An Open Source LaTeX / TeX Platform for Windows

(Mathematical Toolset Series: TeX & LaTeX, Part 2 of 3)

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 reference materials you may find useful as you advance. The instructions below have been tested against WinXP, Win7, and now Win8.

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Writing Modular TeX Documents

(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.

A Course in the Philosophy and Foundations of Mathematics

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.

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Finite Summation of Integer Powers (Part 3)

(Discrete Mathematics Techniques III)

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 S_p(N) = \sum_{k=1}^{N} k^p. Having established in Part 2 that the closed-form solution is a polynomial, the summation is here rewritten as the sum of the p+1 independent monomials a_j N^j (1 \leq j \leq p+1), where the a_j are unknown coefficients. Using the recurrence relation S_p(N+1) = S_p(N) + (N+1)^p, we obtain a linear combination of the monomials, which reduces to an easily solvable (p+1)-by-(p+1) triangular linear system in the unknown coefficients a_j of the closed-form polynomial solution. Maxima and Octave/Matlab codes for directly computing the closed-form solutions are included in the Appendices.

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Why Zero Raised to the Zero Power IS One

Updated! February 5, 2017

The value of zero raised to the zero power, (0^0), 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: Google, R, Octave, Ruby, and Microsoft Calculator choose 1; Hexelon Max and TI-36 calculator choose 0; and Maxima and Excel throw an error (indeterminate). In this article, I’ll explain why, for discrete mathematics, the correct answer cannot be anything other than 0^0=1, for reasons that go beyond consistency with the Binomial Theorem (Knuth’s argument).
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Maxima for Symbolic Computation

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 an active developer base and responsive community, a user gets a secure future lifecycle of the product and plenty of help when dealing with problems. The result: an essential mathematical computing package for students, programmers, engineers, scientists, and mathematicians. This article will help you get started with Maxima.

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