1. Inspiring the next generation of technology builders.

A challenge faced by [Read More...]]]>

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 [Read More...]]]>

Your computer, kitted out with specialised software (mostly free) and configured for efficiency of use, is perhaps the single greatest ‘force multiplier’ that you can have as a Scientist, R&D Engineer, or Mathematician — unless of course you have a large budget and a team of bright minds at your disposal.

With good [Read More...]]]>

(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 [Read More...]]]>

(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 [Read More...]]]>

(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 [Read More...]]]>

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 [Read More...]]]>

(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 [Read More...]]]>

EDIT: 25.Oct.2015 – improved templates added.

You can get started with LaTeX / TeX on Windows within an hour. This article walks you through setting up a working platform, provides basic templates for you to produce your first PDF document, and points you to [Read More...]]]>

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 [Read More...]]]>

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 [Read More...]]]>

Students who are hard-working and otherwise successful, but whose peers, mentors, and home environment are mostly non-technical and disengaged from the ideas behind science and technology, are at substantially higher risk of disorientation, dissatisfaction, and disillusionment with mathematics and science.

In this article, I’ll develop this conjecture and suggest an approach that incorporates philosophical [Read More...]]]>

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 [Read More...]]]>

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 [Read More...]]]>

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), [Read More...]]]>

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 [Read More...]]]>

“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 [Read More...]]]>

The value of zero raised to the zero power, , has been discussed since the time of Euler in the 18th century (1700s). There are three reasonable choices: 1,0, or “indeterminate”. Despite consensus amongst mathematicians that the correct answer is one, computing platforms seem to have reached a variety of conclusions: [Read More...]]]>

Maxima is a symbolic computation platform that is free, open source, runs on Windows, Linux, and Mac, and covers a wide range of mathematical functions, including 2-D/3-D plotting and animation. Capabiities include algebraic simplification, polynomials, methods from calculus, matrix equations, differential equations, number theory, combinatorics, hypergeometric functions, tensors, gravitational physics, PDEs, nonlinear systems. With [Read More...]]]>

C provides the convenience of learning one language while retaining the ability to target a variety of platforms including modern operating systems (Linux, Windows, Mac), real-time operating systems, systems-on-a-chip, and a host of microcontrollers for embedded development. And if you have to “mov” the bits around yourself (device drivers, [Read More...]]]>

Abstract We solve the general case of the finite-summation-of-integer-powers problem for arbitrary , and obtain a -th order recurrence relation that can be used to iteratively obtain the closed form polynomial for for any given . Source code is given for computing these polynomials using Maxima, an open-source (free) symbolic computation [Read More...]]]>

Abstract We motivate an approach that uses recurrence relations to find closed form solutions to the finite-summation-of-integer-powers problem for any individual . The approach is illustrated for small : . Maxima, an open-source (free) software package, is used to demonstrate how a symbolic computation platform can speed up the accurate derivation [Read More...]]]>

…For industry or research.

Over the coming months, I’ll be posting articles as part of a series on setting up a toolset for Mathematics work in industry or research.

I’ll be emphasizing open source software. Though the primary target is the Windows PC platform (dominant in industry), I will list alternatives for Linux/Unix.

[Read More...]]]>

Good mathematical technique can bring the solution to certain mathematical questions within reach. By a proper formulation (one that is both tractable and that generalizes readily) and the use of mechanical techniques, one can often pass from a single insight to the solution of a family of problems, and in some cases, to the [Read More...]]]>

Thoughts on Teaching Mathematics in an Exploratory, Dialectical, Topical format.

Mathematics is a richly spun tapestry, heavy with exciting interconnections from a multiplicity of endeavors, perspectives, and disciplines, both applied and theoretical. Yet contrary to this “non-linear” reality, the typical pattern of school and even university mathematics is both linear and restricted.

For an [Read More...]]]>

The development of mathematics has had many encouraging forces: societal, technological, cultural. These have served to accelerate mathematics and have been accelerated in turn, in many cases the pair becoming locked into a mutually beneficial resonance that has dramatically energized both.

In this article, I look at some of the significant catalysts, from the [Read More...]]]>

… An Overview of Assembly Language Programming

Assembly language programming often evokes images of a time when real programmers hurled boulders the size of small UNIVACs. The mystique is there for those whose computer science training is primarily in higher level languages.

But programming is programming, and one language shouldn’t be much harder to [Read More...]]]>

… for Assembly Language Programming

To get started with assembly language on your x86 box, here is a set of open source (free) toolchain elements that play well together when host and target platforms are an x86 PC running a Windows (or Linux) operating system…

An Open Source Toolset for Assembly [Read More...]]]>

… in a nutshell

The development of mathematics is intimately interwoven with the progress of civilization, influencing the course of history through its application to science and technology.

But mathematics has changed. Even the mathematics of the 1800s can seem quite strange now, so greatly has mathematics evolved in the past 100 years [Read More...]]]>

I’ll consider five groups of characteristics:

Applicability and Effectiveness, Abstraction and Generality, Simplicity, Logical Derivation, Axiomatic Arrangement, Precision, Correctness, Evolution through Dialectic…

Characteristics of Modern Mathematics

In the article What is Mathematics?, I have posited that Mathematics arises from Man’s [Read More...]]]>

Can a definition be given that captures the meaning of Mathematics across the millennia of its recorded history? What unites the practice of mathematics throughout its history and into the present time?

In this article, I will try for a short answer by proceeding iteratively — convergence will be reached in two iterations…. [Read More...]]]>

…Taking into account early human evolution, and in particular, the development of speech, it is likely that the understanding of counting and keeping time far pre-dates the discovered fossil evidence of Homo Sapiens from 30,000 years ago, and reaches back at least as far as 250,000 years ago, coincident with speech, fire, and cooperative [Read More...]]]>

Between Mathematics, Computer Science, Software Engineering, Electrical Engineering, and Statistics, is emerging an area of effort concerned, not just with using data or information gathered slowly over months or years, but with its real-time acquisition, interpretation and analysis, and its real-time use in appropriate decision-making, automatic adjustment, and intelligent response.

For a team capable [Read More...]]]>