## Professional Grade Typesetting with LaTeX / TeX

(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.

## 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.

## 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.

## Finite Summation of Integer Powers (Part 3)

(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 $S_p(N) = \sum_{k=1}^{N} k^p$. 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.

## Bare Metal Programming: The C Language

…for Embedded and Low-Level Systems Development

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, DMA controllers), you can do that too. This is a significant efficiency over assembly languages which are essentially chip-specific control codes and therefore require understanding the architecture of the chip in each target platform.

## Mathematics Toolset

…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.