Proofs... and Complex Analysis
I know a lot of you love proofs and for some reason (which is hugely frustrating to me), you all seem to know how to prove statements with ease. I'm currently doing my 3rd (and final) undergraduate year in Mathematics and Geography, but for the life of me I have no clue how to prove statements in Maths! This semester I'm taking two courses in Mathematics, namely Applied Analysis and Complex Analysis. So far I've found AA pretty easy, but CA has been a huge struggle since proofs started entering the fray. I've worked my butt off but still don't seem to be able to prove things. Luckily I'm not the only one who's having trouble which has been reflected by a class average of 40% for the first test, with only 5 of us passing it (I got a "good" mark of 66%).
Is there a course that most people take, before they reach the analysis courses, that shows you how to prove statements or is it something that we as students are supposed to just pick up as we study from year to year? Surely there are a set of tried and trusted techniques that allow people to formulate a solution to a proof easily? I'm just really starting to stress out because our CA course is becoming more and more proof orientated as we go along and I'm able to answer fewer and fewer questions in our tutorials given to us each week.
I managed to get firsts for all my Maths courses in years 1 and 2, but this year it feels like I've hit a brick wall. I'm not a clever guy, I just work really hard at things until I understand them, but going over proofs, especially when they contain epsilons and deltas just baffles my mind completely.
Does anyone have any words of wisdom that would help me out here. Could you recommend any texts that deal with proof solving methods (if any)? Also, could anyone recommend any good texts related to an undergraduate introductory course into Complex Analysis (I have Visual Complex Analysis by Tristan Needham, but a lot of his examples, no matter how visual, do not shed much light on the matter for me)?
Thanks guys, cheers.