Yegge's Math Site

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Chapter 1 : Speaking Mathematically

1.1 : Variables

1.2 : The Language of Sets

1.3 : The Language of Functions and Relations

Chapter 2 : The Logic of Compound Statements

2.1 : Logical Forms and Logical Equivalences

2.2 : Conditional Statements

2.3 : Valid and Invalid Arguments

2.4 : Digital Logic Circuits

Chapter 3 : The Logic of Quantified Statements

3.1 : Predicates and Quantified Statements I

3.2 : Predicates and Quantified Statements II

3.3 : Statements with Multiple Quantifiers

3.4 : Arguments with Quantified Statements

Chapter 4 : Elementary Number Theory and Methods of Proof

4.1 : Direct Proof and Counterexample I - Introduction

4.2 : Direct Proof and Counterexample II - Rational Numbers

4.3 : Direct Proof and Counterexample III - Divisibility

4.4 : Direct Proof and Counterexample IV - Division into Cases and the Quotient-Remainder Theorem

4.6 : Indirect Argument - Contradiction and Contraposition

4.8 : Algorithms

Chapter 5 : Sequences, Mathematical Induction, and Recursion

5.1 : Sequences

5.2 : Proof by Mathematical Induction

5.6 : Defining Sequences Recursively

5.7 : Solving Recurrence Relations by Iteration

Chapter 6 : Set Theory

6.1 : Set Theory - Definitions and the Element Method of Proof

6.2 : Properties of Sets

Chapter 7 : Functions

7.1 : Functions Defined on General Sets

Chapter 9 : Counting and Probability

9.1 : Introduction to Counting and Probability

9.2 : Possibility Trees and the Multiplication Rule

9.3 : Counting Elements of Disjoint Sets - The Addition Rule

9.4 : The Pigeonhole Principle

Chapter 10 : Graphs and Trees

10.1 : Definitions and Basic Properties

10.2 : Trails, Paths, and Circuits

10.3 : Matrix Representations

10.7 : Spanning Trees and Shortest Path

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