Introduction to Proofs

{| An introductory course from the School of Mathematics
 * bgcolor="#E6CFDD" style="border:1px solid #cfcfcf;padding:1em;padding-top:0.5em;padding-bottom:0em;"| Introduction to Proof and Problem Solving
 * bgcolor="#E6CFDD" style="border:1px solid #cfcfcf;padding:1em;padding-top:0.5em;padding-bottom:0em;"| Introduction to Proof and Problem Solving


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 * bgcolor="#F4E3F3" style="border:1px solid #cfcfcf;padding:1em;padding-top:0.5em;padding-bottom:0em;"|

Course Overview
Students learn the basic concepts and ideas necessary for upper division mathematics courses and techniques of mathematical proof in the context of specific topics. Introduction to sets, relations, elementary mathematical logic, proof by contradiction, mathematical induction, and counting arguments.

Since advanced mathematics courses require students to construct proofs, this class is necessary to study Real Analysis, Abstract Algebra, and beyond.
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Course requirements
The following knowledge is required or desirable on commencement of study of this course:
 * High School Mathematics

Course outline
We're going to follow a number of different sources for this course. First, there is the Wikibooks' Set Theory textbook. We'll also cover material from the Wikibooks' Mathematical Proof textbook. As there are some limitations to those texts, we'll also cover material from outside sources.


 * Introduction to Mathematical Logic
 * Introduction to Sets and Operations on Sets
 * Direct Proof and Proof by Contradiction
 * Mathematical Induction
 * Equivalence Relations and Classes
 * Orderings
 * Functions and Mappings
 * Number Theory and Combinatorial Proofs
 * Countability Arguments

Lecture series

 * Lecture 1 Introduction to Proofs

Assignments
Problem sets will be posted here after a certain number of lectures (to be specified.)

Examinations
The plan is to have two 'midterm' exams and a comprehensive 'final' exam. Exam questions will be based on questions from the problem sets and the lectures.

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