*edit Even though there are already answers to my question, I appreciate anyone that offers their advice!
I am not sure if this is the right place to ask this but I usually ask for help here. I am a computer science major currently taking a calculus 2 class. I am able to do the problems presented in class from looking at examples of similar problems and understand concepts presented. But when it comes to sitting down with the textbook and reading various proofs I have a very hard time understanding them. I have spent hours searching online for different explanations on a particular proof and still do not fully understand it. I have also asked about this proof on this website. I know I can pass Calculus 2 without understanding the proofs but part of me wants to know why this works and how.
Are math proofs important in Computer Science?
After spending hours trying to understand a proof without success, what am I doing wrong? Can anyone offer any advice?
Best Answer
Yes, proofs are absolutely important in computer science. They are of integral importance in topics of theoretical computer science - mathematical logic, graph theory, automata theory, computability theory, complexity theory, etc.
They are also important, though less directly, in your more 'applied' or practical CS: techniques for proving theorems and the structured, logically rigorous thinking that comes with practice in proving theorems is going to be very beneficial for your ability to examine your code, and 'prove' that it works.
Moreover, even if you're not so interested in theoretical CS, if you wish to become a truly good programmer, you will need to know math at the level of fairly complicated proofs. At the very minimum, you will need a good understanding of algorithms and complexity theory, the study of which is quite heavy in proving theorems.
The good thing is that Calculus 2 is not really an introduction to proof-based mathematics. Your performance in Calculus 2 should not intimidate you with regard to your career as a programmer. You may have encountered epsilon-delta proofs. They are confusing, and in my experience, not a very good introduction to proofs at all. You should take some introductory classes to real analysis and linear algebra to really get exposed to proof-based mathematics, and you should read Daniel Velleman's How to Prove It to get acquainted with reading and writing proofs.