|Jan19-07, 10:12 AM||#1|
Need help learning to construct proofs
so, I am in my first upper level math course beyond required calculus and the introductory linear algebra class. I don't know if it's just a great jump or if I slept through something, but suddenly everything is all about doing proofs. I'm okay with that, and I think it's fabulous because proofs seem to yield deeper conceptual understanding, but I have no experience whatsoever with writing/constructing proofs. I can memorize axioms and whatnot, but then how do I get started? anyone have any good texts on proof writing or know of any resources that could help me? I'm clueless here!
I don't know if it makes a difference (with regards to what kind of proof I should study) but the class is Theory of Linear Algebra. I love the topic, just have no idea how to prove things for every case...
|Jan19-07, 10:58 AM||#2|
yes there is a good book called Problem Solving by "C" Larson. Not sure if the C is the write letter.
the main way that I learned how to do proofs was to cram allt he theorems on one page. granted that you actually have to understand these theorems.
The straight forward method is to just rearrange your problem by regurgitating each step via one the theorems that you have learned up till that point.
Larson's Book outlines steps you should take to rearranging a given problem in such as looking for a counterexample(contradiction), recursion(can't remember the proper term...oh induction), look for symmetry and parity.
At the beginning of it all though try to define your problem based on all the previous defintions that you have learned.
...onc eyou become more accustomed to knowing some theorems and techniques then you can skip the majority of steps.
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