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how to learn proofs in mathematics. There are also a number of books which help students understand the basic structure of proofs. You will learn a lot about constructing proofs from studying geometry particularly with regards to projective geometry in the plane and geometry of the sphere.
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This person can help you learn to read and write mathematical statements and they can give you tips on how to approach certain standard proof practices. In highschool or at GCSE students are often taught about triangular geometry and an introductory university module in Geometry will formalise these concepts ultimately with the idea of gaining practice understanding and writing geometric proofs. Try to figure out how to get from the givens to the prove conclusion with a plain English commonsense argument before you worry about how to write the formal two-column proof.
Once youve read a theorem and its proof you can go back and ask some questions to help synthesize your understanding.
As the class advanced we learned increasingly advanced techniques for building these proofs. Write down the statements but not the proofs. The easiest structure for a proof to use is to assume the hypotheses and combine them using previous results to reach the conclusion through a chain of implications. This is KEY What mathematical raw materials are used in the proof.
