Blog, by date: 2011_sep

tcjblog.py (from 2011/09/09)

I've now (for the most part) finished a working version of some software I've wanted to tackle for a while. I call it tcjblog.py. It's a blog platform built using jemdoc.py to format simple text files into nice looking HTML. What're the benefits of this, and features of tcjblog.py in general?

• Simple, text file management of blog posts. (I control these with git.)

• Ability to include LaTeX markup.

• Static HTML for all blog-related pages

• Entries show up on an index of all posts, the category associated with the post, and the month the post was made.

• An RSS feed displays the formatted entries nicely for RSS readers.

• Indexes split posts 10 per page.

• Entry URLs are a sanitized version of the page title, so they're auto-perma-links, at least once you're happy with a title.

There's still a fair bit of work for it, but probably it's time to focus a bit on the content and less on the software, at least until it seems more pressing. This has been a great couple-afternoon project for me–a nice break from the almost 5000 lines of numerical/algorithms stuff in C I've done in the last couple of weeks.

It's worth noting that the static approach generates a fair number of files for this approach: one for each entry, one for each category, and one for each month, plus a tenth of the total number again for the index pages. So I use a makefile to manage all of it.

Five Critical Textbooks for (Applied!) Math & Physics Students (from 2011/09/04)

In the course of working through my first year at grad school, I've come up with five favorites for the basics of an undergrad understanding of the essential topics for applied math and physics. Without ado and in the order I'd take them off my shelf:

• Mathematical Methods in the Physical Sciences - ML Boas. This is my favorite, because it contains almost every technique you need, and it has a ton and a half of problems(over 3400). It contains a good review of complex analysis, linear algebra, differential equations, and calculus, but also chapters on special functions, partial differential equations, probability, tensors, and the calculus of variations.

  • Hidden Gem: Chapter 4, Section 12: Differentiation of Integrals, RP Feynman's favorite trick.

• Calculus - Greenspan. A great reference on calculus.

• Complex Variables and Applications - Brown & Churchill: The most readable book on complex analysis I've read. Not so hidden gem: Most of the solutions are given right alongside the problem–a great book for self-study. Also the material on conformal mapping and fluid flows.

• Linear Algebra And Its Applications - Strang. Nice book on linear algebra theory.

  • Hidden Gem: Chapter 7, Section 4: Iterative Methods for Ax=b and Gershgorin's circle theorem.

• Elementary Differential Equations and Boundary Value Problems - Boyce & DiPrima. Powerhouse of differential equation knowledge. Strangely, it is the book ESAM recommended, but not the book they use for teaching their undergrads.

I've spent probably the most time with Boas’ Mathematical Methods in the Physical Sciences–I've worked nearly 1000 problems out of the book to get ready for the preliminary exams my first year. It was completely worthwhile.