Math 240 – Discrete Math

Notes on Math 240: Introduction to Discrete Mathematics @ University of Wisconsin-Madison

Published

January 30, 2018

Modified

May 24, 2019

Notes on Math 240: Introduction to Discrete Mathematics @University of Wisconsin-Madison Your comments and criticism are greatly welcomed.

Course Website

Textbook

Kenneth H. Rosen, Discrete Mathematics and its Applications, seventh Edition

Lecture Slides

Chapter 00	Chapter 06
Chapter 01 Part 1	Chapter 07
Chapter 01 Part 2	Chapter 08
Chapter 01 Part 3	Chapter 09
Chapter 02	Chapter 10
Chapter 03	Chapter 11
Chapter 04	Chapter 12
Chapter 05	Chapter 13

Past Exams

Spring 2002 - Exam 1

Spring 2002 - Exam 2

Spring 2002 - Final

Spring 2005 - Exam 1

Spring 2005 - Exam 2

Spring 2005 - Final

Spring 2008 - Exam 1

Spring 2008 - Exam 2

Spring 2008 - Exam 3

Spring 2008 - Final

Spring 2011 - Exam 1 (Exam, Solution)

Spring 2011 - Exam 2 (Part I, Part II, Solution)

Spring 2011 - Final (Exam, Solution)

Spring 2015 - Exam 2

Spring 2016 - Exam 2

Lecture notes

0. Introductory Lecture

1.1 Propositional Logic

1.2 Applications of Propositional Logic

1.3 Propositional Equivalences

1.4 Predicates and Quantifiers

1.5 Nested Quantifiers

1.6 Rules of Inference

1.7 Introduction to Proofs

1.8 Proof Methods and Strategy

2.1 Sets

2.2 Set Operations

2.3 Functions

2.4 Sequences and Summations

2.5 Cardinality of Sets

2.6 Matrices

3.1 Algorithms

3.2 The Growth of Functions

3.3 Complexity of Algorithms

4.1 Divisibility and Modular Arithmetic

4.2 Integer Representations and Algorithms

4.3 Primes and Greatest Common Divisors

4.4 Solving Congruences

5.1 Mathematical Induction

5.2 Strong Induction and Well-Ordering

5.3 Recursive Definitions and Structural Induction

5.4 Recursive Algorithms

6.1 The Basics of Counting

6.2 The Pigeonhole Principle

6.3 Permutations and Combinations

6.5 Generalized Permutations and Combinations

6.4 Binomial Coefficients and Identities

7.1 An Introduction to Discrete Probability

9.1 Relations and Their Properties

9.3 Representing Relations

9.5 Equivalence Relations

9.6 Partial Orderings

10.1 Graphs and Graph Models

10.2 Graph Terminology and Special Types of Graphs

10.3 Representing Graphs and Graph Isomorphism

10.4 Connectivity

11.1 Introduction to Trees