Ask HN: Learn Math the Hard Way

#1

Post by nsomaru » Sun, Jul 08, 2012, 12:05 PM UTC

I am looking to teach myself Mathematics, mainly to improve my thinking processes and learn more about the basis for CS based topics like algorithms and proofs, and other practical applications.

Suggestions for resources? (textbooks, videos, etc)

Re: Ask HN: Learn Math the Hard Way

#2

Post by 1331 » Sun, Jul 08, 2012, 12:32 PM UTC

_Concrete Mathematics_ [1] is a good book that is fun to work through. The book can be considered an introduction/prerequisite to Knuth's _The Art of Computer Programming_ series [2], which contains much mathematics. If you would like a book that is not so difficult, _Introduction to Algorithms_ [3] (aka "CLRS") is also highly recommended.

[1] http://www.amazon.com/dp/0201558025/

[2] http://www.amazon.com/dp/0321751043/

[3] http://www.amazon.com/dp/0262033844/

Re: Ask HN: Learn Math the Hard Way

#3

Post by Arun2009 » Sun, Jul 08, 2012, 1:15 PM UTC

In addition to Concrete Mathematics by Knuth, which contains a lot of Mathematical tools and techniques useful in areas of Computer Science, I'd recommend the following to learn how good problem solvers approach Mathematics:

1. The Art and Craft of Problem Solving by Paul Zeitz.

2. How to Solve It by George Polya.

I'd also recommend learning any of the competition Mathematics topics like number theory, combinatorics or geometry as base material to improve your problem solving skills. I have also found the Schaum's series on Combinatorics and Graph Theory concise and useful.

Re: Ask HN: Learn Math the Hard Way

#4

Post by verganileonardo » Sun, Jul 08, 2012, 1:16 PM UTC

I have a business background and use Project Euler to evolve my programming, math and problem solving skills. :)

projecteuler.net

Re: Ask HN: Learn Math the Hard Way

#5

Post by madmanwalking » Sun, Jul 08, 2012, 1:18 PM UTC

The Khan academy (www.khanacademy.org) has plenty of videos and exercises, and if you're looking more at the CS side of things udacity.com runs a few online courses looking at algorithms, discrete maths and the like.

Re: Ask HN: Learn Math the Hard Way

#6

Post by tel » Sun, Jul 08, 2012, 1:21 PM UTC

I'm going to second Arun2009's recommendation for How to Solve It by Polya. And then I'm going to recommend Haskell. I recently realized how much my understand of set theory improved and was solidified purely by programming Haskell a lot.

Re: Ask HN: Learn Math the Hard Way

#7

Post by nimeshneema » Sun, Jul 08, 2012, 1:24 PM UTC

The best text-book I can suggest for you is: "How to Think About Algorithms - Loop Invariants and Recursion" By Jeff Edmonds.

It takes you through all the relevant mathematics required to learn about basics of CS based topics you are looking for (algorithms, proofs and other practical applications).

It also acts as a good primer for learning basic Computer Algorithms. The USP of book is it's noob friendly and I think perfectly suited to your needs.

Check it out here: http://www.amazon.com/Think-About-Algorithms-Jeff-Edmonds/dp...

Re: Ask HN: Learn Math the Hard Way

#8

Post by alex-g » Sun, Jul 08, 2012, 1:26 PM UTC

You might like "To Mock a Mockingbird" by Raymond Smullyan. It's a book of logic puzzles with a focus on combinatory logic (a model of computation related to the lambda calculus). Aside from the logic/math/CS nature of the content, the progression of the exercises should help with mathematical-style reasoning in general.

Re: Ask HN: Learn Math the Hard Way

#9

Post by jcdreads » Sun, Jul 08, 2012, 1:37 PM UTC

The Project Euler problems might be right up your alley. They are little programming exercises that start easy and rapidly become harder. Along the way you figure out enough math to make the programming easier, or at least enough to make better algorithms. The forums are enormously helpful. http://projecteuler.net/

Re: Ask HN: Learn Math the Hard Way

#10

Post by ether » Sun, Jul 08, 2012, 1:42 PM UTC

I don't think you need to learn really hard core math to do CS. In my experience, the one most important "genre" of math was discrete mathematics. My textbook was Elements of Discrete Mathematics, and I think it was a really great intro: http://www.amazon.com/Elements-Discrete-Mathematics-Computer...