So I recently joined university for a BSc in mathematics. I have never been exposed proofs but I have knowledge of algebra, trigonometry, and some differentiation/integration. Now I'm struggling with proofs. I'm having trouble figuring out the best way to write the proofs, since everything seems so random. I don't know where to begin.
After some Googling, I came across some tutorials but they do not help much. I think I lack the basics of proof solving and I think I lack the mathematical language to express what I need. Would anyone experienced have any suggestions for me on where to start and gradually be able to tackle most proofs(contradiction, induction) and I would really appreciate it if you could suggest some great introductory proof-based books which will give me a head start and gradually move to advanced stuff.
Thanks.
Best Answer
Induction is actually pretty easy to teach. You'll get a lot of practice with it in Number Theory, Graph Theory, and Computer Science. Here is a good link for learning how to write a proof by induction: http://www.dreamincode.net/forums/topic/280815-introduction-to-proofs-induction-and-big-o/
As for learning, I'd look at propositional calculus, first order predicate logic, and set theory first. These are the basic tools you'll need to learn math. Linear Algebra and Number Theory are pretty common courses to teach proof writing, if you haven't already had a mathematical fluency type course. With Linear Algebra, make sure to look at materials that talk about vector spaces. A lot of introductory material is more about teaching you how to crunch problems than think about abstract concepts and write proofs.
Number Theory is great for inductive and combinatorial arguments. The material is also familiar and beautiful. You'll see it pop up when you get into Abstract Algebra.