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Duelling with pistols. If you were the one issuing the challenge, your dilemma was that custom dictated that your adversary be allowed to shoot first. Only then, if you were still able to shoot, would you be permitted to seek “satisfaction”. How much of an advantage does the first shooter really have? In this article, we build a simple probability model, and implement a numerical model in a few lines of R code.  Two gentleman face off in the snow. Convention dictates the challenged shoots first. (Statistics and Data Mining II) Automated decision problems are frequently encountered in statistical data processing and data mining. An heuristic filter or heuristic classifier typically has a limited set of input data from which to arrive at a set of conclusions and make a decision: REJECT, ACCEPT, or UNDETERMINED. In such cases, pre-processing the input data before applying the heuristic classifier can substantially enhance the performance of the decision system. In this article, I’ll motivate the use of a radar-tracking algorithm to improve the performance of automated decision making and statistical estimation in data processing. I will illustrate using the website visitation statistics problem. (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. (Statistics and Data Mining I) For a variety of reasons, meaningful website visitation and visitor behavior statistics are an elusive data set to generate. This article introduces the visitor statistics problem, and describes seven challenges that must be overcome by statistical and data analysis techniques aiming for accurate estimates. Along the way, we’ll encounter the “Good News Cheap, Bad News Expensive” Paradox of Data Mining — or, why information is often used “as-is”. This article is the first in a series on algorithms, statistics and data analysis techniques (using free and open source tools) using the visitor statistics problem as a vehicle for illustration.
Introducing the LaTeX typsetting platform If symbols, formulas, and equations comprise a large portion of your professional communication, then you will gain significantly by becoming proficient with the LaTeX (pronounced “lay-tech”) document preparation platform. With the right tools and a little practice, the relative ease of creating beautiful mathematical documents with LaTeX will likely mean that you leave Office in favor of LaTeX for your technical writing. This article introduces the LaTeX platform (short for Lamport-TeX, after the mathematician Leslie Lamport), illustrates its capabilities, and highlights the key differences between using LaTeX or WYSIWYG “what you see is what you get” word processing systems such as Office. For those that like to know the human side of the tools they use, we provide a brief history of the legendary TeX (pronounced “tech”) platform, which underpins all variations of which LaTeX is one, looks at the philosophy motivating the development of TeX, and something about its legendary creator Donald Knuth.  Don Knuth, Leslie Lamport, and an illustration of of why writing mathematics in LaTeX is easier than in Word.
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. Writing Beautiful Mathematics: Getting Started with LaTeX on WindowsIf you haven’t done so already, you may want to start by reading the Preface to the Computing Series: Software as a Force Multiplier, Sections 1-3. 2nd ed. Revised with new templates Sep 21, 2019, 1st ed. May 18, 2010. Getting Started with LaTex  An example of mathematics written in LaTeX, from Finite Summation of Integer Powers (Part 3), A. Ebrahim, C. Ouellette, 2010.
This article curates a reading list (most sources available freely online1) organized into a set of encounters that lie outside the standard mathematics curriculum. They are intended to enrich the reader’s understanding of mathematics and its place in scientific inquiry, increase her/his connection to the historical and philosophical questions behind the mathematics of the past and present, and gain greater satisfaction from further mathematical study. The reader should come away with a better understanding of the culture of mathematics: what mathematics is, mathematical method and meaning, and the relation of mathematics to the empirical world and to science. We look at seven topics. These may be covered in any order, to suit your particular interests.
There is no core body of technical material to master in this course; the important thing is a feel for how, why, and in what context the core ideas of mathematics evolved, getting to the essence of their motivation, and understanding the fruits of these efforts. The course such as the below should appeal to all those who have an itch to scratch beneath the surface of mathematics, who find themselves asking “but why?”. It could be useful in all three tiers of education: secondary, post-secondary (undergraduate), and graduate, appropriately restructured.
Continue reading this article…
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. |
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© 2009-2026 Assad Ebrahim To contact me on email, use: assadebrahim2000 at gmail dot com (do the obvious) |
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