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how to learn proof based mathematics. The goal of the course is to provide you with a detailed overview of the nature of university mathematics including the notions of proof such as proof by induction and proof by contradiction the concept of a map or function as well as the differing types such as the injection surjection and bijection. While m ost students in MAT214 or MAT215-217 have already demonstrated excellence in example-based mathematics courses that emphasize computation learning how to construct proofs and to understand mathematics presented in highly abstract and general form is a new approach and a challenging transition for many students.
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The goal of the course is to provide you with a detailed overview of the nature of university mathematics including the notions of proof such as proof by induction and proof by contradiction the concept of a map or function as well as the differing types such as the injection surjection and bijection. Some educationalists believe that the proof should be abandoned for less formal ways of understanding geometric ideas while others believe that the emphasis of the formal proof is an integral part of learning geometry. A mathematical proof is an inferential argument for a mathematical statement showing that the stated assumptions logically guarantee the conclusionThe argument may use other previously established statements such as theorems.
In principle we try to prove things beyond any doubt at all although in real life people.
However any decrease in proof based lessons is an extreme disservice to our students. Use statements like If A then B to prove that B is true whenever A is true. One way of using the last technique in university mathematics is to write out a formal proof and then erase bits of it. A mathematical proof is an argument which convinces other people that something is true.
