Introduction to Mathematical Proof

Mathematics
By OgbonLab

Where mathematics stops being a vocabulary test and starts being an argument.

Logic, sets, proof techniques, relations, induction, and infinite sets.

8 parts 40 sections Free, browser-native
Start reading → First up: Deductive Reasoning and Logical Connectives

Table of contents

Every section is a working session: text, math, code, interactive widgets. Click any title to jump in.

Part 1: Chapter 1: Sentential Logic

  1. Deductive Reasoning and Logical Connectives
  2. Truth Tables
  3. Variables and Sets
  4. Operations on Sets
  5. The Conditional and Biconditional Connectives

Part 2: Chapter 2: Quantificational Logic

  1. Quantifiers
  2. Equivalences Involving Quantifiers
  3. More Operations on Sets
  4. Bounded Quantifiers and Restricted Domains

Part 3: Chapter 3: Proofs

  1. Proof Strategies
  2. Proofs Involving Negations and Conditionals
  3. Proofs Involving Quantifiers
  4. Proofs Involving Conjunctions and Biconditionals
  5. Proofs Involving Disjunctions
  6. Existence and Uniqueness Proofs
  7. More Examples of Proofs

Part 4: Chapter 4: Relations

  1. Ordered Pairs and Cartesian Products
  2. Relations
  3. More About Relations
  4. Ordering Relations
  5. Equivalence Relations

Part 5: Chapter 5: Functions

  1. Functions
  2. One-to-One and Onto
  3. Inverses of Functions
  4. Closures
  5. Images and Inverse Images

Part 6: Chapter 6: Mathematical Induction

  1. Proof by Mathematical Induction
  2. More Examples of Induction
  3. Recursion
  4. Strong Induction
  5. Closures Again

Part 7: Chapter 7: Number Theory

  1. Greatest Common Divisors
  2. Prime Factorization
  3. Modular Arithmetic
  4. Euler’s Theorem
  5. Public-Key Cryptography

Part 8: Chapter 8: Infinite Sets

  1. Equinumerous Sets
  2. Countable and Uncountable Sets
  3. The Cantor-Schröder-Bernstein Theorem
  4. The Axiom of Choice and Beyond

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