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 9 of 10lesson

Module 9 — Cardinality and infinity

This is more advanced than some introductory proof courses, but it is valuable preparation for analysis, topology and abstract algebra.

Lecture 1 of 8

Intro to Proofs - Cardinality - Intro

Resource summary

This is a video for a university course about Introduction to Mathematical Proofs. Topics covered: 1. Motivation for cardinality 2. Definitions of relative cardinality 3. Basic abstract results about cardinality 4. Cantor-Schroeder-Bernstein theorem This was originally made for the University of Toronto Mississauga in Summer 2020, for MAT102.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 5

practice

Quiz 5 - Solutions

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 9 — Cardinality and infinity

Intro to Proofs - Cardinality - Intro

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