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

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Module 8 of 10lesson

Module 8 — Advanced function concepts

Core competencies: injectivity; surjectivity; bijectivity; inverses; composition; proving that functions possess these properties.

Lecture 1 of 6

Intro to Proofs - Injections Surjections Bijections - part 1/2

Resource summary

This is a video for a university course about Introduction to Mathematical Proofs. Topics covered: 1. Motivation for Injections, surjections and bijections. 2. Definitions of these things. 3. Examples, including arrow notation. This was originally made for the University of Toronto Mississauga in Summer 2020, for MAT102.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/

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 8 — Advanced function concepts

Intro to Proofs - Injections Surjections Bijections - part 1/2

Video lectures