MATH145 Lecture Notes - Modus Tollens, Westron, Mathematical Logic

• School: University of Waterloo
• Department: Mathematics
• Course: MATH145
• Professor: Barry Mc Clinchey

Document Summary

In this course, we are going to take a rigorous approach to some topics in number theory and algebra. This means that rather than simply asserting mathematical statements as facts, we will attempt whenever possible, to pro- vide proofs of the validity of these statements. To do so, we will begin with a set of notions and statements that we will take as being given. For example, we will assume the basic notions of set theory and the algebraic and arithmetic properties of the natural numbers, the integers, the rational numbers and the real numbers. We will introduce as axioms some of the perhaps less well-known properties of these objects such as the principle of mathematical induction for the natural numbers. We will begin with a very brief, and admittedly incom- plete, introduction to the formalities of mathematical logic and to the rules of inference that we will use in constructing our proofs.