Math 109 – Mathematical Reasoning

This is the course webpage for Math 109: Mathematical Reasoning, Spring 2018, MWF 11-11:50AM lecture, taught by Sean Curry.

Math 109 is a foundational course covering the basic ideas that go into constructing a rigorous mathematical argument. The goal is for students to develop their critical thinking and problem solving abilities, and to be able to write clear and logical mathematical proofs.

Office hours and contact information can be found here.

Announcements

(4-1-18) Welcome to Math 109!

(4-1-18) Lectures are in Pepper Canyon Hall 122.

Lecture Notes

Chapter 1: The Language of Mathematics

Chapter 2: Implications

Chapter 3: Proofs

Chapter 4: Proof by Contradiction

Chapter 5: The Induction Principle

Chapter 6: Set Theory

Chapter 7: Quantifiers

Chapter 8: Functions

Chapter 9: Injections, Surjections and Bijections

Chapter 10: Counting

Chapter 11: Properties of Finite Sets

Chapter 12: Counting Functions and Subsets

Chapter 13: Number Systems (Rationals and Reals)

Chapter 14: Counting Infinite Sets

Chapter 15: The Division Theorem

Chapter 16: The Euclidean Algorithm

Chapter 17: Consequences of the Euclidean Algorithm

Chapter 18: Linear Diophantine Equations

Chapter 19: Congruence of Integers

Chapter 22: Equivalence Relations