Core unitUnit 1 of 24

Introduction to Proofs

Introduction to Proofs lays the foundation for higher mathematics by teaching the language, logic, and reasoning used throughout the discipline. This unit is originally Introduction to Mathematical Proofs (MAT102) by instructor: Dr. Mike Pawliuk for the University of Toronto Mississauga.

Difficulty

Beginner

Estimated study

123 hours

Duration

Self-paced

Modules

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About this unit

Unit overview

This unit develops the language and habits required for rigorous higher mathematics. You will work with logic, sets, functions and relations while learning to construct, critique and communicate direct, contrapositive, contradiction and induction proofs.

Learning outcomes

What you’ll learn

01Translate mathematical statements using logic and quantifiers
02Construct direct, contrapositive and contradiction proofs
03Use mathematical and strong induction
04Write clear proofs involving sets, functions, relations and number theory

Introduction to Proofs

Module 1 — Entering University Mathematics

Module 2 — Mathematical language and logic

Module 3 — Fundamental proof strategies

Module 4 — Sets

Module 5 — Functions and relations

Module 6 — Inequalities and mathematical arguments

Module 7 — Induction and recursion

Module 8 — Advanced function concepts

Module 9 — Cardinality and infinity

Module 10 — Elementary number theory

Unit overview

What you’ll learn