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.

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Beginner

Estimated study

123 hours

Duration

Self-paced

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Module 3 of 10lesson

Module 3 — Fundamental proof strategies

Core competencies: direct proof; proof by contrapositive; proof by contradiction; selecting an appropriate proof method; writing a logically ordered argument.

Lecture 1 of 3

Intro to Proofs - Proof Strategies: Direct and Contrapositive

Resource summary

This is the intro video for a university course about Introduction to Mathematical Proofs. Topics covered: 1. Direct Proof 2. Proof by contrapositive 3. Proof of Equivalences This was originally made for the University of Toronto Mississauga in Summer 2020, for MAT102. All material for the course can be found at:https://mikepawliuk.ca/introduction-to-proofs/

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Quiz 1

practice

Solutions to Quiz 1

practice

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

Module 3 — Fundamental proof strategies

Intro to Proofs - Proof Strategies: Direct and Contrapositive

Video lectures

Resources