MATH 201-01, Transition to Advanced Mathematics, Fall 2011

Abstract

This course is an introduction to formal, proof-based mathematics. As you go on in mathematics, you will find that you will spend considerably more of your time learning to prove results rather than applying results to perform computations. This course will prepare you for these activities, introducing different styles of proof as well as the fundamental notions of mathematics such as sets, rules of logic, inference, relations, and functions. We will learn to read and write mathematical proofs, carefully considering the structures of proofs as well as the method of ``finding a proof.” Unlike mathematics with an emphasis on computation, proving theorems is a creative process with no recipe for a solution. Many strong mathematics students express distaste for this style of mathematics early in their education. However, this frequently changes once they are taught how to go about writing proofs. We will consider different approaches to this process as well as the important considerations in evaluating a proof. In addition, we will learn about the mathematical landscape, including understanding the different general areas of mathematics, the history of mathematics, and its culture.