Introduction to Logic and Proof
Revised: September 2020
Course Description
An introduction to the principles of logic and the methods of proof necessary for
the successful study of mathematics. Prerequisites MATH 140 or MATH 153. Three credit
hours.
Student Learning Objectives
By the end of the course, students should be able to:
- Use the principles of logic, mathematical reasoning, and methods of proof writing
to develop proofs for never-before-seen theorems and lemmas;
- Identify the most appropriate proof-writing technique for a given theorem or lemma
based on mathematical setting;
- Demonstrate development in their mathematical writing through practice in communicating
mathematical ideas and arguments, both verbally and orally.
Text
An Introduction to Abstract Mathematics, Robert J. Bond and William J. Keane, Waveland Press 1999.
Grading Procedure
Grading procedures and factors influencing course grade are left to the discretion
of individual instructors, subject to general university policy.
Attendance Policy
Attendance policy is left to the discretion of individual instructors, subject to
general university policy.
Course Outline
- Chapter 1 Mathematical Reasoning
- Section 1.1 Statements
- Section 1.2 Compound Statements
- Section 1.4 Contrapositive and Converse
- Section 2.1 Sets and Subsets
- Section 2.2 Combining Sets
- Section 2.3 Collections of Sets
- Section 3.1 Definitions and Basic Properties
- Section 3.2 Surjective and Injective Functions
- Section 3.3 Composition and Invertible Functions
- Chapter 4 Binary Operations and Relations
- Section 4.1 Binary Operations
- Section 4.2 Equivalence Relations
- Section 5.1 Axioms and Basic Properties (optional)
- Section 5.2 Induction
- Section 5.3 The Division Algorithm and Greatest Common Divisors
- Section 5.4 Prime and Unique Factorization
- Section 5.5 Congruences
Additional topics selected at the instructor’s discretion.