Where to begin?

Question

I was looking at the Mathematica website today and just decided to buy the software. I've spent too much time juggling annoying symbolic expressions by hand that actually learning to do things with a computer should be a worthwhile investment. Similarly for making conjectures about formulas etc. a computer would seem like a useful tool.

My question: Where should I begin? I have a Ph.D. in math and would consider myself an expert level programmer in C, C++, x86 assembler, OCaml and Perl. I understand the functional programming paradigm well, so I don't need any introductions. To begin with, I would like to be able to work efficiently with linear algebra, number theory and random sampling. Oh, and plotting would be nice too and how to embed formulas written in LaTeX into those plots.

Any advice?

Have you already seen the series of books by Trott? They're somewhat bulky and a bit expensive, but if your nearby library has them, you could take a look and see if it suits you. Otherwise, I would suggest also taking a look at Wagon's Mathematica in Action; I personally found the examples there very instructive, and the skills used to be quite generalizable. — J. M.'s missing motivation, May 12 '13 at 00:37
Take a look here: http://mathematica.stackexchange.com/questions/18/where-can-i-find-examples-of-good-mathematica-programming-practice — Szabolcs, May 12 '13 at 00:53
Thanks guys. That discussion about programming references seems like a great place to start after having watched the few intro videos. — evf, May 12 '13 at 00:55
Regarding plotting, see here. The documentation is pretty good and has plenty of examples. You don't write LaTeX in Mathematica. Instead write your equations directly using Mma's front end. — Szabolcs, May 12 '13 at 01:00
...but if need be, you can use Mathematica to produce $\LaTeX$ (though, not always optimal $\LaTeX$). — J. M.'s missing motivation, May 12 '13 at 01:06
My comment with LaTeX is mostly that if I use it to generate graphs for publications, I would like my labels to look the same as the formulas in the text. — evf, May 12 '13 at 02:11
I'm sure you'll get used to it quickly, but to start with I would advocate a little hesitation before extrapolating your experience with other languages to Mathematica, because despite many superficial similarities, it really is quite different to almost anything else. A particularly good and reasonably paced reference for the programming side of Mathematica (rather than the mathematical or presentation aspects) is David Wagner's book, now freely available thanks to the hard work and persistence of several of our own community members. — Oleksandr R., May 12 '13 at 02:44
Well, I only expect to understand syntax easily, but not too much else. I know languages have their caveats. A line by line transformation of an OCaml function is often very slow in Haskell due to thunking etc. so I definitely do not expect to pick it up quickly. — evf, May 12 '13 at 02:59
Browse mathematica stack exchange -- once you get to the point where you are answering questions, you'll find it's a great way to learn. — bill s, May 12 '13 at 04:20
You probably have found the following pages in the built in documentation center, but to be sure: random sampling, number theory, linear algebra overview linear algebra guide. — Sjoerd C. de Vries, May 12 '13 at 08:12
Btw there is a 30 day trial, so you could try that first before buying. — Sjoerd C. de Vries, May 12 '13 at 08:15
Some Mathematica-specific caveats: since you know other functional languages, keep in mind that the basic data structure in Mathematica in an array (of expressions), not a linked list. Ways to make things fast are: avoid mutable state, vectorize (as in MATLAB, if you're familiar with it: if a, b are vectors, a*b is much faster than MapThread[Times, {a,b}]), and use built-in functions as much as possible. Learn how to juggle and transform Mathematica expressions (this is done a lot, in complex ways). — Szabolcs, May 12 '13 at 18:54
Make sure you understand that everything is an expression (including code), understand pattern matching and that "function definitions" such as f[x_]:=x^2 are just transformation rules in reality, read a bit about the evaluation sequence. Understand and learn about FullForm, Head, ReplaceAll, Map, Apply, Table (and Do), Select, Cases, Function. Avoid For as much as you can while you're a beginner (there's Do instead). This is pretty dense, but hopefully it'll give you a very quick start (given your past experience with programming languages). Ask when you get stuck. — Szabolcs, May 12 '13 at 19:00
Oh, and make sure you register on this site! (I noticed you didn't, which means you might even lose commenting rights on this question if you clear your cookies.) — Szabolcs, May 12 '13 at 19:03

score 1 · Answer 1 · answered May 12 '13 at 15:36

I found this book to be extremely useful in learning advanced functionalities in Mathematica: "Mathematica Cookbook" of Sal Mangano http://shop.oreilly.com/product/9780596521004.do

It has many examples of matrices and plots uses and several tips from other topics and uses that go beyond the documentation's.

Hope it helps

score 1 · Answer 2 · answered May 12 '13 at 16:38

Where to begin? I'd pick a problem that is easy, but not trivial, and work it out in Mathematica. After a couple of such exercises, you'll be ready to use it in your real work. Since you mention linear algebra, how about something that gets you using EigenSystem or SingularValueDecomposition? Or maybe you have something you'd like to plot? There are great commands like Plot and Plot3D, but for data you would use ListPlot or ListPlot3D. Or stretch out and try GraphPlot or GraphPlot3D, you can visualize most anything. And then there's Manipulate that let's you animate your plot to see how things change with particular parameter values. Surely you have some data somewhere you've always meant to visualize? And there are a zillion functions involving randomness, like RandomVariate for generating random points/vectors/matrices but also symbolic commands that know a surprising amount about different distributions. Hang out here for a while wrestle with some questions... in no time you'll be answering them, and that's the best way to learn. And don't worry, we won't hold that Ph.D. against you.

Where to begin?

2 Answers2