Learntofish's Blog

A blog about math, physics and computer science

Archive for October, 2009

Improve your programming skills, now!

Posted by Ed on October 27, 2009

Project Euler is a website with over 250 problems. Most of them are of a mathematical type but they are designed in such a way that you need some programming skills to solve them.

Once you’ve registered you can type your solution into a field and get a confirmation about whether it is correct. You will then get access to a forum containing source codes by other users. This is a very interesting feature since it shows how differently a problem can be approached. For example, one solution in C++ had over 20 lines while another one in K had only 1 line.

There is also a rank system depending on how many problems you have solved:
Level 1, Solved: 25-49
Level 2, Solved: 50-99

Level 5, (Expert), Solved: 200-249
Level 6, (Legend), Solved: 250+

So far, I have used Python, C++, Java and Haskell for Project Euler. And my programming skills definitely have improved since then. I learned about techniques like dynamic programming, memoization, using symmetries (for problems involving divisibility), etc. But beware, Project Euler can be addictive :D

Update (October 11, 2010):
Ben Dowling has written excellent articles with a collection of puzzle websites:
10 programming puzzle websites
10 More Puzzle Websites to Sharpen Your Programming Skills
The list goes from Topcoder, Codechef, SPOJ to puzzles for C, Ruby, Prolog and Python.

Here is another nice website with solutions: http://open-cs.net/

Posted in computer science, mathematics | Tagged: , , , | 1 Comment »

How to write Math Proofs

Posted by Ed on October 6, 2009

Proof is the idol before whom the pure mathematician tortures himself.
Sir Arthur Eddington (1882 – 1944), The Nature of the Physical World

The very essence of mathematics is the concept of a proof. But writing one is not so easy. Below is a compilation of notes that describe how to write proofs in mathematics. They are intended for beginners.

PROOF TECHNIQUES

1) Introduction to mathematical arguments (by Michael Hutchings)
http://math.berkeley.edu/~hutching/teach/proofs.pdf

2) How to Write Proofs –
A short tutorial on the basics of mathematical proof writing (by Larry W. Cusick)
http://zimmer.csufresno.edu/~larryc/proofs/proofs.html

3) How to write proofs: a quick guide (by Eugenia Cheng)
http://cheng.staff.shef.ac.uk/proofguide

4) Notes on Methods of Proof (by Peter Williams)
http://www.math.csusb.edu/notes/proofs/pfnot/pfnot.html
Read the rest of this entry »

Posted in mathematics | Tagged: , , , | 2 Comments »