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An Ideal Math Curriculum for Physics Students

I occasionally fantasize about an “ideal math curriculum” for Physics graduate students, based on my experience, in school and out. Which topics make sense, which don’t, what should count as reasonably expected knowledge, what is actually useful?

There are also some textbooks, several of which having been published after I left school, that I would like to use (actually: like to have used) in the appropriate classes.

A Simple Approximation for the Airy Function

Besides the Normal Distribution Function, I occasionally need the Airy Function Ai(x): it arises in perturbation theory and some other contexts. This function is most definitely not part of most standard numerics libraries! While high-quality implementations of it are part of most “serious” numerics libraries (such as SciPy or GSL), these libraries are not always available or convenient.

Here is a really simple numerical approximation: it is numerically “good enough” for casual work, and simple enough to be implemented on the fly as needed.

Exploring SymPy or: What, Really, is the Purpose of Computer Algebra Systems?

I recently got interested in singular perturbation theory , and to get help with the algebra, I turned to SymPy. I had tried to use Mathematica in graduate school in the early 90s, but the experience had been sufficiently frustrating that I had steered clear of computer algebra systems since.

SymPy presents itself as a “friendly”, less intimidating alternative, with a more familiar and conventional language and operating model.

Hot Chocolate

Hot Chocolate

Occasionally, I like to drink hot chocolate — that is, real hot chocolate, from pure cocoa powder and whole milk; not some (sugared, flavored) drink mix.

So, I was somewhat devastated when I learned that the venerable, time-honored Droste (those of the Droste Effect) seems to have gone tragically out of business.

Some replacement was required: at least as good as the original, and satisfying my various purist predilections.

Go's Named Types aren't Types

I always thought that the “types” that are created using Go’s type keyword were, in some vague sense, new, unique, original; but in any case separate and distinct types. It turns out, this is a misunderstanding.

Go: Reading a Plain-Text File

How does one actually read a plain text file in Go? Some searching through the standard library revealed the bufio.Scanner utility, which seems to be the most convenient way to accomplish this task.

Kästner's verlassene Kinder

Erich Kästners Mutterkomplex ist bekannt, hinreichend dokumentiert, und sowieso nicht zu übersehen. Daher ist es interessant, dass es in seinen Kinder- und Jugendbüchern noch zumindest ein anderes durchgehendes Thema gibt, das aber nicht in der gleichen Weise erkannt zu werden scheint: in allen von Kästners Kinderbüchern treten Kinder auf, die von ihren Eltern verlassen worden sind.