This course is an introduction to the methods and language of logical thought. We begin with understanding the logical meanings of "and", "or", "if...then" and "not" and with what it means to deduce something logically. We proceed to the logical meanings of "for all" and "there exists". The central part of the course builds on these ideas by developing the student's ability to build a proof of a mathematical assertion. We do direct proofs, proofs by contradiction and proofs by mathematical induction. The goal is for the student to become confident and comfortable when faced with the problem of giving a proof of something. We develop these skills within the elementary theory of numbers (primes, divisibility etc.) and within set theory, the language of mathematics.
This course will be valuable preparation for anyone who plans to pursue any study in which they will need to think logically. It will be indispensable to mathematics or computer science majors, and will be useful to students wanting to apply mathematics or logical methods to the social, natural or management sciences.
The course is not open to students who have taken or are taking any mathematics course (with second digit different from 5) at 3000 or higher level.
The text is "Discrete Mathematics with Applications 2nd ed." by Susanna S. Epp
The final grade will be based on class tests and a final examination.