
2. Congestion-Reducing Proxy Cache services.
3. Dynamically Allocated IP Addresses.
4. The Absence of Unique Identifiers
5. Content Distributing Feeds and Feed Readers
6. Your Own Organization’s Intefering Traffic
7. Self-Reinforcing Visitation Patterns and Time-Varying Change in Variance

Let’s look at each of the seven reasons in turn. This discussion will set the stage for the reasoning behind the heuristic filters we’ve implemented.

(1) Ubiquitous Autobot Traffic.

For the past several years, there has been an ever increasing volume of autonomous network traffic that does not represent human eyeballs. This traffic consists of autobots, indexers, search engine spiders, content scrapers, link fishers, automatic comment spammers, and automated hacking bots, among others, all of whom generate “hits” and often even page loads that inflate your server-side traffic statistics.

Now, some autobots identify themselves as such, making it relatively easy to filter for them. But the increasing global availability of cheap server space through server farms or low cost cloud computing platforms (such as Amazon’s) has made the identification problem more difficult. Autonomous activity originating from these clusters are now able to draw from a much larger pool of IP addresses and to operate from better and faster platforms. Typically, these autobots are not the helpful type, consisting largely of hacking bots, automatic comment spammers, content scrapers, link fishers, and the like.

The type of autobots that visit your site and the regularity (or lack of it) with which they visit, affect the kind of biases you can expect in your statistics. For example, search related autobots typically return repeatedly to your site, and do so from a small and relatively stable pool of IP addresses. Thus, the visits due to such autobots adds unfounded strength to the apparent proportion of returning (human) visitors than is in fact the case. As another example, indexers typically return within seconds or minutes of a change being made to a page that they are tracking. So, if you tend to make lots of edits “live” on your site, you will generate spikes of autobot traffic correlated with your edits, spikes that may be misinterpreted as interested readers.

Thus, though not all autobots are bad — indexers and search engines are important for your site to be discovered by those who would find it useful. But if your goal is understanding your site’s human readership, then autobots of all types are an undesirable source of noise in your data set, and need to be filtered out.

(2) Congestion reducing Proxy Cache services.

Proxy Caches are servers that cache frequently requested pages on a network so that they can re-serve them without having to send a request for content onward to your webserver and wait for the return. Proxy Caches are often part of wide area network congestion management solutions, and can be quite efficient in reducing traffic. But in order to maintain their relevance, they reach out to your website periodically (many quite frequently), and perform a quick check to see if their cached pages have changed.

The challenge for server-side statistics is that there is no server side indication of how many eyeballs accessed your content pages from the proxy cache server instead of from your webserver. This is one of the areas where client-side statistics do better than server-side, since the tally is generated by tracking code executing with the user’s browser whenever any of your content is loaded, regardless of whether that content is served from your server or from a proxy server.

(3) Dynamically Assigned IP Addresses.

Raw visitor statistics are primarily based on IP Address. But a large proportion of IP addresses are issued dynamically by an ISP or an institutional ASN. So, if you merely look at returning IP Addresses to measure returning visits, your perception of returning visitors will be biased low.

For example, a typical ISP may respond to every IP address request with one of a number of IP addresses available in its allocation space. This may mean a new IP address allocation every time a user connects to the Internet, or after a reboot, or once a particular IP allocation has expired.

At the extreme end of dynamic IP address allocation are ISPs such as AOL that re-issue a new IP address for every page that a visitor views.

Dynamic allocation makes it difficult to equate IP Addresses with visitors, an assignment that requires additional criteria.

(4) The Absence of Unique Visitor Identifiers

Browser privacy being what it is, you typically cannot (nor in good conscience should you) search for an actual identity. However, what you can do is put together a virtual “pseudo-identity” that is likely to be associated with either an individual or a small number of closely associated individuals (e.g. those sharing a computer or access point). This is sufficient to obtain estimates on whether the visitor is new or returning, and on their engagement level with the material?

(5) Feeds and Feed Readers

Feed issuers and feed readers mean that users can (depending on how you set these up) read text versions of your content without actually visiting your site. This is a problem for both server-side as well as client-side statistics, and even for feed stat-keepers such as Google’s Feedburner.

(6) Your Own Organization’s Intefering Traffic

As a site owner, your activity on your site is an additional, possibly non-trivial source of “noise” on your visitor statistics. Depending on how often you review your site, add content, test it, and maintain it — especially in the early stages of a site launch — all of these add to the total number of hits and pages counters. Unless you filter out your own activity, you will be biasing your results high.

Similarly, if your organization spends time on various parts of your site, then these visits should also be filtered out — unless page reads by your team count as ‘reads’ that you want to track.

(7) Self-Reinforcing Visitation Patterns and Time-Varying Change in Variance

As your web-traffic grows, traffic monitors and other bots are attracted, which makes volumetric comparisons tricky. The variance of the time-series is affected both by your and your organization’s beahviors, but also by the behaviors of other users.

The Need for Filtering

The reasons discussed above mean that using raw visitor statistics, without careful cleanup, for estimates of visitor traffic is fraught with inaccuracy. Both the direction of the biases as well as the variance in the estimates may be changing. Trying to untangle the data takes some effort.

This leads to the next problem — a psychological one common in many applications of analytics to business.

“Good News Cheap, Bad News Expensive” — or Why Raw Information is often used “As Is” in Business Decision-Making

As we’ve seen, website statistics are a perfect example of a moving, noisy target. Somehow related to the wealth of raw traffic data, it is clear that there are reasonably good answers. But what these relationships are and how to get at them is not obvious and takes work.

I’ll call this one the “Good News Cheap, Bad News Expensive” Paradox. The name highlights the problem. Everyone wants good news. But, if the raw data already deliver so-called “good news”, in this case through high visition numbers, or a large proportion of returning visitors, then this “good news” is in itself a counter-motivation to investing further time and energy in developing better heuristic filters. This is even more so if it is clear that the advanced techniques are likely to deliver worse news, for example, that your real visitors (the human ones who are likely to be actually reading your articles) are fewer than the raw numbers suggest.

The difference between the two numbers can be quite dramatic. For example, in a small, relatively new site, the difference between raw or lightly filtered visitor stats and thoroughly filtered stats in which a substantial amount of spurious traffic is removed, can be as much 30% of the total traffic. That kind of reduction in “good news” requires substantial additional insights to soften the blow.

Enter data mining techniques.

Escaping the Paradox — the Value of Data Mining

Like many paradoxes, the resolution to the “Good News Cheap, Bad News Expensive” Paradox is a change in point of view. Through the use of data mining techniques, one obtains a more detailed, multi-dimensional characterization of visitor profiles and behavior, something that is impossible when looking only at the raw or lightly filtered statistics. It is this additional information that offers the additional value required to escape the “Good News Cheap, Bad News Expensive” Paradox.

For those willing to put in the effort in pursuit of that elusive better understanding, heuristic filtering and data mining techniques are an approach well worth considering.

In the next article in this series, I’ll turn to the practical matters behind getting your hands on the right data, developing useful heuristic filters, and implementing these to supplement the results of existing open source tools. We’ll use our own visitor statistics to illustrate the examples. Stay tuned!

Abstract

One of the fascinating areas to arise recently in applied mathematics has been Mathematical Finance. From a technical point of view, Mathematical Finance uses a broad range of sophisticated mathematics for its financial models, and relies on state-of-the-art software engineering and computer hardware to implement these financial models, often in real-time.

Whether one is interested [...]]]>

Abstract

One of the fascinating areas to arise recently in applied mathematics has been Mathematical Finance. From a technical point of view, Mathematical Finance uses a broad range of sophisticated mathematics for its financial models, and relies on state-of-the-art software engineering and computer hardware to implement these financial models, often in real-time.

Whether one is interested in technology or not, there is a kernel of core financial ideas at the heart of the global free market capitalist system that every literate citizen should understand. Whether we agree with their principles or with the inequities that are, arguably, the result, these ideas are in place across most of the world today. A closer look at mathematical finance will offer a better understanding of the mechanics of the modern financial world.

In this article, I’ll motivate the need for financial mathematics through a simplified account of the rise of the modern financial marketplace.

What is Mathematical Finance?

Introduction
One of the fascinating areas to arise recently in applied mathematics has been Mathematical Finance. This is a field whose development has occurred largely within the past forty years, with explosive growth taking place over the past twenty years.

From a technical point of view, Mathematical Finance uses a broad range of sophisticated mathematics for its financial models: from the partial differential equations of mathematical physics, to stochastic calculus, probabilistic modeling, mathematical optimization, statistics, and numerical methods.

But mathematics is just one of a two-headed technology requirement. The practical implementation of trading strategies based upon these mathematical models requires designing efficient algorithms as well as exploiting the state-of-the-art in software engineering (real-time and embedded development, low latency network programming) and in computing hardware (FPGAs, GPUs, and parallel and distributed processing).

Together the technical aspects of mathematical finance and financial engineering lie at the intersection of business, economics, mathematics, computer science, physics, and electrical engineering.

Whether one is interested in technology or not, there is a kernel of core financial ideas that every literate citizen should understand. These ideas are at the heart of the global free market capitalist system that, for better or worse, is in place across most of the world today. Whether we agree with its principles, its structures, or the inequities that are arguably exacerbated as a result, a closer look at mathematical finance offers a better understanding of the mechanics of the modern financial world. For the technologically inclined, there are ample opportunities to contribute.

What is Mathematical Finance?
Mathematical Finance, also called Quantitative Finance, is that branch of applied mathematics that is applicable to the needs of financial markets. Mathematical Finance develops and extends the models of financial behavior that are suggested by financial economics. Since the future is inherently unknown, mathematical finance is a data-intensive, stochastic subject and relies on simulations for many of its modelling formulations, for computing expected values of investment portfolios, and for evaluating and enhancing its trading strategies. Those who work in this field are called “quants”, an abbreviation for quantitative analyst, or financial analyst.

Financial Engineering, also called Computational Finance, is focused on the practical implementation of the models of mathematical finance and the simulations necessary to evaluate trading strategies. The mission is the engineering design and development of platforms and systems, often real-time, that are able to take in financial data and rapidly perform the large scale numerical simulations (monte-carlo, simulated annealing, etc.), for computing the likelihood of various outcomes and exploring refinements toward a preferably risk-minimizing strategy.

How did financial mathematics arise and why is it needed? In what follows, I’ll motivate the need for financial mathematics through a simplified account of the rise of the modern financial marketplace.

A Simplified Account of the Rise of the Modern Financial Marketplace

For all its present complexity, the evolution to the modern financial marketplace appears quite natural when viewed as the response to three basic questions that have been asked, over time, by increasingly more powerful actors, and involving increasing larger sums of capital. The three basic questions are:

1. I have excess capital (cash) – where can I put it safely?
2. I need capital – where can I get it reliably?
3. I want to improve upon my present capital position and reduce the exposure of my capital to risk – how can I do this?

Let’s take a look, moving from early history to more modern times. To keep the narrative light, I’m going to assume for the first part that you’re the one with excess capital. In the second part, I’ll take up the perspective from the point of view of a banking house in the pre-modern era of emerging statehood, national interests, expanded commerce and larger standing armies.

Along the way, observe how the increasing complexity of possible financial transactions leads to increasingly complicated questions of valuation, risk, terms, discounts, offers, and profit margins. These are the calculations that, carried forward to modern times and the modern financial landscape, form the subject of mathematical finance.

From Excess Capital and Mattresses to Money-lending and Banking Houses

Stage 1: Keeping Excess Capital in your Mattress or in a Hole

You have excess capital. Where do you put it? You could keep it in your mattress. There, it will earn no interest. And there is the attendant risk of theft, fire, rats, moisture and other ways in which your capital can be diminished.

Why? Because you are a little guy. Living in a little home. Vulnerable to being bullied, robbed, and ransacked. If it were known that you had a lot of cash in your mattress, you can be fairly sure of the outcome. You would undoubtedly have the pleasure of marauders whose perception of the risk of harm from you or chance of being caught by the authorities is less than their expectation of the profitability of breaking down your bedchamber door and un-stuffing your mattress.

Burying your capital in a hole in the ground is only slightly better. In effect, a hole in the ground is a fee-free deposit vault, but unfortunately the combination is simply the location. If at best, no one sees you make your deposit and you tell no one, your funds are safe assuming no accidental discovery – wind, earthquake, a dog, or someone digging another hole in the same place. At worst, your deposit is seen or you are followed, and your capital is dug up soon after you disappear around the corner.

Even assuming that you are able to dig, bury, and cover your deposit in absolute secrecy, there is another downside: once deposited you no longer have ready access to your funds. Every access to your funds requires unearthing and reburial, and any failure of secrecy in the process can mean the disappearance of the remaining funds.

So, where do you keep your money safe against unexpected impoverishment but also get reasonably reliable, safe access to your funds?

Stage 2: Armed Security: A “Safe Mattress” For a Fee

In such circumstances, you might decide to arm yourself so that you can personally protect your small fortune. But this puts at risk the one thing that is required in order to enjoy your wealth – your life.

So, it is reasonable to consider placing your money into the care of an agent whose business is the safe keeping and defense of many people’s money, not just yours. They would have to be well armed and well protected in order to provide a vigorous defense of the physical security of your money. You would, of course, have to trust the agent, and they would have to be worthy of that trust, otherwise you have just watched your money run away under an armed guard of your own choosing. And ideally, you would like to be able to withdraw all or part of your money readily at any time.

Now, armed deposit takers who would offer these services of safekeeping and ready access to deposited money, would do so for a fee since the services involve no small risk of attack, and require arms and guards to address this risk. But since this is a more appealing choice than either a hole in the ground (access problems) or your mattress (security problems), there would be those more than happy to pay a fee for the service.

In this way, those with substantial excess wealth either become their own fortified depositories, or pay a fee for that service, leading to the development of professional money-holders.

Stage 3: From Money-holders to Moneylenders to Banks

Switching perspectives to the point of view of our armed agent: over time, he has become a well known and trusted money-holder who, for a fee, holds sums from an increasing number of members of the community, amassing an increasing volume of physical wealth. What does the money-holder do with all the money that is deposited with him?¹

In all likelihood, those on sudden hard times needing a short infusion of capital, would have already come to the money-holder to inquire about the possibility of obtaining a loan. Under the pressure of their own circumstances, they are likely to be willing to pledge an additional fee (interest) in addition to repaying the principal, for the benefit of being able to borrow.

But before making loans with deposited capital, the money-holder would have to consider carefully: firstly, the risk of a default by the borrower. In the event of a default, the money-holder would himself have to make whole the entire amount to repay the original depositor’s deposit, himself bearing the loss from default.

What does the money-holder do? If he is ambitious and risk-taking, he charges interest for loans and begins to function as a (non-insured) bank. On the one hand, he accepts deposits for a deposit fee and pledges to hold your money safely for you until such time as you want it back. But behind closed doors, he loans out your money to borrowers, and charges them a lending fee (interest). (We’ll discuss interest in more detail later.)

As this goes on, the money-holder/moneylender must consider a second risk and must decide how much of the deposited capital should be held in reserve and how much should be allowed to be let out the back door as loans to others. The risk from lending too much is the situation of not having enough liquidity to return a deposited amount when a depositor attempts a withdrawal. This situation becomes extreme when war, rumors, fear, unrest, or other unstable circumstances cause a large number of depositors to rush to withdraw their money in a short space of time.

However, apart from the risk of having insufficient liquidity to cover withdrawals, all other self-interested considerations strongly support the money-holder lending a portion of deposited capital. By doing so, he increases his profits. Not only is he taking fees from depositors, but he is collecting regular interest on loaning out the deposited capital, which otherwise would sit idle. The additional profits from interest can be structured so as to cover expected losses from defaulting borrowers, or those from whom collection attempts fail. Finally, in the event of attack, his loss exposure is reduced since the deposited assets are dispersed among borrowers.

From excess capital to money-holders, and from money-holders to moneylenders, we see individuals that formerly acted as holders of money or that had reserves of excess capital, begin to make loans and collect interest on these while continuing to charge fees to depositors to hold their money safely and make it available on demand. Thus, the origin of banking houses.

Why Ordinary Citizens Do Not Easily Become Moneylenders
If this is indeed a natural pathway, one might expect larger numbers of ordinary citizens with a sufficient amount of excess capital attempting to directly invest by making loans and collecting interest.

But doing so profitably requires an increasingly specialized infrastructure. There is the requirement of maintaining a sufficiently strong armed force to protect your capital and your person You would also need goons to collect the debts and payments from borrowers reluctant to meet their obligations. You would need a “counter”, or store front, to which depositors could come to withdraw or add funds, and to which prospective borrowers can come to request loans. Finally, you would need an accounting function to keep track of the payouts and receipts, as well as the profitability of the operation.

The two functions of rudimentary banking houses, money-holding and money-lending, have become a specialized business of their own, and it is this specialization that limits the number of participants.

How a Strong State Provides Further Impetus to Finance

The evolution of simpler money-lending and collection, to the more complex systems of contractual, asset backed loans accompanies the maturation of the nation state and its attendant institution: the rule of law, courts for claimants, the honoring of contracts as a state value, and state-backed enforcement.

All of these developments contribute to the maintenance of good order in financial transactions. The resulting financial stability benefits banking houses as well as all those engaged in capitalist activity: borrowers, lenders, merchants, speculators.

The Evolution of Lending
As time goes on, banking houses that hold money and lend money become an essential part of the fabric of personal and commercial life. With increasing accumulated reserves of capital among banking houses, and increasing familiarity and patronage by the affluent and ambitious of the city, banking houses now begin to compete with each other to try to attract depositors and borrowers, knowing that they earn fees from both and require both in order to continue their profitable business.

One area of competition among them is the terms for deposits and loans. For depositors willing to fix their deposit for a longer period, the banking house may offer a discounted deposit fee as incentive. This provides long term reliable liquidity – good news for lending.

For loans, there may be different fees for different types of loans: unsecured loans (risker) and secured loans (safer). Whereas defaulting on a loan in earlier times often meant enslavement or indentured servitude, the onset of state enforced debt protection laws limited the recovery of unsecured loans to the pittance that a debtor’s prison might afford – effectively these loans were write-offs.

Secured loans on the other hand, are backed by the title deed to an asset which is then held by the lending agent in case of the borrower’s default on the loan. Borrowers who secure their loan with an asset that they own reduce the lender’s risk of loss from default, since in such a case the lender gets the asset. A lending house being asked for a secured loan might therefore charge less interest to such clients.

Profiting from secured loans, however, requires that the lender (banking house) be able to accurately assess the value of the asset against the eventuality of having to dispose of it at some point in the future in order to recover the outstanding amount of the loan on which a borrower might default.

The Role of the State
Notice that evolution of the financial marketplace to one offering diversified loan products requires a vital change, brought about by the increased strength of the state. Most importantly, the notion of a secured loan requires a stronger notion of private property, of contracts, and an arena for the enforcement of contracts that is more than simply a contest of strength between debt collector and delinquent. Of course, a stronger state and stronger voices of the people also mean additional limitations. For example, the abolition of penal consequences for debt default makes unsecured loans increasingly risky from the lender’s point of view of guaranteed profit. But rather than stifle the market for these loans, banking houses have responded to these and other constraints by factoring these into their risk and profit calculations.

The Rise of the Modern Financial Marketplace

With increasing confidence in the enforcement apparatus of the state and the reliability of contractual obligations, the stage is set for money to be borrowed by those offering incentives other than the typical interest or asset backed security. We then have venture capital, bonds, stocks, securities, and insurance.

And every diversification in the borrowing and lending business increases the incentive to develop better means of evaluating risks, assessing non-cash value, and forecasting valuations into the future, strengthening the role of financial analysis in the profit engine of the banking house.

From Moneylender to Financier (Venture Capital) and Investor (Bonds and Stocks)
One opportunity open to those with excess capital is the partial financing of a venture. A banking house or moneylender provides part of the capital in return for a share of the expected profits. The venture might be a trading expedition that requires capital to buy goods, a ship, and to pay a crew. A successful trading voyage promises to return with locally scarce items (spices, tea, woods, furs, metals) that will fetch a premium and allow the trader to repay the investment plus pay out a portion of the profits and still make out handsomely for himself and possibly the crew (if their labor was taken as an investment instead of for wages).

A less direct investment is the buying of a bond. A bond is issued by an individual or organization looking for capital and willing to repay the capital with interest. The only way to lose on a bond is if the bond-issuer defaults. In which case you will obtain a portion of the proceeds from a fire-sale of their assets.

Still less direct is the buying of a stock. A stock is issued by a company looking for capital and willing to pay out a dividend (share of the profits). Because a company that is doing well will be increasing likely to pay out dividends, their stock price rises. However, there is a risk that the opposite can happen, in which case the stock holder may lose all or part of their initial investment. But the fact that selling stock at the right time can yield substantial profits means that the stock market becomes attractive to those interested in relatively short-term speculation on the fortunes of businesses and industries.

In all three situations (venture funding, bonds, stocks), banking houses, through the 1700s and 1800s provided the crucial capital responsible for significant expansion of economic activity through overseas exploration, colonization, business expansion, infrastructure development, indeed, the bankrolling of governments, and the funding of warfare and standing armies. In return for their capital, they negotiated either some form of ownership in the venture or entitlement to a share of the profits. The arrangement meant profit for them, and liquidity for merchants, traders, adventurers, speculators, and governments – a Faustian bargain for some, but a source for dramatic economic benefits for others.

From Money-holder to Insurer: The Rise of Insurance
With the increasing complexity of the financial landscape and various contracts, loans, transactions, and investments, the desire increases for different kinds of insurance to offer protection against different loss scenarios: life, health, value, assets, business, fire, flood, earthquake, travel, default, a drop in value either through accident, attack, damage, loss, or insolvency.

The desire for insurance is obvious: one perceives a risk to ones wealth or investment and wishes to protect ones assets against diminishment due to unpredictable losses of various kinds. Clearly one would expect to have to pay a fee to the insurer for taking the risk of having to make whole the insured value. And, over time, these fees would diminish your capital. But, in the event of a catastrophe, you would at least not lose the entire asset.

From the point of view of the insurer, insurance is another business opportunity for those with excess capital. For a fee, one could insure the assets of others. Success in the business of insurance, even more so than the loan business, is directly related to the ability to accurately assess risk, likelihoods of various outcomes, and to charge appropriate premiums to allow the business to be profitable. The mathematics of profitable insurance pricing is actuarial science.

The Sovereign as a Borrower in the Financial Market
Perhaps the largest player in the evolution of finance to its modern day situation has been the entry of the sovereign himself. What institution can offer the greatest security against default? Historically, it was the sovereign himself, later the state, or government. But why does the government require liquidity? Typically it has been the desire for or threat of war, and the rapidly increasing cost of standing armies and modern warfare in general, that has forced the sovereign to seek additional liquidity beyond its natural base of income. Other reasons have been the construction of heavy infrastructure: roads, bridges, ports, airports, stadiums – all of which require cash. Or perhaps its treasuries are low and inadequate to cover the day-to-day needs of the state.

The sovereign or state typically has a good credit rating, i.e. is trusted to repay the loan. They have wealthy citizens, flourishing businesses, farms, etc., from all of which they collect taxes, a significant source of national revenue. So the sovereign issues a bond: that is, a contract that can be purchased. The contract is a pledge by the government to repay the face value of the bond at a fixed time in the future (maturity) and with a fixed interest rate.

In this manner, the rise of big government, nation states, and the exponentially increasing cost of warfare, of raising and financing standing armies, of building infrastructure, maintaining overseas holdings, all expanded the needs, volumes, and clients of financial activity to an inter-state level, including the government issuing of bonds.

Just as stocks did, bonds also become something that can be traded. They become assets with a face-value worth plus additional interest to be paid on them, and a (typically small) risk of default. By brokering the buying and selling of bonds, the financial markets have made lending an activity that everyone can participate in – small amounts from many people – thus the democratization, if you will, of money-holding and money-lending “to the masses”.

Expanded Mercantilism as a Catalyst for Financial Activity
Coincident with the rise of nations was the dramatic expansion of the middle class and the development of extensive and regular commerce and trade internationally, along with expeditions of exploration, conquest, and colonial exploitation. These activities also required capital, often on credit, often as investments, venture capital, or stock.

The accompanying proliferation of financial activity led to the creation of trading exchanges, brokers, insurers and re-insurers. Larger streams of cash flow, easier capital, all led to the rise and expansion of commodities markets, stock markets, bond markets, and various specialized exchanges for the trading of contracts, securities, and investment vehicles.

The various elements of the modern financial landscape were thus born: capitalists (those with excess capital), banks, financiers (banks, wealthy individuals), insurers and re-insurers, brokers, and exchanges becoming fixtures in the financial life of modern cities.

From Financial Analysis to Mathematical Finance: Investment, Valuation, and Risk Assessment
As the transactions and arrangements of capitalists and financiers (banks, wealthy individuals, moneylenders, insurers) became increasingly complex, there arose the need for better ways to compute the optimal strategies for assessing fees, generating profits, minimizing losses, forecasting changes in value, and developing profitable investment strategies.

Mathematics has always been involved, but in the past thirty years, the application of techniques of advanced mathematics have transformed both the ability to more accurately model financial behavior, and to manage risk more analytically. The collection and refinement of the techniques of valuation, risk assessment and investment strategy are at the heart of mathematical finance.

A PDF version of this article is available here.

Footnotes

¹The money-holder could bury it in a hole, but this has the same disadvantages associated with an individual, only on a larger scale. Certainly, from the fees levied for this service, the money-holder would fortify his home and employ a larger group of better armed men to guard against attack. But if all of the capital resides in one location, even a well-guarded fort becomes an increasingly attractive target for coordinated assault, or treachery from within. Over time, simply holding money in one location becomes an increasing burden.

(Mathematical Toolset Series: TeX & LaTeX, Part 1 of 3)

If symbols, formulas, and equations comprise a large portion of your professional communication, then becoming familiar with the LaTeX / TeX platform should be high on your to-do list. With the right tools and a little practice, the relative ease of creating beautiful documents with [...]]]>

(Mathematical Toolset Series: TeX & LaTeX, Part 1 of 3)

If symbols, formulas, and equations comprise a large portion of your professional communication, then becoming familiar with the LaTeX / TeX platform should be high on your to-do list. With the right tools and a little practice, the relative ease of creating beautiful documents with TeX may mean that you soon leave your favorite Office suite in favor of TeX for your technical writing.

This article introduces the LaTeX / TeX platform, illustrates its capabilities, and highlights the key differences between using TeX for document preparation and more commonly used word processing systems.

For those that like to know the human side of the tools they use, a little history of TeX, the philosophy motivating its development, and something about its legendary creator, is included.

TeX Appeal

LaTeX, spoken “lay-tech” or “lah-tech”, is a professional document preparation system built atop TeX, spoken “tech”. The name, TeX, is from the Greek, technos, meaning craft, or technology. Together LaTeX and TeX form a powerful typesetting platform that produces “camera-ready” print with a minimum of fuss, even for difficult material such as mathematics. Using TeX means that you can communicate complex ideas in an aesthetically pleasing form, which means your ideas are more likely to be read, understood, and hopefully absorbed.

Here, for example, is what you would get after typesetting the binomial formula in LaTeX.


$(a + b)^n = \sum_{k=0}^n \binom{n}{k} a^k b^{n-k}$


To really get a feel for the quality of automatic typesetting that TeX produces, look at a few articles created in LaTeX:

This is how an article looks that was created in LaTeX and contains mostly words:
Mathematics in Pre-History (PDF)

And here is an article, created in LaTeX, having complicated formulas, equations, images, and code listings:
Finite Summations of Integer Powers , PART THREE (PDF)

Download these and browse through their formatting and display. Notice the automatic typesetting details such as kerning (spacing between letters), and subtle differences in how adjoining letters look: vs. ff, for example. These, and a host of typesetting subtleties are what distinguishes professionally typeset camera-ready copy from, for example, a Microsoft Word document turned into a PDF. The effort that would be required to manually typeset a similar looking article in Microsoft Word or Sun’s Open Writer would be prohibitive, and not least because of the in-depth knowledge required akin to that of a professional typesetter. By now, if you are not already using LaTeX / TeX, you are hopefully persuaded to give it a try. (If not, here are 10 further reasons to consider.)

“WYSIWYG” vs. the TeX Way — a Philosophical Difference

“WYSIWYG” is an acronymn for “What You See is What You Get”, and represents the idea that the writer is in charge of every aspect of the typography and layout of his product. LaTeX / TeX adopts the opposite point of view, namely that the competence of most writers is highest in the area of creating content, and diminishes as the aesthetic standard for beautifully laid out documents is raised. Thus, the driving idea behind the creation of TeX is that if a computer can be programmed to perform typesetting and layout with the same aesthetic sense of a master typesetter, then most writers would gladly relinquish the responsibility of having to manually make their work look beautiful.

Thus, the heart of the difference between LaTeX/TeX and the so-called “WYSIWYG” programs such the Microsoft, Corel, and Sun Office suites, originates in this philosophical view of the appropriate division of responsibility between writer and typesetter. But this simple philosophical difference results in substantial practical differences, and document preparation platforms that are substantially different in usability, suitability for various writing activities, and quality of the finished product.

The good news is that with the right tools and a little practice, creating documents using LaTeX is relatively easy. And once you get used to the beautiful look of TeX-ed documents, you’ll soon find it onerous to go back to the usual “WYSIWYG” programs such as the Microsoft, Corel, and Sun Office suites, among others, and let TeX do a professional job typesetting for you.

Understanding the Platform: Engine vs. Wrapper

The key to understanding the LaTeX / TeX platform is to recognize the different roles that each of the two software systems plays. TeX is the master typesetting engine that makes it all possible. TeX is versatile and powerful, but complex, with many settings, switches, and configurations possible. Most users don’t compose their documents directly in TeX. So although TeX is the typesetting engine, it is actually LaTeX that you will be using.

LaTeX is wrapper software that encapsulates the powerful functionality of TeX but presents to the user a friendly interface for getting on with the business of document preparation. All of the capability of TeX is still present, but with defaults that are intelligently chosen so that you can proceed out of the box and need only dig deeper when you wish to make major changes to layout or formatting.

Finally, there is the optional, but desirable graphical environment within which most users, especially new users, will actually compose their documents. This provides a pleasant, mouse-enabled method for selecting styles, mathematical and symbolic objects, and the markup elements that go into specifying a TeX document. The markups are descriptive — they inform the typesetting system of your intent. Unlike the WYSIWGY programs, they do not prescribe how to perform the layout. That decision is left to the master typesetter — TeX.

The Creation and Impact of TeX

The significance of TeX and, through it, Knuth’s impact on the field of technical publishing, is hard to overstate. A little background helps put in context the tremendous affection that technical users have both for TeX and for its creater, the legendary Stanford mathematician and computer scientist, Don Knuth.

TeX was not created by a company or corporation. It was designed and created by Knuth during a 10 year labor of love, born out of both necessity and the desire for aesthetic and technical perfection. Remember, this was before Microsft and Windows as we know them, before the ubiquitous world wide web, and before Google search, a time when technical materials were still often written by hand, or typed on a typewriter, with hand written symbols to supplement the missing typography. Once created, TeX and all of its attendant technology were given for free to the user community. LaTeX was created, similarly, by the mathematician and computer scientist Leslie Lamport, to ease document preparation, and was also given away for free to the community. Together TeX and LaTeX (along with Adobe’s Postscript) revolutionized publishing and brought the tools for quality communication out of the hands of specialists and into the technical community itself.

Today, LaTeX / TeX is the de facto platform of choice for technical communications. In fact,

at least in mathematics, computer science, and physics, the adoption of TeX has been so universal that failure to use it is now a reliable crackpot indicator. (Scott Aaronson, Computer Scientist)

To both Knuth and Lamport are owed a tremendous debt of gratitude by the hundreds of thousands of scientists and authors who use the software every day for their research publications, textbook writing, and book writing. If the author of every document generated freely using TeX were to give Knuth a moment of silence for good karma, he would likely have enough to last several lifetimes. For what it’s worth, let me here add mine!

This is the first in a series of three articles intended to give you all that you’ll need to begin working with LaTeX / TeX on Windows, using free, open-source software.

Articles two and three get you set up and on your way.

>> Continue reading: Part 2: Setting up a TeX / LaTeX Platform on Windows with Open Source Tools

>> Continue reading: Part 3: Thinking Modular in TeX

LaTeX / TeX on Windows has had the rather unfortunate reputation of being difficult to install and use. But with the quality of today’s open source tools and references, this is no longer the case, and should not be a reason to deter you from [...]]]>
(Mathematical Toolset Series: TeX & LaTeX, Part 2 of 3)

LaTeX / TeX on Windows has had the rather unfortunate reputation of being difficult to install and use. But with the quality of today’s open source tools and references, this is no longer the case, and should not be a reason to deter you from trying it out.

This article takes you through the practical business of getting a LaTeX / TeX platform running on Windows, using free, open-source software. From downloading and installing, to providing reference materials and basic templates, this article should get you going quickly and provide a decent toolkit from which to build.

Note: All the steps in this article have been tested on Windows XP and Windows 7.

Setting up LaTeX / TeX on Windows

LaTeX / TeX on Windows has had the rather unfortunate reputation of being difficult to install and use. But with the quality of today’s open source tools and references, this is no longer the case, and should not be a reason to deter you from trying it out.

Here’s a preview of the process.

• Step 1: You’ll obtain and install the various software tools that comprise a LaTeX / TeX platform. For this you’ll need a reasonable swift download connection to the internet. Unfortunately, a dial-up connection probably won’t cut the mustard.
• Step 2: There will be a minimal bit of configuration you’ll make, after which you’ll be ready for a test run!
• Step 3: Exercise your platform by producing your first PDF document using a basic template file. I’ve included a test file / basic template file that you can use to immediately get started, and to check that everything is working properly.
• Step 4: Collect the ready references materials you’ll need. I’ll point you to a collection of ready reference materials — the kind you can call up in a pinch to remind yourself of a particular command: short and sweet. Keep in mind: You’ll be using the very pleasant TeXnic Center for your document composition, so you’ll have before you most of the reminders that you’ll need, as well as their good reference material. I’ll also point you to the more full bodied references, the kind that are meant for a nice sit down read.

That’s it! So let’s get you started.

Step 1: Downloading and Installing the Components

1a. Download MiKTeX. This is the distribution of LaTeX / TeX that you’ll be using. The MiKTeX distribution has built into it the most common packages you’ll need, including AMS-TeX, BibTeX, as well as facilities for producing PDF, PostScript, or DVI document outputs. You won’t actually interact with MiKTeK — but it will provide all the required back-end facilities.

• Click the latest version under the Download sidebar on the left: MiKTeX 2.8 as of this writing.
• Scroll down and click the Download button next to “Basic MiKTeK 2.8″ Installer (or whatever is that latest version at the time you’re reading this.)

Be warned: MiKTeX is a LARGE download: 110 MB for the basic installation. You will need to have a fast internet connection: broadband or cable. On a reasonable internet connection with a nominal download speed of 750KB/sec, this takes about 3 minutes to download.¹

• Run the MiKTeX Installer, noting the following recommended settings as you proceed:
• Accept the copying condition (nothing alarming here)
• Install for anyone… (less hassle if you have multiple user accounts on your machine)
• NOTE WHERE the software is being installed (you’ll need to know this to configure TeXnicCenter)
• Choose your preferred paper (e.g. A4 in UK, Letter in US)
• Install missing packages on the fly: Yes (easier if you’re new to MiKTeX)
• Start the install. It may take several minutes.

1b. Download GhostScript from here and GhostView as a 32-bit X86 Windows executable from here.
Ghostscript is an interpreter for the PostScript page description language used by laser printers. GSview is a graphical interface for Ghostscript that allows PostScript pages to be viewed or printed.

• Install both programs using their default settings.
• In particular, NOTE DOWN the path where the programs are being installed. You’ll need to know this to configure TeXnicCenter in Step 1d. If you keep the default settings (recommended), GhostScript and GhostView will be installed, respectively, to paths that look something like this:
  • c:\Program Files\gs
  • c:\Program Files\Ghostgum\gsview

1c. Downloading a free PDF Viewer that is better than Adobe Acrobat (Optional but Highly Recommended) You will need a PDF Viewer. Most computers have Adobe Acrobat Reader pre-installed. However, consider trying PDF Xchange Viewer. It is free, is much faster than Adobe’s Reader, and has a host of annotating, editing, and other features that you have to pay quite heavily for in Adobe’s non-free software.

• You can download PDF Xchange Viewer from here. Look on the right-hand side-bar, and choose the EXE installer option.

• Install PDF Xchange Viewer using the default installation settings EXCEPT on the LAST page of the installer:
• Important Note: on the last page of the installer you are asked whether you wish to install the Ask Search toolbar. Suggestion: Decline this. It is a “partner product” that is not in any way related to the PDF Viewer you want.

1d. Download TeXnicCenter from here. TeXnicCenter is a pleasant visually oriented environment, also called an IDE — Integrated Development Environment. You’ll almost certainly want to be composing your documents here, unless you are seasoned with the LaTeX toolchain and have strong reasons why the convenience of an integrated development environment is not preferable.

• Run the TeXnicCenter Installer, noting the following recommended settings as you proceed:
• Keep the default selections, including “Custom” package, which contains everything
• Under “Additional Tasks”, select the checkbox “Add TeXnicCenter to the Send menu”

Summary / Check
This completes the installation step. You should now have installed on your computer four (or optionally five) applications:

1. MiKTeX (TeX/LaTeX distribution),
2. GhostScript (PostScript and PDF engine),
3. GhostView (Postscript viewer),
4. (optionally), PDF Xchange Viewer (free, fast, feature rich PDF Viewer), and, finally,
5. TeXnicCenter (LaTeX Document preparation environment).

Step Two: Configuring TeXnic Center

To give your new TeX editor setup a whirl:

• Fire up TeXnic Center (use the Desktop shortcut, or the Start menu).
• After a Startup Tip is shown, the Configuration Wizard will be brought up automatically. Go through the configuration step as follows:
• When prompted with: “Enter the full path of the directory where the executables (latex, tex, etc.) of your TeX distribution are located”, you should: Browse for the MiKTeX binaries folder. This will typically be at:
  c:\Program Files\MiKTeX 2.8\miktex\bin\

• If you installed PDF Xchange Viewer in Step 1c. above, you may be prompted to enter additional optional settings for PDF viewing. You can ignore this and simply click Next.
• Armed with this information, TeXnicCenter will automatically create the main output profiles for you to create DVI, PS, and PDF documents.²

If everything has gone ok up to this point, great! You’re ready for Step 3.

Step Three: Typesetting and producing your first document

• In TeXnic Center, start a new document: File > New.

  Copy and paste the following “Hello World!” code into your new LaTeX document and save it somewhere. (Or can download it from here.)

  
% A minimal test template for the LaTeX / Tex platform
\documentclass{article}
\begin{document}
Hello World! This is a test.

  A tribute to Leonhard Euler:
$$-e^{i \pi} = 1$$
\end{document}


• Choose the LaTeX => PDF output profile (Figure 1).
• You’re ready to build the document and to view the result. There are several ways to go about this. For now, let’s use the quickest way (assuming there are no problems³): Ctrl+Shift+F5 is the keyboard shortcut for Build and View. There is also a toolbar icon (Figure 2) and a menu command: Build > Build and View Output.
• You should see a PDF that looks something like this.

  If everything’s gone right, you’re ready to strike out on your own. The test code above was minimal. You’ll need a template.

• Here’s the source code for the basic template (listed below), which is adequate for getting started with. When you compile it, you should get a PDF that looks like this.

The basic template code listing is below, for reference.


% Basic Template for using LaTeX
% Assad Ebrahim
% Aug 4, 2008
% ------------------------------

\documentclass{article}
\title{Basic Template: Your Title Here}
\author{Your Name Here}
\date{\today}

% For more advanced usage, you'll list packages and other document formatting commands here
\begin{document}
\maketitle
\tableofcontents
%\newpage % if you want the title page on its own

% vvvvvvvvvvvvvvvvvvvvvvv Your Text starts below here vvvvvvvvvvvvvv

\section{A Basic Template}
Hello Mathematical World!

Let's take a look at some simple \TeX.

\paragraph{A tribute to L. Euler}
The following displayed equation expresses a profound insight that unifies geometry, trigonometry, analysis, and complex variables.
$$-e^{i \pi} = 1.$$

\paragraph{A question of class}
Let's illustrate the use of mathematical symbols and footnotes.

Is $\pi^{\sqrt{2}}$ algebraic\footnote{A number is algebraic if it is the root of a polynomial with rational coefficients. Algebraic numbers include the rationals but also selected irrationals such as $\sqrt{2}, \sqrt[3]{2}$, and in general $\sqrt[n]{p}$ for any prime number $p$ and any positive integer $n$.} or transcendental\footnote{A number is transcendental if it is not algebraic, i.e. if it is irrational and is not the solution to any polynomial with rational coefficients. Examples are $\pi$ and $e$.}? (See the footnotes for an explanation.)

% ^^^^^^^^^^^^^^^^^^ Your Text ends above here ^^^^^^^^^^^^^^^^^^^^^^^^^^^
\end{document}


Step Four: Get your LaTeX reference sheets and resource links.

Rapid References

• 2 page LaTeX Reference Card / Cheat Sheet (PDF) (Thanks to Winston Chang)
• Symbols List (on the web)
• Listing of Mathematical Symbols (PDF)
• Short Guide to Math in LaTeX (using AMS-TeX) (PDF document)
• BibTeX entries reference sheet

Comprehensive References

• Master list of useful LaTeX / TeX Resources on the Web

Advanced Tippery
Here are a few places that offer valuable advanced tips, tricks, and exceedingly useful little routines, organized by category:

• Preserving Your Sanity and Your Time: Good Practises in Modular Document Development with LaTeX
• A number of advanced tips and tricks, including:
  • Keeping your code inclusions OUT of LaTeX documents (Dynamically Including Program Listings)
  • Rotating Tables and Figures to fit without cutting off the edge
  • Typesetting Mathematics Easily with AMS-LATEX
  • Text inside Mathematics Displays with AMS-LATEX and \text{ }

Getting Help

There are many things that one may want to do in LaTeX that are not obvious. Perhaps the quickest route to finding out is to run a Google Search.

If all else fails, there are communities where you can ask questions and have good hope of a swift and correct answer:

• Stack Overflow — LaTeX Topic This is a site where intelligent questions can get answers in less than a minute. There are hundreds of thousands of smart eyeballs trolling through the lists on Stack Overflow. You can ask a question without registering or becoming a member, so it’s easy to participate.⁴

Happy TeX-ing!

With this introduction, you are hopefully on your way to using LaTeX / TeX for your technical document preparations needs.

When you’re ready for more, I’d suggest reading the final article in this series and recommend using some sort of modular scheme for organizing the components of your LaTeX documents. The final article explains the modular approach to document development that may help to make your TeX-ing easier to manage and more efficient. Perhaps more importantly, you’ll find there a collection of modular templates to get you started.

Happy TeX-ing!

>> Continue reading: Part 1: LaTeX / TeX: Professional Grade Typesetting for Scientific Writing

>> Continue reading: Part 3: Thinking Modular in TeX

Footnotes

If you write frequently, it is likely that you have certain stock or administrative material that is included in each of your documents. You also likely spend a substantial portion of your overall effort re-writing, editing, or re-arranging material. In this situation, one of [...]]]>
(Mathematical Toolset Series: TeX & LaTeX, Part 3 of 3)

If you write frequently, it is likely that you have certain stock or administrative material that is included in each of your documents. You also likely spend a substantial portion of your overall effort re-writing, editing, or re-arranging material. In this situation, one of the best ways of preserving your time and your sanity is to adopt a modular approach to document development.

In this final article of the three part series on LaTeX / TeX, I will discuss a modular approach to document preparation using TeX. I’ll also provide modular templates that should make your use of TeX more efficient.

Why Modular Documents?

A modular approach to document design can be more efficient if you have common elements in your documents, especially when you begin to make changes to these common elements. By using decoupled text modules, you can readily re-arrange or re-order them, creating documents for different purposes, from the same stock of core content, modularly organized.

Thinking Modular in TeX

In TeX, taking a modular approach means partitioning your typical document into more or less independent pieces, many of which you will want to re-use from document to document. Provided that you have kept the re-usable parts of your document separate from the main content, they can be brought into the main document using various \include directives.

The advantages of the modular approach to organizing the components of your document are that it allows you:

• (i) to avoid copy / paste whenever possible,
• (ii) to re-use specific parts of your document wherever possible, and
• (iii) to be able to make corrections in only one place and have these corrections propagate easily into all documents that use the module, without having to make the same change over and over again in each document.

I’ve found it advantageous to compose and maintain, at a minimum, the following as separate modules:

1. a separate Title Page. The key here is not so much the fact that you may wish to change your title or content. The key is that you may, down the road, wish to combine content from various different articles into a coherent larger unit. For example, you may wish to combine multiple short articles into a longer article, or take a collection of articles and organize them as separate chapters of a book. By keeping the titles of your articles separate from their content, you give yourself the flexibility, without changing either title or content, to generate a short article or to incorporate the same content in another vehicle, be it larger article, report, or book.
   

2. separate Author Attributions. This allows you to designate your authors and craft their details once, and include the same composition in all your documents. The savings comes when author information changes — contact information, position, and so on. Instead of having to manually go through each document and make the same changes over and over again, you make the required change in one place, and all documents compiled thence forward will pick up the corrected attribution.
3. separate Document Settings (Preamble section). The settings section of a LaTeX should most definitely be organized for re-use. As you evolve your style, you will begin to collect settings and macros. If these are in one place and pulled into each document, you will find it much easier to produce consistently good documents. The advantage is that when you recompile a document created with an older template, you will automatically get all of the improvements you have added to your separate Document Settings file. The alternative: keeping track of dozens of settings and making sure that changes find their way into all of your documents, is fraught with headaches and mistakes.
4. a separate Bibliography. Establishing a separate repository for all of your bibliographic information is a strongly recommended practice. Doing so means that you are building a reference list that is comprehensive and uniform. The key is that TeX (specifically BibTeX) automatically pulls only those citations that are used in a particular article when creating that article’s list of references. So comprehensiveness without the hassles of having to manually copying and pasting and then maintain specific, often overlapping subsets of references for related articles — this is a big win! You should make the effort and invest in using BibTeK.
5. separate Code Listings. If you include algorithms, program listings, or other similar external material in your papers, you should not copy and paste the content directly into your article. With every copy and paste comes the serious and taxing burden of making a correction in the original source code and forgetting to update the article text. By dynamically including program listings directly from wherever the source code resides (in version control, a separate folder, and so on), you set yourself up for success. Any changes made to the original source code will be reflected automatically in every recompilation of the document — i.e. one button click. The key: keep your code listings OUT of TeX.

   Modular Templates for LaTeX

   To give modular document organization a try, it is helpful to have ready-to-use templates that you can use as boilerplates to experiment with for your own work. So, attached is a collection of modular templates similar to ones that I use in my own LaTeX work. They are available as ZIP archive from the Downloads section or can be downloaded individually by following the links for each template below.

   1. _TeXdefs.tex, containing the preamble definitions, macros, style settings, and other layout details
   2. paper-title.tex, containing the title and optionally the abstract. This is the main vehicle that pulls together the pieces of the document. You will be compiling this to create the paper.
   3. paper-content.tex, consisting of one or many content specific modules, perhaps separate chapters, sections, or other organization of material that is naturally decoupled. A good litmus test here is that it should make sense to be able to interchange the order of your content modules without affecting the logical flow. The specific order in which they appear in the paper will be fixed in the paper_title
   4. authors.tex, containing the simple, crafted attributions of authors with contact information and the obligatory acknowledgements.
   5. bibliog.bib, consisting of a collection of all your references, not just the ones cited in a particular paper. This is a much more efficient way of maintaining comprehensive reference lists and avoiding the duplication that is otherwise required for commonly used citations.

   Instructions:
   To test these templates, put them all into the same folder and point your LaTeX compiler to paper-content.tex. This PDF is what should result.

   Notes

   • Don’t forget! You have to compile a fresh batch of files three times in succession before all warnings are resolved — the first compilation builds pulls references to citations, footnotes, headings, etc., the second fills in these references into the table of contents and other automatically numbered objects, which means the third compilation can produce your final document.
   • If you’re using the platform I’ve described in Part 2, you will be loading paper-content.tex into TeXnicCenter.
   • If the words “compiling” and “building” are a mystery to you, you probably haven’t yet gotten a LaTeX / TeX platform working in Windows. No worries! Just follow the steps in Part 2 to get yourself set up and comfortable. Then come back and test these files.

   Happy TeX-ing!

   This closes the series of three articles intended to get you started working with LaTeX / TeX on Windows, using free, open-source software.

   If you have adopted LaTeX / TeX, I hope you’ll find its practicality freeing and the beauty of its output inspirational. Happy TeX’ing!

   ---

   If you’ve started with this article, please note that Parts One and Two provide the background to “the TeX Way” and help you set up your a LaTeX / TeX platform on Windows. You’ll need a LaTeX / TeX platform to try out the example templates provided above.

   >> Continue reading: Part 1: LaTeX / TeX: Professional Grade Typesetting for Scientific Writing

   >> Continue reading: Part 2: Setting up a TeX / LaTeX Platform on Windows with Open Source Tools

   ]]> http://mathscitech.org/articles/latex-3-modularity/feed 0 http://mathscitech.org/articles/assembly-value http://mathscitech.org/articles/assembly-value#comments Sun, 02 May 2010 08:37:53 +0000 Assad Ebrahim http://mathscitech.org/articles/?p=1149

   On the Value of Assembly Language, and Resources to get you started in Digital Logic, Computer Architecture, and Assembly Language programming.

   Despite advances in programming technologies since the 1970s, there are still reasons to understand and learn assembly language programming. Contrary to what one may imagine, Assembly Language is not a relic of the past, [...]]]>

   On the Value of Assembly Language, and Resources to get you started in Digital Logic, Computer Architecture, and Assembly Language programming.

   Despite advances in programming technologies since the 1970s, there are still reasons to understand and learn assembly language programming. Contrary to what one may imagine, Assembly Language is not a relic of the past, even though a typical applications programmer will almost never need to drop into assembly.

   In this article, we’ll look at practical situations in embedded systems development in which assembly language programming is still used, pedagogical reasons to learn assembly language, and provide resources and projects for gaining a working knowledge of digital logic, computer architecture, and assembly language programming.

   ---

   Learning for Embedded Systems Development

   Despite advances in programming technologies since the 1970s, there are still reasons to understand and learn assembly language programming. Contrary to what one may imagine, Assembly Language is not a relic of the past, even though a typical applications programmer will almost never need to drop into assembly. Certainly assembly language is NOT recommended for writing general applications software or graphical user interfaces. Yet a decent understanding of assembly language is important both practically in embedded systems development, as well as for developing a solid general understanding of computer engineering, the underpinnings of the software development toolchain (compilers, assemblers, linkers, loaders, debuggers, and so on), and in the analysis and implementation of algorithms.¹

   The transition to embedded systems development is difficult without a reasonable understanding of assembly language and computer architecture. As embedded computing enters almost every aspect of the modern technology landscape, from intelligent gadgets of all kinds to remote and autonomous systems, not having this knowledge becomes a fundamental impediment to seeing and being able to seize the many opportunities for participating in this interesting and rapidly expanding area.

   (I.) Practical reasons for understanding Assembly Language programming
   There are at least four practical situations in embedded systems development, in which assembly language programming cannot always be entirely avoided:

   1. when developing for platforms that do not have C compilers — and these do exist — assembly language becomes, in most cases, the programming interface. The popular Microchip PIC microcontrollers used to be without a targeting C compiler for many years, in part because of the idiosyncratic PIC architecture and the absence of facilities (like a deeply nestable parameter stack) that general compilers require. With their low cost (many under $3.00) and extensive array of built-in peripherals, incorporating these powerful microcontrollers was often done using assembly language programming.²
   2. when systems require hard real-time performance in the absence of a real-time operating system (RTOS), assembly language on a RISC platform allows interacting directly with the silicon and being able to obtain accurate timing characteristics by counting instructions. This is one of the advantages of the RISC (reduced instruction set computing) architecture — it is a simplified architecture in which each instruction takes a fixed and uniform time for the CPU to execute.
   3. when writing device drivers or obtaining peripheral access in the absence of an operating system that provides this functionality, or when writing drivers for an operating system.
   4. when it is required to directly supervise the storage of values to specific registers or the use of specific elements of an underlying CPU architecture, C is often unable to help. Being able to drop into assembly, either inline or through functions, is then the most direct method of access.

   This is not to say that the disadvantages of assembly language programming are any the less — assembly language is not portable and almost always has higher overhead when coding, debugging, and maintaining. But in these few areas of embedded systems development, the benefits occasionally outweigh the trade-offs.

   It should also be clear that none of these four conditions is ordinarily encountered by a typical applications software engineer. Indeed, these conditions do not always arise in embedded systems development either, especially if the embedded development is done atop an OS or RTOS sitting on a computing platform for which there is a quality C compiler.

   So the question remains: for the large number of programmers and engineers for whom the practical reasons are unlikely to materialize, is it useful to learn an assembly language?

   (II.) Pedagogical advantages of learning assembly language

   Programming in Assembly Language requires a non-trivial understanding of the innards of digital systems and software toolsets. It provides a fruitful hands-on context within which to acquire and exercise this understanding. Compared to higher level languages, assembly language programming requires greater understanding of the following:

   • digital logic and digital circuit concepts
   • computer architecture: register, bus, memory, the instruction cycle
   • microprocessor organization: opcodes, characteristics (timing, organization, peripherals)
   • hexadecimal, binary, and decimal numbers and how to use them
   • stack
   • memory access and pointers
   • assembler syntax: pseudo ops, directives, syntax, number formats
   • calling conventions
   • operating system facilities
   • the parts of a software toolchain
   • linkers and their idiosyncrasies
   • loaders, when loading the binary program into memory on a target platform that isn’t the source platform
   • using a low-level debugger

   Grappling with assembly language programming gives a much better understanding of computing architectures. Once you understand digital circuits and computer architectures, assembly language programming and its toolchain, you will have the working knowledge needed to embark on the road to microcontroller programming and the development of small and medium scale embedded systems applications: reading in sensors (A/D, filters, signal processing), digital I/O, and real-time numerical methods. ³ In addition, the patterns of thought involved in thinking in assembly, and the discipline involved in writing readable code in assembly, are both invaluable in understanding the details that a higher-level optimizing compiler handles “under the hood”.

   ---

   Recommendations and Learning Resources

   The best way to gain a working understanding in the areas discussed above is to do some digital logic design and assembly language coding yourself. The tools are not difficult to acquire and the materials to begin are available for free.

   For digital logic and computer architecture, the Digital Works simulator is a simple, freely available, and user-friendly way to get started in digital logic and computer architecture. [Download from Resources]

   It is helpful when embarking on learning ventures to identify a defining project that is grand enough to whet your ambitions but is also chosen to guide your learning efficiently through the essential areas you’ll need in order to have a strong working knowledge.

   Project (Digital Logic and Computer Architecture)

   Design an ALU in hardware to form the heart of a simple calculator. Build up the necessary logic elements using your own ICs that you package up in Digital Logic to be pin-compatible with ICs that you might buy off the shelf.

   Excellent IC lists with pinouts are available from GIICM. Datasheets and practical issues like availability and alternatives are available through the DigiKey parameterized product selection index. [See Resources for links].

   For assembly language programming, the x86 is an adequate platform for learning the basic techniques, including how to extend assembly language with higher level calls, how to embed assembly language directly into higher level languages, and using all the elements of the software development toolchain: compile, assembler, linker, loader, debugger.

   A companion project to the digital logic project above is given below:

   Project (Assembly Language)

   Develop, in assembly language, computational routines for a simple calculator, including fixed and floating point routines and some basic vector operations (sum, difference, and scalar product).

   After getting your feet wet in pure assembly, the way to go here is to migrate into C or Basic (gcc or FreeBasic are two recommended open source packages) and learn how to embed assembly language into higher level languages.

   MicroASM is a simple, freely available, and user-friendly way to get started with assembly language programming, after which migrating to NASM, gas, gcc, and the other elements of an open source toolchain is next. [Download from Resources]

   Next steps

   Once this understanding has been obtained, assembly should be viewed as a tool to use when it is practically needed. In all other cases when a C compiler exists that targets your intended platform, you should be writing in C. Optimized compiler technology has become so good that it is better to let a computer do what it is better at: detailed automatic attention to the placement and organization of assembly code, while your creativity directs the implementation via a higher level language (C or higher).

   Two directions then open themselves, one taking the road into computer science: assemblers, compilers, parsers, and higher level languages, and the other taking the road into microcontrollers, sensors, and embedded development.

   Stay tuned!

   ---

   Related Reading and Resources

   Related Reading

   • Introduction to PIC Microcontrollers Andrew Kilpatrick provides an excellent practical introduction that will take you down the road into microcontrollers, sensors, and embedded development.
   • A Home-Built 4-bit Computer Viktor Toth describes his journey in designing and building, a simple but functional 4-bit computer from low-level electronic components (TTL logic gates.)
   • hurling-boulders-assemblyHurling Boulders: Assembly Language Programming
   • x86-assembly-toolsetAn Open Source Assembly Language Toolset

   
   Downloads & Resources

   Digital Logic & Computer Architecture

   • Download Digital Works 2.0 (freeware)
     written by D. J. Barker at the University of Teesside.

   • Download Digital Works 3.0 (shareware)
   • Quick tutorial for Digital Works by Bob Brown of Southern Polytechnic State University
   • A license for DW 3.0 can be purchased here — worth it once you start building more intricate bus-based designs.
   • Principles of Computer Hardware by Alan Clements, 3rd Ed., 2000, Oxford University Press: an excellent introduction to Digital Logic and Computer Architecture. Incorporates Digital Works in its pedagogy.
   • The GIICM: a online, easily browse-able compendium of IC pinouts
   • DigiKey’s Parameterized Search Index with PDF Datasheets on all Parts

   Assembly Language for x86

6. Download MicroASM v1.00 (freeware) an 8086 assembly language platform and 8086 visual emulator for beginners to learn assembly language concepts and programming. Note: requires VB6 runtimes, which can be obtained from Microsoft here.
7. Download MicroASM v4.08 (shareware)
8. x86-assembly-toolsetAn Open Source Assembly Language Toolset contains a discussion of an intermediate level Open Sources assembly language toolset for the x86

   ---

   Footnotes

   1. Using Assembly Language for Algorithm Analysis

      This is what Knuth does in The Art of Computer Programming, a Tour de Force in the detailed analysis of fundamental problems and methods in computer science, their techniques and complexity analysis. For these analyses, Knuth assumes an ideal machine, MIX (for the 1960s) and MMIX (for the 2000′s) – a RISC style computer. He abstracts away specific details that aren’t relevant to the essence of algorithm complexity — i.e. the number of registers etc.

      It is often useful and helpful to taste implementing an algorithm in assembly language. For this to be practical, you need the facilities of disk access, data loading and saving, and display. These are most practically handled by the OS on a modern CPU, so it is easiest to use the OS functionality. It is also easiest to do all of this within a higher level language in which this interaction is usually quite easy. So the best way to proceed is by embedding (inlining) your assembly language implementations within a higher level language such as C/C++ or Basic. ↩

   2. Microchip PIC18 and dsPIC, Atmel AVR, and Intel 8051 are all families of microcontrollers that have reasonable optimizing compilers available today, a large and helpful user community, and easy pathways to entry level embedded systems projects. ↩
   3. When you are ready, an inexpensive, RISC based, non-x86 platform for experimentation becomes handy. Microchip PIC, Atmel AVR, and Intel 8051 are all widely used microcontroller platforms worth considering. ↩
   ]]> http://mathscitech.org/articles/assembly-value/feed 0 http://mathscitech.org/articles/meta-questions-impact http://mathscitech.org/articles/meta-questions-impact#comments Thu, 15 Apr 2010 16:53:29 +0000 Assad Ebrahim http://mathscitech.org/articles/?p=1101

   Abstract

   “It seems that students who are hard-working and otherwise successful, but whose milieu (peers, mentors, and home environment) are at once non-technical and disengaged from the ideas behind science and technology, are at a higher risk of disorientation, dissatisfaction, or disillusionment with mathematics and science.”

   In this article, I will explore this conjecture, and suggest a [...]]]>

   Abstract

   “It seems that students who are hard-working and otherwise successful, but whose milieu (peers, mentors, and home environment) are at once non-technical and disengaged from the ideas behind science and technology, are at a higher risk of disorientation, dissatisfaction, or disillusionment with mathematics and science.”

   In this article, I will explore this conjecture, and suggest a potential course of action, rooted in the methods of inquiry of philosophy and the humanities, that may help reverse an otherwise tough pedagogical situation.

   ---

   Updated May 21, 2010

   ---

   Some Observations

   In students who are otherwise quite successful, difficulties with mathematics and science often seem to boil down to what are essentially meta-questions — of more philosophical or human interest than technical problems. In these otherwise good students, unaddressed meta-questions seem to cause greater lasting damage than one might expect. In the mildest cases, we have good students well able to perform computations but who have missed the essential ideas underpinning the material at hand; in the severest cases, otherwise good students dismiss mathematics as inaccessible, irrelevant, or both. Though I have less evidence for the situation in the hard sciences, I suspect the same to be true, especially in physics and chemistry. The unfortunate departure from mathematics and science subjects by students who are otherwise capable, engaged and hard-working, seems particularly tragic.

   The Origins of a Conjecture

   The ideas behind this conjecture have taken shape over some time now as I have mentored an increasing number of secondary and post-secondary students. The ideas were strengthened the more I encountered good students who were turned off to mathematics, but who, after being satisfied on what were essentially meta questions about mathematics, seemed to feel less alienated from the goals and methods of mathematics. The questions themselves were often more of a philosophical or humanistic nature. Nonetheless, it was these questions that seemed to have created a hurdle that was hampering the students’ ability to freely absorb new mathematical ideas. For some, there was renewed energy and effort in mathematics, often accompanied, in these cases, by a step change in attitude, engagement, and performance.

   Encounters such as these prompted me to reflect on my own pathway through secondary and higher education. Certainly, I can trace my continuation in mathematics and science to positive encounters with key mentors and structured experiences allowing the active pursuit of engaging mathematics. Curious to see how others who stayed in the field came to be there, I followed up these informal investigations with industry and academic colleagues. The results of the conversations suggest that there is perhaps a common thread that runs through a specific class of difficult educational experiences.

   The Conjecture

   Here’s what I currently believe:

   It seems that students who are hard-working and otherwise successful, but whose milieu (peers, mentors, and home environment) are at once non-technical and disengaged from the ideas behind science and technology, are at a higher risk of disorientation, dissatisfaction, or disillusionment with mathematics and science. This disadvantage can be partially addressed by providing an opportunity to philosophically examine the meta aspects of mathematical activity. Addressing this “cultural omission” in a structured fashion, and guiding the student toward greater personal intellectual engagement with the subject can turn potential unhappy departures into continuing and successful science and technology students.

   The Why’s and Wherefore’s

   The rather sophisticated perspectives that are required in order for students to satisfactorily resolve for themselves the most common meta questions in mathematics are frequently absorbed, almost by osmosis, when the student’s milieu has within it mentors with this so-called “cultural knowledge”. The important exchanges typically happen informally in general conversation with mathematically or technologically literate parents, uncles, aunts, or mentors within the student’s community. Or they happen silently if the student has had the good fortune to observe or participate first-hand in how mathematics or mathematically related concepts are used in areas that they find interesting, be it physics, technology, computer games, artificial intelligence, robotics, digital graphics, social research, monetary policy, or business.

   For students whose environments lack the opportunity for such interactions, the typical school or even university curriculum is not well suited to compensate for the lack. For such students, there is little further opportunity for meta questions to be addressed, putting them disproportionately at risk, with the expected disengagement and lack of success in science and technology education. Though reversing this situation is difficult, there are initiatives underway¹ to improve the situation, recognizing as they do that improvement in this area is crucial both for individual student success and for the success of science and technology education.

   Suggestion Action

   The Course Reading Materials provided here as part of a Course on the Philosophy and Foundations of Mathematics, are intended to address that portion of students who are attracted to Science, Technology, Engineering, and Mathematics (STEM) subjects, but whose background may not have included the cultural pre-requisites required to resolve common meta questions without supplementary sources. Making these cultural assumptions and perspectives explicit for these students will hopefully lead them to be able to study further and with greater urgency in both theoretical mathematics and its applications than they might otherwise do, and by doing so, enable them to continue more confidently and comfortably with their science and technology education.

   In each of these contexts, the primary intent is to head-off the otherwise inefficient blind search for this cultural perspective early enough in the students’ technical education so that they better understand the origins and meaning of what they are doing, why mathematics has evolved in the way it has, and have a useful sense of perspective to ensure that the forest is not missed for the many, many trees they will encounter. The secondary intent is to help catalyze the development of that elusive “mathematical maturity”, a characteristic often desired by instructors but unfortunately less frequently found.

   It is my opinion that a course such as this would be fruitfully offered initially as an elective, but then possibly required for undergraduate mathematics majors as well as beginning graduate students in mathematics, preferably during the first year of graduate school. With appropriate modifications, an approach such as this may be useful for talented secondary students in an abbreviated, colloquium setting run in tandem with faculty from a university mathematics department interested in school partnership and outreach.

   ---

   >> Continue reading: A Course in the Philosophy and Foundations of Mathematics

   ---

   Footnotes:

   1. The recent Mathematical Needs Conference held by the Royal Society’s Advisory Committee on Mathematics Education (ACME) led to some fruitful discussion. In particular, the working group on “The mathematical needs of higher education” explored obstacles to student engagement with mathematics in the UK and how these could be reduced. The results from this working group and the findings from an extensive research project sponsored by the Mathematical Needs committee of ACME and led by Huw Kyffin will be contained in a forthcoming report, to be available from the ACME website. ↩
   ]]> http://mathscitech.org/articles/meta-questions-impact/feed 0 http://mathscitech.org/articles/course-philo-math http://mathscitech.org/articles/course-philo-math#comments Thu, 15 Apr 2010 16:36:30 +0000 Assad Ebrahim http://mathscitech.org/articles/?p=1095

   An examination of mathematical methods and the search for mathematical meaning.

   During your studies of mathematics, physics and engineering, you may find yourself distracted or troubled by meta questions about mathematics — questions that fall outside the syllabi of most of the coursework that you’ll take.

   For those for whom this itch is persistent, what [...]]]>

   An examination of mathematical methods and the search for mathematical meaning.

   During your studies of mathematics, physics and engineering, you may find yourself distracted or troubled by meta questions about mathematics — questions that fall outside the syllabi of most of the coursework that you’ll take.

   For those for whom this itch is persistent, what follows is an outline and reading list for a Course in the Philosophy and Foundations of Mathematics. Among the topics included are the relation of mathematics to science, the examination of mathematical method, and the search for mathematical meaning.

   ---

   A Course in the Philosophy and Foundations of Mathematics

   An examination of mathematical methods and the search for mathematical meaning.

   Overview

   This course weaves together two lines of inquiry:

   1. The first track looks at subjects: Mathematics, Science, and Logic.
   2. The second track considers characteristics: Certainty and Doubt, Empiricism vs. Theory, Abstraction, Proof, Truth and Knowledge.

   Within each track, the following questions are considered: what are these concepts? what are their relations and differences with each other? Are any two of them the same? And can they lead us to a better understanding of the enterprise of mathematics? Our investigations along these tracks are facilitated by studying seven topics:

   • Topic 1. What is Mathematics? (Its Nature and Characteristics)
   • Topic 2. Mathematics and Science
   • Topic 3. Some Readings in the History of Mathematics and the Evolution of Its Ideas
   • Topic 4. Reality, Truth, and the Nature of Mathematical Knowledge
   • Topic 5. The Search for Foundations in Mathematics
   • Topic 6. What is Proof? and the Problem of Certainty
   • Topic 7. Thoughts on Mathematical Practice and Mathematical Style

   The mathematical material of this course moves fluidly from ancient history to modern times, with much in between, and brings in ideas from different branches of mathematical development. But remember, it is not the mastery of the technical material that is the goal of this course. Rather, the important thing is observing the evolution of the ideas, getting to the essence of their motivation, and understanding the characteristics of their development and the fruits of these efforts.

   Risks and Rewards

   A meta-mathematics itch, once awoken, can take a lot of scratching to satisfy. You should be aware that the ideas you encounter here may pose distractions for you as you proceed along the regular course of your mathematical or technical studies. However, my hope is that an itch such as this, and the ideas you will encounter through this course will inspire you to study further, more broadly, and with greater urgency in both theoretical mathematics and its applications than you might otherwise do. With persistent inquiry and hard work, you will find at some point that you have a much more intimate understanding of your chosen subject, an understanding that should give you a sense of well-being, of historical and philosophical connectedness to the mathematics of the past, and pleasure at the prospect of continuing to participate in mathematical discovery, whether for yourself as an amateur or as a professional mathematician, engineer, or applied scientist.

   Course Materials

   To keep the course-materials inexpensive and readily accessible for the interested reader to pursue, I have adapted the original readings list for this course to favor materials that are now available freely online.¹

   ---

   Syllabus and Reading List

   Topic 1. What is Mathematics? (Its Nature and Characteristics.)

   1. Article: What is Mathematics? (Davis/Hersh) [DH81], pp. 6-8
      • [Read article online (Google Books)]
   2. Article: A General View of Mathematics (Aleksandrov) [Ale56], in Mathematics: Its Content, Methods, and Meaning (Aleksandrov/Kolmogorov/Lavrentev) [AKL63], pp.1-64
      • [Read Sections 1 & 2 online (History of Mathematics, St. Andrews)]
      • [Read entire article online (Google Books)]
   3. Book: Proofs and Refutations: The Logic of Mathematical Discovery (Lakatos), [Lak63] pp.6.ff (entire book)
      • This book is worth buying for your library.
      • [Read online - Partial Preview only (Google Books), pp.6-18]

   Topic 2. Mathematics and Science

   1. Article: The Unreasonable Effectiveness of Mathematics in the Natural Sciences (Wigner)
      • [Read online] (Dartmouth)
      • [Download PDF] (Originating server is Univ. Wuerzburg)
   2. Article: The Unreasonable Effectiveness of Mathematics (Hamming)
      • [Read online] (Dartmouth)
      • [Download PDF] (Originating server is UC Davis)
   3. Article: Science and Hypothesis: Author’s Preface (Poincare) [Poi05], pp.xxi to xxvii
      • [Download Article] (Originating server is Internet Archive (Entire Book))
   4. Article: Mathematics as an Objective Science (Goodman) [Goo79]
      • [Preview Article -- first page only] (from JSTOR)
   5. Article: Why a little bit goes a long way: Logical foundations of scientifically applicable mathematics (Feferman)
      • [Download PDF] (Originating server is Author’s webpage)

   Topic 3. Some Readings in the History of Mathematics and the Evolution of Its Ideas

   1. Article: Pre-modern algebra: A concise survey of that which was shaped into the technique and discipline we know (Hoyrup)
      • [Download PDF] (Originating server is Author’s webpage)
   2. Article: Evolution of the Function Concept: A Brief Survey (Kleiner)
      • [Download PDF] (Originating server is Mathematical Association of America)
   3. Article: The Evolution of Group Theory: A Brief Survey (Kleiner)
      • [Download PDF] (Originating server is Tom Conklin’s collection)
   4. Article: Excursus into the History of Calculus (Kutateladze)
      • [Download PDF] (Originating server is arXiv)
   5. Article: History of the Formulas and Algorithms for (Goyanes)
      • [Download PDF] (Originating server is arXiv)
   6. Book: A History of Astronomy Ch.1–5, pp.1-62 (Pannenoek)
      Astronomy as a catalyst driving the increasing sophistication of arithmetic, algebra, geometry and calculational methods in Ancient Mathematics (Babylonia, Assyria, Egypt, Vedic India, Greece, and Alexandria), Muslim mathematics (Arabia, Persia, Central Asia), and in Renaissance Europe.
      • [Read Ch.1--5 online (Ancient Mathematics)] (Google Books)
   7. Book: A History of “Modern” Mathematics (from the start of the 1700s to the end of the 1800s) (Smith)
      • [Download entire eBook as PDF] (Originating server is Project Gutenberg)

   Topic 4. Reality, Truth, and the Nature of Mathematical Knowledge

   The problem of determinism and error. Is nature continuous of discrete? What is Reality? What is Truth? Are the real numbers useful? Empirics and description vs. axiomatics and deduction?

   1. Article: The Nature of Truth (Schatz)
      • [Download PDF] (Originating server is: (Author’s PhD student’s page)
   2. Article: Inevitable Experimental Errors, Determinism, and Information Theory (Brillouin)
      • [Abstract free online] (Elsevier – Information and Control)
   3. Article: Poincare’s Theorem and Uncertainty in Classical Mechanics (Brillouin)
      • [Abstract free online] (Elsevier – Information and Control)
   4. Article: Mathematical Intuition vs. Mathematical Monsters (Feferman)
      • 
        [Download PDF] (Originating server is Author’s webpage)

   Topic 5. The Search for Foundations in Mathematics

   1. Article: The development of programs for the foundations of mathematics in the first third of the 20th century (Feferman)
      • [Download PDF] (Originating server is Author’s webpage)
   2. Article: Does Mathematics Need New Axioms? (Feferman)
      • [Download PDF] (Originating server is Author’s webpage)

   Topic 6. What is Proof? and the Problem of Certainty

   “You can be certain and be wrong.”
   - John Kerry, 2004 Presidential Election against George W. Bush

   1. Article: Rigor and Proof in Mathematics: A Historical Perspective (Kleiner)
      • [Download PDF] (Originating server is Tom Conklin’s collection)
   2. Article: There’s More to Mathematics than Rigour and Proofs (Tao)
      • [Read article online]. Also, his on a “heuristic stage” and a language metaphor for why order matters in one’s formal training]
   3. Article: How to Write a Proof (Lamport)
      An argument for heirarchically structured proof instead of the commonly used prose-proof style.
      • [Download PDF] (Originating server is Author’s webpage, along with commentary on the context in which he wrote the paper
      • An undergraduate’s impression of Lamport’s talk and paper.
   4. Article: A Collection of Beautiful Proofs (Dijkstra)
      • [Download PDF] (Originating server is Author’s collected works page)
   5. Article: The Mathematical Divide (Dijkstra)
      An argument for why computational proof methods should be encouraged.
      • [Download PDF] (Originating server is Author’s collected works page)
      • [Read online]

   Topic 7. Thoughts on Mathematical Practice and Mathematical Style

   1. Essays on the Nature and Role of Mathematical Elegance (Dijkstra)
      • [Download PDF] (Originating server is Author’s collected works page)
      • [Read online]
   2. On the Quality Criteria for Mathematical Writing (Dijkstra)
      • [Download PDF] (Originating server is Author’s collected works page)
      • [Read online]
   3. What is Good Mathematics? (Tao) [Tao07]
      • [Download PDF] (Originating server is arXiv:math)

   ---

   Related Articles:

   >> Continue reading: Meta-Questions and their Impact on Successful Mathematics, Science & Technology Education

   Share Your Experiences. . .

   1. . . . if you have enjoyed the materials or have suggestions,
   2. . . . if you’re a student and have taken a course such as this, or
   3. . . . if you have taught a similar course

   drop me a line. I would welcome hearing from you.

   Further Work (Collaborators welcomed!)

   A course such as that outlined in the preceding would, I believe, be useful in all three areas of education: secondary, post-secondary (undergraduate), and graduate, appropriately restructured:

   • as a secondary school elective to encourage bright students in mathematics, science and technology to enter the university with a broader perspective on the mathematics they will be rapidly learning there.
   • as a university elective course, offered as a writing-intensive seminar, intended primarily for students in the sciences and engineer: mathematics, physics, engineering.
   • as a graduate level course, offered in the first year of graduate school in mathematics or applied mathematics as a supplementary seminar.

   There is much that can be done.

   If collaborating on future work in this direction sounds interesting, your efforts would be welcomed!

   ---

   Footnotes:

   1. To ensure that the materials are always available for download, I am serving them from copies held on this site. If you are the author of any of these articles and would prefer to have the primary download originate from your site, please send me an email, and I will make the change. ↩
   ]]> http://mathscitech.org/articles/course-philo-math/feed 0 http://mathscitech.org/articles/finite-summations-3 http://mathscitech.org/articles/finite-summations-3#comments Fri, 02 Apr 2010 10:41:39 +0000 Assad Ebrahim http://mathscitech.org/articles/?p=1030 (Discrete Mathematics Techniques III)

   Abstract We find a direct closed-form solution, i.e. one that does not require iteration, for the general case of the finite-summation-of-integer-powers problem . Having established in Part 2 that the closed-form solution is a polynomial, the summation is here rewritten as the sum of the independent monomials (), where the [...]]]> (Discrete Mathematics Techniques III)

   Abstract
   We find a direct closed-form solution, i.e. one that does not require iteration, for the general case of the finite-summation-of-integer-powers problem . Having established in Part 2 that the closed-form solution is a polynomial, the summation is here rewritten as the sum of the independent monomials (), where the are unknown coefficients. Using the recurrence relation , we obtain a linear combination of the monomials, which reduces to an easily solvable -by- triangular linear system in the unknown coefficients of the closed-form polynomial solution. Maxima and Octave/Matlab codes for directly computing the closed-form solutions are included in the Appendices.

   ---

   NOTE: This paper contains many formulas. As such, you may prefer reading the paper as a typeset PDF.

   ---

   Finding a Closed-Form solution for using a Direct Method

   Motivation

   Our goal is to obtain, without using iteration, a closed form solution for the general case of the finite-summation-of-integer-powers problem:
   

   

   Recall that in Part 2 of this paper , we used a method of recurrence relations to obtain the following results about :

   1. may be expressed as a linear recurrence relation that uses the lower order formulas and as follows:
      

      .

      
      The in (2) are the coefficients from the -st polynomial solution , while the terms are defined in terms of binomial coefficients¹ as:

      

   2. The closed form solution of is a polynomial in of degree with rational coefficients and a constant term equal to zero.

   While the expression for in (2) is indeed accurate, it requires repeated iteration to obtain the closed form expression for any particular . Such an approach without the assistance of a computer algebra system such as Maxima² would be prohibitively time-consuming and prone to error.

   We are hence left with the following question:

   Can we find a closed-form solution for the coefficients of the general solution polynomial that can be obtained directly, i.e. that does not require iteration?

   This paper uses linear algebra and matrices to achieve precisely this goal.

   The Direct Approach

   Polynomial with Undetermined Coefficients

   Since we have established in (2) that is a polynomial of order with no constant term, we may write down the closed form solution of in the form:
   

   

   where , are coefficients that have yet to be determined. As a first step towards determining these coefficients, observe that every finite summation can be written as a first order recurrence in by peeling off the last summand:
   

   

   Substituting (3) into (4) gives:
   

   

   Summation Manipulations

   What follows is a sequence of summation manipulations³ and simplifications of (5) aimed at obtaining an expression from which a closed-form solution for the coefficicents becomes transparent:

   • Expand the binomial powers using the binomial formula on both the left-hand side (LHS) and right-hand side (RHS) of (5):
     

     

   • Modify the LHS and RHS of (6) as follows, exploiting the fact that :
     
     • LHS: Extend upper range of inner sum to match upper range of outer sum.
     • RHS: Peel off 0-index term and add a vacuous -index term to last sum.
     • Result:

       

   • • LHS: Interchange order of summations.
     • RHS: Combine terms.
     • Result:

       

   • • LHS: Peel off 0-index term from the (now outside) summation on .
     • RHS: Change dummy index variable.
     • Result:

       

   • Bring everything over to the left-hand side to obtain a homogeneous linear combination of the monomials :
     

     

   Linear Independence Reveals Equations for Unknown Coefficients

   Since the monomials are a basis for the vector space of polynomials of degree less than or equal to , any linear combination of the will equal zero if and only if each coefficient equals zero.

   Therefore, setting the coefficients from (7) equal to zero gives us a system of simultaneous linear equations in the unknown coefficients , one equation for each of the coefficients of :
   

   
   

   
   

   
   Observe that (*) reduces to , since for all , and when . Thus we are left with a square system of equations () in unknowns , ().

   By observing that for , we can combine (8) and (9) into the single set of linear equations:
   

   

   Taking into account the inequality , and noting once again that when , (10) simplifies to a triangular linear system:
   

   

   and hence all equations in the system are linearly independent.

   From Linear System to Matrix Equation

   The triangular linear system (11) may be readily solved by combining the summations into a single matrix equation and using any one of a number of matrix solver packages. But this requires that the system (11) be re-indexed⁴ so that the start value of index matches that of index . Following the usual matrix convention, referred to as 1-indexing, we choose the start indices to be .

   The 1-indexed system is:
   

   

   Maxima code for solving the 0-indexed⁵ triangular linear system (13) is given in Appendix B. Octave/Matlab code for solving the 1-indexed triangular linear system (12) is given in Appendix C.

   The matrix equation equivalent to (12) is: , where
   

   

   Since is an upper triangular matrix with all non-zero upper triangular entries, we know we can readily solve this for any given values of and using a matrix solver system such as Maxima/Mathematica, Octave/Matlab, or Maple, among others. Source code for solutions in Maxima and Octave/Matlab are given in Appendix B and Appendix C, respectively.

   Computing the General, Closed-Form Solution

   We know from (2) that the general, closed-form solution to (1) is a -degree polynomial (3) in with rational coefficients given by solving the triangular linear system (12), or equivalently (14).

   The highest few coefficients can be readily computed by hand. For all , we have:

   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
   7. .
   8. In particular, we claim (without proof) that
      

      

      where the are rational coefficients independent of , and for all even positive . Hence we have:

      

   Substituting the above coefficients into the general closed-form polynomial solution gives us:
   

   

   

   A listing of the solution formulas for the first ten values is given in Appendix A.

   Conclusion

   Reviewing the path we have taken in this 3-part paper: Part 1 motivated the problem and illustrated a recurrence relation method for obtaining the solution for small . Part 2 generalized this method and found a -th order recurrence relation for the solution. Part 2 also illustrated, by an induction argument, that the closed form solutions for all are polynomials of degree with rational coefficients and no constant term.

   This paper used the closed-form polynomial expression motivated in Part 2 to obtain a direct solution. By writing out the polynomial form with undetermined coefficients, the recurrence relation (4) was manipulated into a linear combination of polynomials (7). Using a linear independence argument, (7) was reduced to a triangular linear system (12) and associated matrix equation (14).The general closed-form solution is (16).

   Solving the finite-summation-of-integer-powers problem , for arbitrary positive integers and has provided a natural setting to use a variety of techniques from discrete mathematics and linear algebra, and poses additional interesting questions (characterization of the denominators in the coefficients of (16) (the in (15)) and divisibility properties of for various ). In particular, we have obtained a direct method for solving the finite-summation-of-integer-powers problem that invokes a matrix solution and does not require iteration.

   ---

   Appendix A: Listing of Solutions to (1)

   A listing of the solution formulas for the first ten values is as follows:

   

   

   

   

   

   

   

   

   

   

   Appendix B: Maxima Source Code for Solving (14)

   For particular , the coefficients for the closed form solutions are immediate. Maxima code, is given below, for determining this solution using the 0-indexed triangular linear system (13):

        solution(p):= block([a, eq],	/* give subroutine variables local scope */
        v : makelist(a[i], i, 0, p),	/* create list of unknowns (0-indexed) */
   					/* create list of equations (0-indexed) */
        eq : makelist(sum(binom(j+1,i)*a[j],j,i,p) = binom(p,i), i, 0, p),
        linsolve(eq, v)
     )$
   

   A more elaborate function that computes the series form and factored forms of the solution is given below. This was used to generate the first ten solution listings.

   	SpN_mat(p):= block([a, eq],	/* give subroutine variables local scope */
   	v : makelist(a[i], i, 0, p),	/* create list of unknowns (0-indexed)   */
   					/* create list of equations (0-indexed)  */
   	eq : makelist(sum(binom(j+1,i)*a[j],j,i,p) = binom(p,i), i, 0, p),  
   
   	/* find coefficients of solution polynomial by solving linear system */
   	sol : linsolve(eq, v),
   
   	/* create polynomial: inner product of {N^i} with coefficients */
   	pol : makelist(N^(i+1),i,0,p),	/* monomials {N^i} */
   
   	/* closed form formula */
   	cff : rhs(sol.pol), 	/* inner product of {N^i} with coefficients */
   	cff 				/* return closed form formula in series */
     )$
   

   Download the complete Maxima source code listing here.

   Appendix C: Octave/Matlab Source Code for Solving (14)

   For particular , the coefficients for the closed form solutions are immediate. Octave/Matlab code, is given below, for determining this solution using the 1-indexed triangular linear system (12):

   % Functions listing coefficients from a_p+1 to a_1 as fractions
   
   function c = sumkp_matrix(p)
       M=zeros(p+1); 		% initialize matrix M
       for i=1:p+1
           for j=i:p+1		% set upper triangular elements
               M(i,j)=nchoosek(j,i-1);  %  Equation (12)
           end;
       end;
   
       b=zeros(p+1,1); % initialize column matrix b
       for i=1:p+1
           b(i)=nchoosek(p,i-1);  %  Equation (12)
       end
   
       c=inv(M)*b;  % Solve to obtain coefficients
   
       c=fliplr(c');		% List from highest index to lowest
       sml=abs(c)<1e-8;	% Numerical correction: set tiny coeffients to exactly zero
       c(find(sml==1))=0;
   
       disp("Solution Coefficients (High to Low order):")
       c=rats(c);  		% return coefficients as fractions
   
   end;
   

   Download the complete Octave source code listing here.

   ---

   This article is available for download as a PDF here.

   The Maxima and Octave complete source code listings implementing the direct matrix solution are available for download here.

   ---

   References

   [Ebr10a]

   Assad Ebrahim.
   Finite summation of integer powers x^p, part 1.
   January 2010.

   [EO10b]

   Assad Ebrahim.
   Finite summation of integer powers x^p, part 2.
   February 2010.

   [GKP]

   Ron Graham, Donald Knuth, and Oren Patashnik.
   Concrete Mathematics: A Foundation for Computer Science.
   Addison Wesley.

   [Knu]

   Donald Knuth.
   The Art of Computer Programming (3 Volumes).

   ---

   Footnotes

   1. The notation used above denotes binomial coefficients, often expressed verbally as "n choose k". Other representations of these coefficients include and . ↩
   2. Maxima code for automatically computing solutions to (1) using solution formula (2) is given in Part 2 of this paper . ↩
   3. Such manipulations are taught in material such as (GKP) and (Knu). ↩
   4. Index manipulation is covered in (GKP) and (Knu). ↩
   5. 0-indexing is more convenient for various computational software packages and programming langauges, including Maxima. The 0-indexed system is:
      

      

      ↩

   ]]> http://mathscitech.org/articles/finite-summations-3/feed 0 http://mathscitech.org/articles/sensor-networked-comms-1 http://mathscitech.org/articles/sensor-networked-comms-1#comments Fri, 19 Mar 2010 16:18:00 +0000 Assad Ebrahim http://mathscitech.org/articles/?p=930

   The past five years have seen the emergence of a growing array of autonomous swimming, flying, and rolling vehicles, each highly sensored and capable of real-time communication with processors external to themselves. Practical designs are now commercially available for each of the four primary areas of our environment: terrestrial, marine (subsea, surface, and amphibian), [...]]]>

   The past five years have seen the emergence of a growing array of autonomous swimming, flying, and rolling vehicles, each highly sensored and capable of real-time communication with processors external to themselves. Practical designs are now commercially available for each of the four primary areas of our environment: terrestrial, marine (subsea, surface, and amphibian), atmospheric (gravity constrained), and space (orbital and planetary).

   A look at a selection of these achievements in networked sensor systems will set the stage to discuss the communications layer of the ubiquitous computing stack.

   ---

   The Advance of Sensor Networks and Autonomous Systems

   Both sensors and embedded processors are becoming increasingly more capable and less costly, requiring lower power and occupying smaller footprints. More significantly, the means and bandwidth available for information exchange between sensors and processors continues to grow, and costs are decreasing here also.

   Together, these advances are the technological foundation for a reality in which high-quality, quantitive responses to an ever-changing environment can be made in real-time by a networked collection of autonomous, decision-making nodes (hardware and software). And these nodes are not only for fixed position sensing.

   Autonomous Mobile Platforms: Swimming, Flying, and Rolling

   The past five years have seen the emergence of a growing array of autonomous swimming, flying, and rolling vehicles, each highly sensored and capable of real-time communication with processors external to themselves. Practical designs are now commercially available for each of the four primary areas of our environment: terrestrial, marine (subsea, surface, and amphibian), atmospheric (gravity constrained), and space (orbital and planetary).

   These designs come in a wide variety of configurations and sizes, from ultra-portable to those capable of carrying large payloads. But regardless of size, all are fully loaded with sensors, on-board imaging or vision systems, ranging and navigation systems, and networked communications. There are autonomous sea surface craft, autonomous subsea gliders, autonomous aerial drones, and autonomous tracked and wheeled vehicles.

   The technological future that is unfolding is one of networked sensors, embedded processing (ubiquitous computing), and sophisticated, adaptive systems that are able to monitor their environment using a fusion of sensors and, when the conditions are deemed right by their on-board software programs, to adapt or intervene. Networked, self-powered subsea and surface craft are capable of performing unmanned precision missions. “Drive-by-wire” land vehicles with sophisticated decision processing software can safely navigate a recreated urban environment, obeying all traffic laws. Hand-launched aerial drones are capable of autonomous surveillance missions. These and similar systems have been engineered, seemingly out of the pages of science fiction, and are presently deployed in field sites of the offshore oil and gas, military defense, space, and automotive sectors.

   These and similar systems have been engineered, seemingly out of the pages of science fiction, and are presently deployed in field sites of the offshore oil and gas, military defense, space, and automotive sectors.

   A Selection of Achievements

   A look at a selection of these achievements in networked sensor systems will set the stage to discuss the communications layer of the ubiquitous computing stack.

   1. DARPA’s Urban Grand Challenge of 2007 saw the successful completion of the six-hour built-city challenge by six, fully autonomous “drive-by-wire” unmanned vehicles from Carnegie-Mellon, Stanford, and others. Almost all of the designs incorporated high-definition terrestrial LiDAR communicating via UDP/IP, among a host of their other networked sensors.
   2. iRobot Corporation, the maker of the famous floor-cleaning Roomba autonomous robot, has, over the past decade, been developing and deploying autonomous military robots on track-and-belt platforms for hazardous mission critical operations in Afghanistan and Iraq such as cave exploration, mine-sweeping, IED de-activation. These have in-built orientation sensors, on-board vision systems, ultrasonic proximity sensors, amongst others, all streaming data for on-board processing, mechnical control and adaptive response.
   3. For use in the deep ocean, the Applied Physics Lab of the University of Washington developed the SeaGlider, an autonomous, long-range, ultra-low powered UUV that dives deep and then surfaces, communicating its data via Iridium satellite link, before diving again. (The SeaGlider is now part of the iRobot stable of technologies, as part of a technology transfer agreement in 2009.)
   4. On the surface of the ocean, Liquid Robotics has developed energy-efficient unmanned surface vehicles that are being used to undertake the kind of long-range, leisurely oceanographic observing research that would previously have required an ocean vessel or an anchored ocean buoy. Complete with on-board navigation, telemetry, solar panels, and a wave energy harvesting plaform, the WaveGlider is capable of accurately traveling a pre-defined transect of a thousand miles or more, or staying in place as a “un-anchored” buoy, all the while carrying a payload of oceanographic sensors.
   5. And for the interface between land and sea, in the near-shore surf zone, iRobot has developed the Transphibian, a shallow water mine sweeping autonomous robot.
   6. In the air, Aerovironment has developed back-pack portable, hand-deployable unmanned aerial surveillance drones that have been used to tactical advantage by fighting forces at the front-lines of counter-guerilla combat operations. These ultra-portable micro-UAVs are equipped with low power, high resolution cameras that wirelessly transmit images to the solder’s in-field console for the kind of “over the horizon” look-ahead capability that is pressing back the fog of war.
   7. Finally, in space, the Mars Rover Program of NASA’s Jet Propulsion Laboratory developed the much celebrated twin autonomous rovers Spirit and Opportunity that, after six years since their arrival onto the Red Planet, are still exploring the martian surface and telemetering their data back to earth. These rovers are not only kitted out with a king’s ransom of sensors, but they have on board processing and mission control software modules that allow for adaptive response and on-the-fly adjustment of tactics to suit the particular situation.

   Communication Technologies in the Four Primary Environments

   What is common to all of these systems, and to the many more applications not mentioned (some listed at the end of this article), is that they require a host of sensors to be integrated into a local-area network on board the system but also the ability to communicate wirelessly with other devices across a wider geographical area.

   The examples have been chosen specifically to show that sensored and networking technologies are not limited to particular environments. They can be developed for each of the four principal environments: subsea marine, rugged or urban terrestrial, gravity-constrained atmosphere, and gravity-free and/or atmosphere-free space.

   Given the widely varying physics in each of the four disparate environments mentioned above, and given the fact that no single communication technology can operate across all of these different environments, it is worth discussing the background to digital communication in general and wireless telemetry in particular, before turning to the details of particular communications protocols and how to use them.

   ---

   Stay tuned for the next article on Communications in Sensor Networks.

   If you enjoyed this article, subscribe to our RSS feed — don’t miss the next article.

   ---

   References and Related Reading

   Cited in the article

   • DARPA’s Third (Urban) Grand Challenge (2007) for a completely unmanned autonomous ground vehicle capable of negotiating an active urban environment.
   • iRobot’s Unmanned Military Robotic Vehicle SUGV for hazardous military operations
   • iRobot’s SeaGlider Long Range Unmanned Underwater Vehicle for long range oceanographic research or military surveillance missions, with technology from the Applied Physics Lab of the University of Washington
   • iRobot’s Autonomous Transphibian Bottom Crawler for mine-sweeping operations near-shore and in the land-water interface
   • Liquid Robotics’s Wave Glider Unmanned Surface Vehicle for long range oceanographic research or coastal security applications
   • Aerovironment’s Unmanned Micro-Air Vehicle WASP III Click on the Aqua WASP – Open Water and Aqua WASP – Jungle videos. Impressive. (More detail here)
   • NASA’s Jet Propulsion Laboratory Mars Rover Program: the Spirit and Opportunity rovers have been exploring for six years since their landing on Mars in January 2004.

   Related reading

   • Autonomous Satellite Surveillance: NASA’s Earth Observing satellites now run autonomous software to allow them to adaptively respond to targets of opportunity and change their mission priorities on the fly
   • Knowledge Engineering and the Emerging Technologies of the Next Decade
   • Sensors and Systems: Integrating Sensors into the Ubiquitous Computing Stack
   ]]> http://mathscitech.org/articles/sensor-networked-comms-1/feed 0 http://mathscitech.org/articles/micro-rovs http://mathscitech.org/articles/micro-rovs#comments Fri, 19 Mar 2010 10:19:05 +0000 Assad Ebrahim http://mathscitech.org/articles/?p=957

   A Versatile Tool for Marine Operations, and a Portable Undersea Platform for Small Sensors

   Micro-ROVs (Remotely Operated Vehicles) are becoming increasingly capable even as their size and cost drop, opening up new possibilities for the application of undersea inspection, imaging, and measurement.

   In this article, I’ll discuss four reasons why Micro-ROVs should be a routinely used part [...]]]>

   A Versatile Tool for Marine Operations, and a Portable Undersea Platform for Small Sensors

   Micro-ROVs (Remotely Operated Vehicles) are becoming increasingly capable even as their size and cost drop, opening up new possibilities for the application of undersea inspection, imaging, and measurement.

   In this article, I’ll discuss four reasons why Micro-ROVs should be a routinely used part of a marine and water-side operations toolkit, and review some stand-out choices in the Micro-ROV category.

   ---

   Micro-ROVs: A Versatile Tool for Marine Operations

   Micro-ROVs (Remotely Operated Vehicles) are becoming increasingly capable even as their size and cost drop, opening up new possibilities for the application of undersea inspection, imaging, and measurement.

   Members of this relatively new class of ROVs are distinguished by their ultra-small size (typically 3-10kg / 7-20lbs) and comparatively low cost (from $6000 to $15,000 to buy and from $600/day to lease). But of course, as compared to their larger, more pricey cousins, they offer less thrust, are typically rated for shallower depths, have correspondingly shorter tether lengths, and can accomodate fewer add-ons and accessories.

   As in most technology applications, cost and capability are the common trade-off variables. The goal for each application is to find the right mix of the two.

   Reasons to Consider Adding a Micro-ROV to your Marine Technology Toolkit

   In my experience, the following are four reasons why Micro-ROVs should be a routinely used part of a marine and water-side operations toolkit:

   Reason 1. In certain situations it can be quicker and safer to use an ROV than a dive team. With a dive team, you have to observe strict safety procedures, current conditions, daylight hours, water temperature, the possibility of debris strikes, hazardous materials, and time in the water. In faster flowing waters, operational problems can mean overrunning a tide window of opportunity and delays of 6 to 8 hours. With crews on standby and big rigs in the water, the loss of a working day can hit the budget hard. If the required work involves multiple up and down trips, this can be exhausting on divers and require diver rotations or rest time. Where visibility is limited, temperatures are low, or otherwise hazardous, an inspection Micro-ROV is a useful tool to consider. In all of these situations, being able to go in with a Micro-ROV either in addition to, or instead of, a diver, can save valuable project time.

   Reason 2. Even when a dive team is necessary, and it often is, Micro-ROVs can be a useful supplement to the dive team, providing initial first-review of a situation and allowing the diver response mission to be adjusted after reviewing footage from the Micro-ROV. The additional advantage is that the customer’s technical staff can be viewing the footage alongside project staff and dive staff. This reduces the chance of misunderstanding or errors in judgment that can occur when all sub-surface information is being relayed back to the customer based solely on the visual observation and memory of a single diver.

   Reason 3. Where routine inspection would be advisable but is neglected due to the cost or availability of dive teams, having a rapidly deployable, pier-side Micro-ROV can substantially improve a waterside operation. There is no longer a reason not to start off with an inspection while the rest of the operation is gearing up. Frequently, problems can be caught early, before they become worse, or before testing or installation operations begin.

   Reason 4. Getting live footage while an expensive equipment trial is underway is often considered as an after-thought. For important trials or prototype evaluations, footage is very helpful. If the test run goes well or an installation goes as planned, then comes the celebration and preparation for presentations — but where’s the compelling footage? Or, in the opposite case, if there were problems with the test, the equipment, or the operational procedures, and if a costly failure occurred, a detailed post-mortem would be helpful — but no one actually witnessed the underwater failure, and there’s no footage. In both of these cases, having a Micro-ROV unobtrusively taking underwater high-definition color video footage of the action can be a boon, be it for customer presentation, business development, engineering analysis of problems, or project documentation.

   Costs, Benefits, and Ease of Use

   Micro-ROVs are coming down in cost. Capable systems can now be obtained from $6,000 – $15,000, depending on options and accesories. Systems can be leased from $600/day, $1500/week to $5000/month (USD).

   In the right situation, this cost is small compared to the total cost of recovering from mistakes, delays, or testing failures.

   How often have expensive crews waited while technical staff wrestled with equipment and deployment challenges and discussed alternatives in the absence of a way to see the problem underwater? Throw in a Micro-ROV, take a careful look, and then decide what exactly needs to be done.

   The ability to setup and deploy within minutes — in many cases literally “drop it in” — is one of the most appealing aspects of the Micro-ROV platform.

   Traditional work ROVs have a steep learning curve, are expensive, require lifting equipment to deploy, and are typically driven by a trained ROV operator. The Micro-ROVs now available have simpler control interfaces, can be deployed off the side of a pier or rubber boat simply by lowering the Micro-ROV into the water from its cable, and a first-time operator can be trained up comparatively quickly.

   The ease of use is due to the high degree of manoeuvrability of many of these Micro-ROVs. As an example, the AC-ROV (reviewed below) has full 5 degrees of freedom and 6 thrusters: 4 vectored horizontal thrusters and 2 vertical thrusters. This simplifies flying the Micro-ROV. Lateral movements can be made keeping the surface in view, and if the target is passed, the operator does not have to fly difficult manoeuvers to get back into position.

   Recommendations

   Given the foregoing discussion, I would recommend the following:

   • If you are a dive team, you may want to invest in a Micro-ROV as part of your infrastructure.
   • If you are involved in frequent waterside operations or equipment testing that involves coordinating groups of contractors or other “on-the-clock” resources, you should consider leasing a Micro-ROV as a contingency plan for when (not if!) things begin to go wrong. (And they always do). Think of it as an investment in giving your technical staff eyes below the surface to ensure that the operation goes smoothly.
   • If you are a marine consultant or ocean engineering company on a fixed-bid contract, you may wish to include the cost of such leases in your bids/proposals. It is part of your contigency planning to help reduce the likelihood of costly over-runs or re-work.

   Micro-ROV Product Choices

   There are now a number of choices for quality Micro-ROVs on the market. From among the half-dozen candidates that I have considered, the AC-ROV is particular impressive. Granted, there are always tradeoffs, and every application needs to consider the right mix of performance requirements and vehicle capabilities. But for an ultra-portable, rapidly deployable, shallow learning curve Micro-ROV that packs an impressive range of capabilities in a low price point, the AC-ROV is a head-turner. I’ll be scheduling a test drive soon.

   Below, then, is a quick overview of the AC-ROV. More information is at the manufacturer’s site. Information on the best of the other half-dozen candidates that I considered is also below.

   Useful white-papers and additional reference material is also given below.

   AC-ROV (AC-CESS, UK)

   Mar-17-2010 by Assad Ebrahim

   The AC-ROV is an impressive 3kg (6.6lbs), ultra compact (LWH: 203mm x 152mm x 146mm / 8″ x 6″ x 5.75″), highly portable tethered micro-ROV outfitted with a digital CCD camera and optional additional sensors. The small size, portability, and rapid deployability make this piece of kit an attractive option for underwater inspection and flying-through large diameter pipes (8″ or more) or for work in tight spaces.
   (Spec | Comparison | Images)

   AC-ROV Appeal: the AC-ROV has full manoeuvrability (5 degrees of freedom), has automatically tracking camera lights, and can be flown with one hand, leaving the other free. It is depth-rated to 75msw (meters sea water), can fly out 120m from the operating unit (with tether deployment system), and can carry 0.5 lb (200g) payload.
   It has 4 vectored horizontal thrusters and 2 vertical thrusters. The thrusters are designed to prevent catching and fouling — and in the event that one of the vertical thrusters gets jammed with kelp, you still have the redundancy to manoeuvre vertically.

   • Input: Power (300W – AC)
   • Basic Output: Composite Video from the on-board digital CCD camera
   • Additional Sensors: the AC-ROV can be outfitted with a USBL (ultra-short baseline) transponder for tracking or precise positioning, an optional rear-view camera and light, depth and pressure sensors, a laser scaling head for measurement of surface features, a thickness gauge for measurement of metal thickness
   • Operating Information: The six independent thrusters allow full range of motion and manoeuvrability. This, coupled with the ability to attach the cable at the rear, top or bottom, allow the AC-ROV to be used for forward-fly-through, drop-down, or up-rise inspection missions in close quarters (mininum opening 8″ diameter is required in forward flying mode, 9″ diameter in drop-down mode).
   • Clean Profile: The AC-ROV has a clean profile and is free of protrusions that are likely to snag the tether
   • Portability: The AC-ROV, together with all required parts and pieces, fits into a single storm case that weighs in under 20kg (40lbs) — light enough for checked baggage on most airlines.

   Other Vendors with MicroROVs and some MiniROVs

   VideoRay (US) | Seabotix (US) | Cetrax (UK) | Subsea Tech (France) | Albatros (Spain) | Gnom (Russia)

   ---

   Related Reading, Further Interest

   1. Each of the vendor sites has useful information on applications, case studies, and success stories.
   2. (PDF)The Role of MicroROVs in Maritime Safety and Security, M. Molchan, Ops, April/May 2006.
   3. (PDF) A Micro-ROV Simulator, Z. Fabekovic, Z. Eskinja, Z. Vukic; IEEE Proceedings Electronics in Marine; 2007; pp.97-101;
      Keywords: Mathematical Modeling, VRML platform, 3-D visualization

   4. Sensors and Systems: Integrating Sensors into the Ubiquitous Computing Stack

   ---

   Stay tuned for the next article on Marine Technologies.

   ]]> http://mathscitech.org/articles/micro-rovs/feed 0 http://mathscitech.org/articles/sensor-systems http://mathscitech.org/articles/sensor-systems#comments Fri, 05 Mar 2010 06:55:19 +0000 Assad Ebrahim http://mathscitech.org/articles/?p=782 … Integrating Sensors into the Ubiquitous Computing Stack

   “Smart dust”, tiny leaf sensors, wearable computing — these and a host of other sensors that make measurements and communicate without requiring human intervention can now be readily integrated into dispersed systems to provide ambient intelligence, situational awareness, and the capability for adaptive behaviors or intelligent process automation. [...]]]>
   … Integrating Sensors into the Ubiquitous Computing Stack

   “Smart dust”, tiny leaf sensors, wearable computing — these and a host of other sensors that make measurements and communicate without requiring human intervention can now be readily integrated into dispersed systems to provide ambient intelligence, situational awareness, and the capability for adaptive behaviors or intelligent process automation.

   Whether the sensor’s output is used to control the opening and closing of relays or thermostats, or to automatically raise alerts — the integration of sensors into systems is at the heart of the promise of ubiquitous computing. And with the ability to place hundreds of embedded sensors within a given coverage area, each wirelessly streaming information, the possibility of self-organizing sensor networks is increasingly becoming a reality.

   This article takes a look at the sensor layer of a basic ubiquitous computing stack.

   ---

   Integrating Sensors into Systems

   In Knowledge Engineering, I broadly outlined where I believe the emerging technologies of the next decade are going and the disciplines that are fueling these developments. Whether this area is called Knowledge Engineering, Ubiquitous Computing, or Ambient Intelligence — the fundamentals are the same: sensors, tiny processors and controllers, situational awareness, wireless communication, and robust networking capabilities.

   Here, I’ll take a look at the sensors layer of a basic ubiquitous computing stack (Figure 1).
   

   

   Figure 1. The Basic Computing Stack (Sensor to Communications) in Ubiquitous Computing Designs. The top layer is optional and is typically an application layer geared for end-user interaction.

   The interest is with devices that are capable of making physical measurements (”sensing”), filtering or computing in real-time using these measurements (”processing”), and reporting the results (”communications”) in a form that allows a machine, unassisted by a human, to read and potentially take action on the data. Communications can be via a visual display, logged to a file, or via packets of information transmitted wirelessly using one of a variety of communication protocols.

   Theory vs. Practice: Direct and Surrogate Measurement

   In principle, sensors can be designed to measure any physical property that is of interest. But direct measurement is often difficult, costly, or otherwise infeasible for a variety of technical reasons. So, in practice, it is often the case that a sensor is measuring a surrogate quantity whose correlation with the quantity of interest is known to vary linearly over a useful range of the quantity of interest.

   Examples
   For example, to measure temperature by directly measuring the heat energy present, i.e. the rate of molecular collisions, is difficult, but measuring the volume expansion of a fluid is comparatively easy. Thus, the discovery by Galileo, at the end of the 1500s, that water volume varied stably with apparent change in temperature, led directly to his invention of the water thermometer (sensor). Similarly, the discovery by Gabriel Fahrenheit, almost a century later in the early 1700s, that mercury has a more stable relationship between volume and temperature change, and maintains this relationship across a wider temperature range, led directly to his invention of the mercury thermometer and the Fahrenheit scale.

   Time is another example: hard to measure directly, but with steadily improving precision as new surrogates are used for indirect measurement — shadow clocks, sand clocks, water clocks, pendula, mechanical clocks, crystal oscillators, and now atomic clocks. Similarly, devices that measure position and direction typically exploit surrogate quantities in their computation of position, range, distance, or direction: the magnetic compass, the sextant, the astrolabe, the surveyor’s level, laser range finding, the total station (optical-mechanical), radar (RF waves), sonar (pressure waves), and satellite navigation (GPS). Most electric measurements are also made indirectly, exploiting changes induced in an associated magnetic field to exert a force that leads, for example, to a mechanical deflection that can then be read off a scale or sensed by a strain gauge or displacement meter.

   Thus, it is the investigation, discovery and calibration of surrogate measurements that makes sensor design and development a blend of applied science and creative engineering.

   Active Elements, Scales and Calibration

   Sensors can be usefully organized into two groups according to their primary function:

   1. sensors that indicate the presence or absence of the phenomenon of interest, e.g. detectors and alarms, and
   2. sensors that can quantify variation in a measured quantity, e.g. gauges or meters.

   Four components are typically at the heart of a sensor’s design: an indicator element, a transducing element, a calibration standard, and a measurement scale.

   An indicator element is something that reacts in a known manner to the phenomenon of interest. Understanding the nature and behavior of the indicator element typically emerges from pure science, be it chemistry (for material indicators), physics (for electromagnetic or optical indicators), or mechanics (for deflection strengths). Integration of the indicator element into a sensor design requires familiarity with both the science underlying the sensor’s mechanism as well as the engineering technologies involved in allowing the sensor to function appropriately.

   A transducer element is something that transforms energy of one kind into another. Some transducers are one-way, other are two-way. For example, piezo-electric ceramic elements are well known two-way transducers that transform pressure into voltage and vice versa. One can view the human eye as a one-way electro-optical transducer, transforming radiated energy (the energy from photons, or light) into electrical impulses traveling along the nervous system into the brain. Similarly, the human skin can be viewed as a one-way electro-mechanical transducer: transforming the pressure from contact into electrical impulses.

   But without a scale and calibration standard, you have at most a correspondence indicator and possibly coarse detector or alarm. For example, a windmill’s motion corresponds to wind speed, but until the windmill’s motion is calibrated and a scale presented, one cannot determine wind speed with any more precision than the relative fuzzy sense of “slower” or “faster”. This level of imprecision might be acceptable if the goal is simply to detect the presence (or absence) of wind, or to trigger an alarm when wind speed passes the threshold needed to begin turning the blades. But more would be needed if the desire is the ability to compare wind speeds at different times, or to quantitatively characterize variations in wind speed with time.

   Having a sensor that can be used for reliable (precise and accurate) quantification will typically require active elements (indicator or transducer), knowledge of how the chosen surrogate quantity behaves across the desired variation range of the phenomenon of interest, and, most importantly, a scale and a standardized method of calibration.

   A Cornucopia of Off-the-shelf (COTS) Sensors

   There are an enormous variety of sensor types and costs: mechanical sensors, electro-magnetic, optical, chemical, biological, environmental, proximity, position, kinematic, acoustic/pressure, and various combinations of these.

   Perhaps the most common categories of sensors are as follows:

   • sound, vibration, pressure sensors: these convert forced displacement (force, pressure) into voltage. E.g. geophone for measuring earth tremors, hydrophone for measuring pressure (sound) in the water, microphone for measuring pressure (sound) in air.
   • kinematic sensors: these convert the sensor’s motion characteristics into voltage. E.g. accelerometer, speedometer (pit log, airspeed indicator)
   • position and proximity sensors: these measure position, deviation from position, or closeness. E.g. crank sensor, GPS, optical or ranging sensors, parking sensors, ultrasonic sensors, Hall effect sensor, variable reluctance sensor, water level sensor
   • motion detecting sensors: these measure the presence or characteristics of movement in the field of view of the sensor. E.g. burglar alarms, radar guns (that indicate the velocity of the motion), tachometer (detecting rotation speed)
   • chemical sensors: these measure chemical composition. E.g. oxygen sensor, water sensor, breathalyzers, CO, , catalytic bead sensor (measuring gas levels), various chemical transistors, gas sensors, electronic nose, , optrodes (for optically detecting the presence of various chemical substances), ion/acid sensor, smoke detector
   • optical and radiation sensors: these use a variety of radiation techniques. E.g. radar, LIDAR, infra-red sensors, laser range finders, pyranometer for detecting solar radiation levels.
   • electro-magnetic sensors: these exploit the relationship between electricity and magnetism, typically using conductor coils and magnets. E.g. current sensors, hall effect sensors, charge detect sensors, magnetic anomaly detectors, metal detectors, radio detection finder, Wheatstone bridge.
   • environmental sensors: these use a variety of techniques to measure environmental conditions. (E.g. rain gauge, snow gauge, dewcheck, moisture sensor for soil (soil moisture probe) or rain (rain sensor) or condensation/relative humidity (dewcheck), temperature sensor (mercury or conductivity, etc.), tide gauge.)

   Evaluating and Comparing Competing Sensors

   For just about anything that one wishes to measure, there will be a variety of off-the-shelf sensor technologies providing that capability, each employing different methods for measuring the quantity of interest, and each exploiting different physical relationships to make and condition these measurements.

   The obvious considerations when choosing a sensor are, of course, cost, size, weight, and performance range. But there are a host of deeper issues that should be considered carefully, since the engineering time and cost of integrating a sensor into a system is not small. Selecting between two otherwise similar sensors often boils down to evaluating the differences between them in calibration, accuracy, precision, reliability, vulnerability to disruptions, and communication protocol.

   What follows, then, is a selection of important issues not to overlook in your sensor selection:

   Issues related to all sensors

   1. output type (analog or digital): sensors with analog outputs are typically less costly, but the analog signals may require conditioning or filtering, cannot travel as far without loss, are more susceptible to noise, and require post conversion to digital in order to record and/or transmit data; digital outputs typically comes at a higher cost, but is easier to integrate since the engineering involved in getting the signal path from raw analog output to conditioned digital output has been done for you.
   2. calibration: is the sensor calibrated (providing an absolute measurement) or uncalibrated (providing a relative measurement)?
   3. type of calibration: manual or automatic?
   4. sensitivity: how fine is the ability to discriminate between similar strength inputs?
   5. accuracy: how closely does the measurement of a known quantity match its known value?
   6. precision: how repeatable are its measurements of the same quantity?
   7. linearity range: what is the variation range over which the sensor performs linearly?
   8. sources of bias: these can be materials, known interference sources, internal noise in the instrument (self-noise), among others.
   9. smoothing / volatility: the presence and type of averaging algorithms that are used to reduce measurement volatility and the susceptibility to noise.
   10. performance degradation: this can be due to aging, shock/vibration, and environmental change (temperature, humidity).
   11. drift rate: the rate at which a sensor’s performance changes.
   12. longevity: the expected life of the sensor.
   13. reliability: the extent to which the sensor continues to perform within its stated characteristics throughout its expected life.
   14. robustness: the continued and proper functioning of the sensor in the face of environmental or performance stresses.
   15. vulnerability to disruption: causes of failure, malfunction, or worse — the unannounced introduction of bias.
   16. mean time between failure: statistically determined estimate on lifetime.
   17. communication protocol: the means by which the sensor communicates or logs its data.

   The Promise of Sensored Systems

   Sensors that can make measurements and communicate without requiring human intervention can be readily integrated into systems, providing ambient intelligence, situational awareness, and the capability for adaptive behaviors or intelligent process automation.

   So a mercury thermometer with only a visual scale etched on the glass housing is an example of a sensor that would require a second sensor in order to take a reading automatically, whereas a digital thermometer that transmits digital information or logs the measured data is one that we can use as part of an integrated automated system.

   Whether the sensor’s output is used to control the opening and closing of relays or thermostats, or to automatically raise alerts — the integration of sensors into systems is at the heart of the promise of ubiquitous computing.

   Indeed, continually streaming information from deployed sensors is creating a knowledge engineering industry built around providing real-time analysis, interpretation, and automated decision-making capabilities to applications as varied environmental monitoring, marine renewables, high-tech agriculture and aquaculture, industrial automation, high frequency trading (financial systems), oil & gas infrastructure, and homeland defense.

   Miniaturized Sensors
   The constituent elements of sensors (power, integrated circuits, antennae, etc.) can now be so small that the potential for widely dispersed deployment is a rapidly becoming a reality. There is sensing dust, used by the military, leaf sensors used in agriculture, wearable computing, and sensors in everything from car steering wheels, elevators, cameras, washing machines, indoor lights, and even shoes.

   In each of the various applications where sensored systems have become a key part of the landscape, there is a similar pattern: miniaturized sensors provide real-time signals. These are digitized and fed into a computer. Whose software produces reports. That can be analyzed as time-series. Which guides decisions. And influences outcomes. That leads to the optimization of scarce resources. Which saves money, increases productivity and effectiveness, and at least in theory, boosts profits.

   This pattern is touching every industry, from automated check-out stations in supermarkets, to RFID applications in warehousing (think Amazon), to large scale sensored ocean observing systems, missile guidance systems, marine renewables, aquaculture, smart cars, and everything imaginable in between.

   Successful Commercialization and the Challenging Economics of Sensor Integration and Deployment

   But sensors are not free. In most cases they are highly engineered devices, and the integrated systems and software of which they are a part represent further engineering development — all of which comes at a cost that can be a significant deterrent to their uptake.

   Thus, although prototype systems technology and COTS chip and sensor sub-components are increasingly available, and although the upsides to adoption are often impressive, there are three crucial challenges that must be overcome for a sensored product, system or service to enjoy commercial success:

   1. having a compelling economic model rooted in an accurate cost-benefit analysis for the intended customer,
   2. having a practical deployment strategy that reduces risk to early adopters, and
   3. being able to demonstrate that the sensored system can deliver the hoped for results reliably, repeatedly, and throughout its expected life.

   These three challenges should therefore be kept closely in mind through-out the system design, sensor selection and sensor integration phase, and should guide the strategy for developing new sensor applications. For those that can deliver the goods (Apple’s iPhone and iRobot’s Roomba, for example) successful commercialization and widespread adoption are a sweet reward!

   ---

   Related Applications: Sensored Systems, Ambient Intelligence, Automated Monitoring & Control

   • Smart Dust — Millimeter Scaled Self-Organizing Wireless Sensor Networks (DUST NETWORKS)
   • Networked Ocean Observing System off the West Coast of Canada (NEPTUNE CANADA)
   • Cabled Ocean Observatories: MBARI’s MARS (MBARI)
   • An Underwater Acoustic Sentinel System for Homeland Defense (BIOSONICS)
   • Networked Sonar Observation of Selected Seabed Environments, U.S. Patent #7457196, T. Acker, A. Ebrahim, J. Dawson, July 17, 2006 (Priority Date), November 25, 2008 (Issue Date)
   • (PDF) Digital Scanning Sonar for Fish Feeding Monitoring in Aquaculture, T. Acker, J. Burczynski, J. Hedgepeth, A. Ebrahim, Proceedings of the 6th European Conference on Underwater Acoustics, Gdansk, Poland. pp. 671-675, June 2002, (BIOSONICS)
   • Extracting Energy from the Oceans: Wave and Tidal Power Developments, International Water Power, August 2009
   • Semi-Automated Sonar Monitoring of the World’s First Grid-Connected Array of Tidal Energy Turbines (VERDANT POWER)
   • The Technology Behind Unmanned Sonar Monitoring (BIOSONICS)
   • Biologically Triggered Automatic Control of Fish Bypass Gates (BORALEX DAM / NEW YORK STATE)
   • Tiny Leaf Sensor for Sensoring Orchards, Aeroponic (Soil-less) Farming, and Space Flight Agriculture (AGRIHOUSE)

   Related Articles

   • Knowledge Engineering: The Emerging Technologies of the Next Decade
   • Bare Metal Programming: The C Language for Embedded and Low-Level Systems Development
   • Hurling Boulders: Assembly Language Programming

   ]]> http://mathscitech.org/articles/sensor-systems/feed 0 http://mathscitech.org/articles/zero-to-zero-power http://mathscitech.org/articles/zero-to-zero-power#comments Thu, 25 Feb 2010 13:56:16 +0000 Assad Ebrahim http://mathscitech.org/articles/?p=672 The question of what value 0^0 should evaluate to has been discussed since the time of Euler (1700s). There are three candidate choices: 1,0, or “indeterminate” (i.e., throw an error).

   In this article, I argue that the only reasonable choice (for discrete mathematics) is 0^0=1 (), and I’ll give a tangible, feel-the-grit-in-your-palms reason [...]]]> The question of what value 0^0 should evaluate to has been discussed since the time of Euler (1700s). There are three candidate choices: 1,0, or “indeterminate” (i.e., throw an error).

   In this article, I argue that the only reasonable choice (for discrete mathematics) is 0^0=1 (), and I’ll give a tangible, feel-the-grit-in-your-palms reason why it can’t be any other way.

   There are important implications for software developers, in particular, the developers of various popular mathematical computing platforms have adopted differing conventions: R, Octave, Maxima, Ruby, Google, Excel, and various software calculators.

   ---

   Why Zero Raised to the Zero Power Ought to Be One ()

   The question of what value 0^0 should evaluate to has been discussed since the time of Euler (1700s). There are three candidate choices: 1,0, or “indeterminate” (i.e., throw an error).¹

   Context of the Debate: Discrete and Continuous Mathematics

   The reason for having three choices becomes clear when considering as a function of two continuous variables. If we take , and then consider , we have . But if we consider , then we have . Clearly, , as a function of two variables, is discontinuous at . This is the reason for L’Hopital’s rule in Calculus that requires treating limits of ratios of quantities that each tend to 0 by considering the relative rates of their approach (i.e. the limit of the ratio of the derivatives).

   But in discrete mathematics, the situation is somewhat different. There is no “approaching” — you are either at or you are away from it: at , or at .²

   Now, Euler in the 1700s and, in more recent times, Knuth (of The Art of Computer Programming, and TeX fame) each argued strongly that , Knuth based upon consistency with the binomial theorem and its frequent appearance in discrete mathematical computations:

   “Some textbooks leave the quantity undefined, because the functions and have different limiting values when decreases to 0. But this is a mistake. We must define for all , if the binomial theorem is to be valid when , and/or . The theorem is too important to be arbitrarily restricted! By contrast, the function is quite unimportant.”
   – from Concrete Mathematics, p.162, R. Graham, D. Knuth, O. Patashnik, Addison-Wesley, 1988 (Citation)

   Different Conventions Among Mathematical Computing Platforms

   Though “majority opinion” is never an acceptable reason in mathematics, it is interesting to consider how implementations of differ even among various modern common computing platforms:

   • Google: 0^0 is 1.
   • Ruby: 0^0 is 1.
   • R: 0^0 is 1.
   • Octave: 0^0 is 1.
   • Microsoft’s Calculator: 0^0 is 1.
     
     

   • Maxima: 0^0 is indeterminate — throws an error.
   • Microsoft Excel (2000): 0^0 is indeterminate — throw an error
     
     

   • Hexalon Max (software calculator): 0^0 is 0.
   • TI-36 Hand calculator: 0^0 is 0.
     

   Principles for a Decision in Mathematics: Extension and Consistency

   Often in mathematics, where there is more than one choice, or where a definitional decision is required, the decision is made by arguing the desirability of an extension into what is otherwise undefined, and then the decision is made to maintain consistency with the evidence that is already accumulated and accepted. It is precisely in this way that ordinary multiplication of positive numbers is extended, first to multiplication by a single negative number, then to multiplication by two negative numbers, i.e. .

   To see that we must have , take the view of elementary mathematics as an empirical science and not as an axiomatic science, since it is as an empirical science that mathematics is taught to young children, and where this arithmetic rule is first encountered, typically along with some sort of reference to authority:
   

   “Minus times minus is plus.
   The reason for this we need not discuss!”
   — W.H. Auden

   From the point of view of an empirical science, the multiplication of two positive numbers has a well-defined, tangible meaning as repeated addition, and this meaning remains valid even with the extension of one of the products to a negative number. But both products negative is ill-defined from this point of view.

   It is at this point that the mathematician sees an opportunity. The consequences of declaring something to be undefined (throwing an error) is an enormous loss of efficiency. Any product now has to be checked for the case that both factors are negative, and this case has to be treated separately. If a definition could be found that remains consistent with all other empirically obtained rules, and if that definition means that multiplication can proceed indifferent to the sign of the factors, well, then that is a big win. The consistency in this particular case is the distributivity of multiplication over addition, a law which, for positive numbers, can be accepted on entirely empirical grounds. (The full argument is given in the footnote: ³)

   Forced to a Decision: A Tangible Computation That Requires an Answer

   I claim that the case of is similar. Not only would it be a significant loss of efficiency to treat this case separately, but indeed, in the finite summation of integer powers, we have a problem with a real, tangible result (a finite sum), whose value (an empirically determinable fact) depends unavoidably on the chosen value of . The crucial step in this argument occurs in the derivation of (*1b) from (*1a) in Finite Summation of Integer Powers, Part 2.

   Extracting the relevant part of that derivation, we have:

   

   After expanding the binomial power using the binomial formula and further manipulation, we arrive at:

   
   
   
   (Pull the term out of both summations. Note: )
   
   
   
   (which, after additional manipulation, yields)
   
   
   

   The key step happens in (***) above: we peel off the term of the inner summation to get: . Peeling this out of the outer summation requires considering the expression for all . Now, 0 raised to any positive power is 0, so we can dispel the case of .

   But what is ? A decision must be made: it is either or . Indeterminacy is not an option, since the situation is real and is required to continue the simplification.

   The Argument for

   What are the consequences of choosing the other definition, i.e. ? In this case, the final formula for is off by a linear constant , while the choice leads to the exact formula and a computed value that matches a brute force summation. For , the difference is between 220,825 (the correct, verifiable answer), and 220,815 (verifiably NOT correct). In the face of counting pebbles, trees, integer powers, the correct choice seems clear.

   Compelling? For discrete mathematics, I think so. Certainly, the possibility of being open for continued consideration seems to shut, and the choice of abstention by throwing an error is weakened as well. The evidence, I claim, provides strong support for adopting the convention by definition at least in discrete mathematics⁴:

   Definition (Empirical) for , where are discrete variables.

   ---

   (If you’re a software developer of a mathematical package, I’d be interested in how you arrived at your decision. You can send me an email using the Comments link below.)

   If you enjoyed this article, feel free to click here to subscribe to my RSS Feed.

   ---

   Footnotess

   1. Further discussion of is at: The Math Forum ↩
   2. You might also be at , but that, I believe we would all agree, is division by zero, and so appropriately remains undefined (unless working in the extended reals, in which case it is .) ↩
   3. Considering that any quantity times zero is zero, and that one times any quantity is the quantity, we have no hesitation in granting . But then observe that we way write , which means, combining the two expressions, we have . If we accept the law of distribution of multiplication over addition for positive whole numbers, purely on empirical grounds, and if we wish negative numbers to behave in the same manner as our empirically accepted positive whole numbers, then we want the distributive law to hold as well. And therefore we have Which means that must be the oppositive (additive inverse) of , and hence ↩
   4. The implications for continuous mathematics are a consideration for another discussion. The statement that a discontinuity exists at the origin isn’t quite enough. ↩
   ]]> http://mathscitech.org/articles/zero-to-zero-power/feed 0 http://mathscitech.org/articles/maxima http://mathscitech.org/articles/maxima#comments Mon, 22 Feb 2010 06:33:13 +0000 Assad Ebrahim http://mathscitech.org/articles/?p=710

   …By virtue of its unbeatable low cost (free), ready availability for all three major operating systems, and its raw power in all areas of mathematics and analytic engineering, Maxima is a mathematical computing package that ought to be in the toolbelt of every programmer, engineering, scientist, and mathematician.

   From garden-variety algebraic simplification, polynomials, calculus, [...]]]>

   …By virtue of its unbeatable low cost (free), ready availability for all three major operating systems, and its raw power in all areas of mathematics and analytic engineering, Maxima is a mathematical computing package that ought to be in the toolbelt of every programmer, engineering, scientist, and mathematician.

   From garden-variety algebraic simplification, polynomials, calculus, matrix equations, differential equations; to exotic areas of number theory, combinatorics, hypergeometric functions; to state-of-the-art areas in tensor and gravitational physics, PDEs, and nonlinear systems, Maxima is a firehose of mathematical capability, able to blow through hairy computations with symbolic accuracy, leaving more time for the advancement of application development or research.

   ---

   Maxima for Symbolic Computation

   What is Maxima?

   Maxima is an impressive symbolical computation package that is free, open source, and has an active, responsive developer base and community that ensures both the future lifecycle of this software package and plenty of help when dealing with problems. It falls in the category of Computer Algebra Systems (CAS).

   Now, there are certainly a number of well-known and less known computer algebra systems available to choose from: Mathematica, Maple, Macsyma, MuPAD, Sage, etc. Many are commercial packages. But by virtue of its unbeatable low cost (free), ready availability for all three major operating systems, and its raw power in all areas of mathematics and analytic engineering, Maxima is a computing package that ought to be in the toolbelt of every programmer, engineering, scientist, and mathematician.

   From garden variety algebra, polynomials, calculus, matrix equations, and differential equations, to exotic areas of number theory, combinatorics, hypergeometric functions, to state of the art areas in tensor and gravitational physics, PDEs, nonlinear systems, Maxima is a mathematician’s garden.

   This page should get you started with downloading and installing, and then provide a few examples and resources to help you on your way.

   Obtaining Maxima

   You can download Maxima from here (Windows, Linux). (If you’re confused, there are instructions here.)

   Installing Maxima

   Paul Lutus has written a step-by-step installation walkthrough here. Specifically, take note about the Windows firewall when first running wxMaxima:

   “When you first run wxMaxima (an icon is placed on your desktop by default), your firewall software may complain that a socket is being opened. This is a local socket that wxMaxima (the user-friendly graphical front end) uses to communicate with Maxima (the computation engine), it is not an attempt to take over your computer or communicate your personal secrets to ruthless Russian mobsters. Suspend your paranoia and allow the socket to be created.” (from Arachnoid’s Installation Guide)

   Getting Started

   Depending on your level of experience with computers, you may find the following starting points useful:

   For a Quick Start

   • Here’s a succinct Maxima command reference sheet (cheat sheet).
   • If you are familiar with Mathematica, this Mathematica / Maxima Syntax Conversion Chart will get you going quickly.

   Then all you need are some good examples, which you can find here:

   • Antonio Cangiano’s 10-minute Tutorial for Solving Math Problems with Maxima is a good start.
   • Follow this with Richard Rand’s more advanced whirlwind tour: Introduction to Maxima, including a discussion of writing subroutines/scripts/programs for Maxima. You’ll like it better as a well formatted PDF instead of ill-formatted HTML.
   • To see how Maxima can be used in verification and validation of a result in discrete mathematics, see Finite Summation by Recurrence Relations, Part 1 (Motivation and Low Order Examples) and Part 2 (General Recurrence Solution).
   • To see how Maxima can be used to solve linear systems (matrix equations), see Finite Summation by Recurrence Relations, Part 3 (Closed Form Direct Matrix Solution).
   • For an example Maxima script (iteratively solving the finite sums p-th order recurrence relation), see sumkp_recurrence.mac
   • If you’re looking for using Maxima for solving real Engineering problems, consider Javed Alam’s 22 sessions of Maxima, Paul Lutus’s differential equations and circuit theory and Fourier (Spectral) Analysis.

   More advanced references are here.

   A full list of the mathematical packages and capabilities built into Maxima can be found in the 900+ page (5MB) Maxima Manual. (You’ll probably want to download the PDF version for offline reading.

   For Basic Users
   Paul Lutus has leisurely hands-on tutorial style introduction to Maxima. In addition, there are a number of good “book-style” tutorials that develop familiarity with Maxima thoroughly.

   For Advanced Users

   Robert Dodier’s Minimal Maxima (PDF) breaks down the syntactical, evaluation, and data structures underlying Maxima. A good understanding of this is essential when you are trying to go beyond using Maxima as a powerful calculator, or when writing your own functions/subroutines in Maxima.

   Getting Help
   The Maxima mailing list is a responsive, expert community that can not only help you out of a jam, but also raise the level of your proficiency and your familiarity with “natural” Maxima programming style.

   ---

   Links and References

   Obtaining and Installing

   • Download Maxima from here (Windows, Linux)
   • The Maxima Page for Windows, Linux
   • Installation Walk-Through — take note about allowing the firewall exception for wxMaxima!. Also, how to get Greek fonts to display properly in your Maxima session.
   • Installation Prerequisites for Maxima for Mac, Windows, Linux

   Cheat Sheets / Ready Reference Sheets

   • A Maxima CheatSheet / Ready Reference Sheet
   • Mathematica / Maxima Syntax Conversion Chart, and Maxima Cheat Sheet: Harvard University, Department of Mathematics
     

   Basic Guides

   • Antonio Cangiano’s 10-minute Tutorial for Solving Math Problems with Maxima: Math~Blog
   • Richard Rand’s Introduction to MaximaA More Advanced Whirlwind Tour of Maxima, including a discussion of writing subroutines/scripts/programs for Maxima — You’ll like it much better as a formatted PDF.
   • Paul Lutus’ Symbolic Mathematics Using MaximaA Leisurely Tutorial in 9 parts.

   Topics by Example

   • Javed Alam’s22 sessions of Maxima for solving real-world Engineering problems
   • Paul Lutus’s differential equations and circuit theory and Fourier (Spectral) Analysis.
   • Tensor Algebra in Maxima
   • Leon Brin’s Maxima and the Calculus
   • Gregory Astley’s Using Maxima for Plotting Direction Fields of First Order ODEs

   Advanced Guides

   • Robert Dodier’s Minimal Maxima (PDF) breaks down the syntactical, evaluation, and data structures underlying Maxima. A good understanding of this is essential when you are trying to go beyond using Maxima as a powerful calculator, or when writing your own functions/subroutines in Maxima.
   • Maxima mailing list is a responsive, expert community that can not only help you in a jam, but also raise the level of your proficiency and your familiarity with idiomatic Maxima (that intangible called Maxima style).

   “Book-Style” Tutorials (PDF or HTML)

   • Gilberto Urroz’s Maxima Book: Comprehensive, each chapter organized by mathematical area.
   • The Maxima Book, P. de Souza, R. Fateman, J. Moses, C. Yapp: Comprehensive, well-written, well-organized. Not the most up-to-date, but the organization, comprehensiveness, and quality of the material makes this a valuable reference.
   • Edwin Woollet’s 11 chapterMaxima By Example: a leisurely description of Maxima’s capabilities.

   System Documentation

   • Maxima Manual Online: 900+ page (5MB) comprehensive manual and listing of all mathematical functions and capabilities built into Maxima.
   • Maxima Homepage: Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors. Maxima yields high precision numeric results by using exact fractions, arbitrary precision integers, and variable precision floating point numbers. Maxima can plot functions and data in two and three dimensions.
   • wxMaxima Homepage: A Windows GUI for Maxima
   • Maxima Manual Online
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