1 Review of Counting &Probability Basics

    1.1 Introduction

    1.2 Basic Counting Techniques

    1.3 Basic Probability Techniques

    1.4 Expected Value

    1.5 Pascal's Triangle and the Binomial Theorem

    1.6 Summation Notation

    1.7 Summary

2 sets and Logic

    2.1 Introduction

    2.3 Operations on Sets

    2.4 Truth and Logic

    2.5 Quantifiers

    2.6 Summary

3 A Piece of PIE

    3.1 Introduction

    3.2 PIE With 2 Properties

    3.3 PIE With 3 Properties

    3.4 Counting Problems With PIE

    3.5 PIE With Many Properties…

    3.6 Counting Items With More Than 1 of Something

    3.7 Some Harder PIE Problems

    3.8 Summary

4 Constructive Counting and 1-1 Correspondences

    4.1 Introduction

    4.2 Some Basic Problems

    4.3 Harder Constructive Counting Problems

    4.4 1-1Correspondence Basics

    4.5 More Complicated 1-1 Corespondences

    4.6 Clever 1-1 Correspondences

    4.7 Summary

5 The Pigeonhole Principle

    5.2 It's Just Common Sense!

    5.3 Basic Pigeonhole Problems

    5.4 More Advanced Pigeonhole Problems

    5.5 Summary

6 constructive Expectation

    6.1 Introduction

    6.2 Basic Examples,

    6.3 Summing Expectations Constructively

    6.4 A Coat With Many Patches(Reprise)

    6.5 Summary

7 Distributions

    7.1 Introduction

    7.2 Basic Distributions

    7.3 Distributions With Extra Conditions

    7.4 More Complicated Distribution Problems 

    7.5 Summary

8 Mathematical Induction

9 Fibonacci Numbers

    9.1 Introduction

    9.2 A Motivating Problem

    9.3 Some Fibonacci Problems

    9.4 A Formula for the Fibonacci Numbers

    9.5 Summary

10 Recursion

    10.1 Introduction

    10.2 Examples of Recursions

    10.3 Linear Recurrences

    10.4 A Hard Recursion Problem

    10.5 Problems Involving Catalan Numbers

    10.6 Formulas for the Catalan Numbers

11 Conditional Probability

    11.1 Introduction

    11.2 Basic Examples of Conditional Probability

    11.3 Some Definitions and Notation

    11.4 Harder Examples

    11.5 Let's Make a Deal!

    11.6 Summary

12 Combinatorial ldentities

    12.1 Introduction,

    12.2 Basic Identities

    12.3 More Identities

    12.4 Summary

13 Events With States

    13.1 Introduction

    13.2 State Diagrams and Random Walks

    13.3 Events With Infinite States

    13.4 Two-player Strategy Games

    13.5 Summary

14 Generating Func ions

    14.1 Introduction

    14.2 Basic examples of Generating Functions

    14.3 The Binomial Theorem(as a Generating Function)

    14.4 Distributions (as Generating Functions)

    14.5 The Generating Function for Partitions

    14.6 The Generating Function for the Fibonacci Numbers

    14.7 Summary

15 Graph Theory

    15.1 Introduction

    15.2 Definitions

    15.3 Basic Properties of Graphs

    15.4 Cycles and Paths

    15.5 Planar Graphs

16 Challenge Problems