Ganesh Swami

I must be on a roll here. For the last few days, I’ve been spitting out about 500 words of coherent, easy to understand text for my coop report. I’ve never enjoyed writing technical documents so much before.

Everytime I intend to write a report, I always start with the LaTeX template that I made. This time, I decided to push the limits of what LaTeX has to offer.

I’ve included some pictures from my half-baked document. Includes pictures of Table of Contents, PDF indexes, Table of Notation, Glossary, and References. All of them cross-referenced and hyper-linked automatically. Click on the images for higher resolution. Resolution is not meant to be able to read the text, it’s still a bunch of FIXMEs.

All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like), hydrodynamics (supported by manufacturers of atomic submarines) and celestial mechanics (financed by military and by other institutions dealing with missiles, such as NASA.).

Cryptography has generated number theory, algebraic geometry over finite fields, algebra (the creator of modern algebra, Viete, was the cryptographer of King Henry IV of France), combinatorics and computers.

Hydrodynamics procreated complex analysis, partial derivative equations, Lie groups and algebra theory, cohomology theory and scientific computing.

Celestial mechanics is the origin of dynamical systems, linear algebra, topology, variational calculus and symplectic geometry.

– Vladimir I. Arnold. Polymathematics: is mathematics a single science or a set of arts? In Mathematics: Frontiers and Perspectives. American Mathematical Society, 2000, pp. 403-416.

Vladimir Arnold is one of my favorite authors. He along-with Professor Jerrold E. Marsden must have written some of the best books on mechanics (this one and this one.) I’m writing the section connecting geodesics, metrics and Euler-Lagrange equations and I wasn’t sure how to introduce the material and looked to these books for inspiration.