Ask HN: How to best acquire theoretical computer science knowledge?

IamA graduate student in theoretical computer science.

I don't know that I agree with the poster above with respect to:

"a top school would require you to study a bunch of mathematics to gain a certain level of rigor of your thinking"

Most good schools require only two courses in "pure theory": first an introduction to discrete mathematics, where you learn about logic and how to prove stuff, a smattering of number theory/crypto, graph theory, probability, and automata theory; second an algorithms course that teaches you to analyse and construct algorithms according to certain design methods. Together this is really only a year of mathematics, and both courses are quite fun.

Note that discrete mathematics as taught by a good CS program is NOTHING like the math you learned in high school or elementary school, it teaches you to think creatively about mathematical structures and then justify that creativity with logic.

If you're already a developer, you'll probably have a bunch of latent structures hanging around in your brain that will let you have an easy/fun time with the material in these two courses. I suggest that you study discrete mathematics and algorithms in depth, to the level of some decent undergrad course on each. Learning this material will give your thinking the sort of quantitative/logical "edge" you might want -- these two courses contain the basic mathematical tools common to much of computer science. I do agree with the post above that they are not the most practical things in terms of everyday engineering, though.

Addendum: if you find that you really enjoy the mathematical angle and you think machine learning is cool, also learn linear algebra, because a bunch of machine learning theory and implementation relies on linear algebraic algorithms and concepts. Linear algebra actually would be practical to know if you ever do anything with data analysis.

>It depends on how you learn. Some people will recommend Coursera et al., which are great. I tried some Coursera courses, but found that I found the pace too slow and became bored quickly.

You can watch the lectures at 2x speed. ;)

You might like to try the old "go down the stack" process as a first exercise then. There was a post about it recently on here. A Web app developer who knows a lot about things work right down to the metal is a lot more valuable than one who doesn't.

How do the processes behind your webapps work? Why or why can't your app support 10,000 clients hitting it at once? What's happening at the HTTP level? The TCP/IP level? Just understanding some of the algorithms behind routing and TCP congestion avoidance could give a ton of food for thought, still get you into learning algorithms, notation, and reading CS papers, but still be more directly beneficial to the day job. I wish you luck however you end up approaching it! :-) The only bit I want to repeat is take a lot of notes.. do blog posts, write articles.. anything to ensure you retain that knowledge because it's so easily lost as you get older.

In answer to the first part of the question (how to get more theoretical CS knowledge), I studied an extremely theoretical degree and the materials are online to dig through - if I were to self-teach now, I'd start at the final year's course list (http://www.cl.cam.ac.uk/teaching/1314/part3.html) and work backwards to chart a path to the modules that sounded most interesting.

In terms of "taking knowledge to the next level", though, it could mean anything from you wish you knew what red-black trees and big-O notation were, to you'd love to be able to design your own programming language and write a compiler, to you wish you could administer a Linux box. I would actually suggest the best approach here is to find someone with the job you want and talk with them 1:1 to figure out where your knowledge could be most improved.

Also, for Coursera, etc, there are local study groups at places like Hacker Dojo you could join to get some of the benefits of college without the expense.

This is the core of a CS degree, each one is class, sometimes multiple classes that go into more detail. All interview questions will basically only cover these topics.

1. Algorithms & Data Structures 2. Baremetal Hardware. ASM, goes into the design of a physical cpu with ALUs, etc. Sometimes you make your own basic CPU. I suggest using a course with ARM ASM, simpler than x86 ASM.

3. Operating Systems & Multithreading Theory. You usually do a bunch of C language work here. Maybe combine it with a project on an ardunio or similar.

4. Discrete Mathematics

5. Databases

6. (Optional) Compilers. Write your own compiler, do this after the ASM course.

7. (Optional) Artificial Intelligence. Learn cool things such as machine learning. AI can be very statistical at times, so I suggest adding a Statistics & Probability course to supplement. Statistics is used a lot in business, so it's useful to know for life in general.

8. (Optional) Computer Graphics, using OpenGL!

On top of that I suggest you learn a functional language like Clojure or Haskell. Or both of them. Also learn a language where you have to do memory management and deal with pointers (like C, C++, Objective-C) if you don't include it in your Operating Systems course. After that you can basically do anything in software. Any new language and platform will be just covering concepts you already understand at that point, so you'll be able to learn them extremely quickly.