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

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# Course Website

# Textbook

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

# Lecture Notes

1. The Foundations: Logic and Proofs

1.2 Applications of Propositional Logic

1.3 Propositional Equivalences

1.4 Predicates and Quantifiers

1.8 Proof Methods and Strategy

2. Basic Structures: Sets, Functions, Sequences, Sums, and Matrices

3. Algorithms

4. Number Theory and Cryptography

4.1 Divisibility and Modular Arithmetic

4.2 Integer Representations and Algorithms

4.3 Primes and Greatest Common Divisors

5. Induction and Recursion

5.2 Strong Induction and Well-Ordering

5.3 Recursive Deﬁnitions and Structural Induction

6. Counting

6.3 Permutations and Combinations

6.4 Binomial Coefficients and Identities

6.5 Generalized Permutations and Combinations

7. Discrete Probability

7.1 An Introduction to Discrete Probability

9. Relations

9.1 Relations and Their Properties

10. Graphs

10.2 Graph Terminology and Special Types of Graphs

10.3 Representing Graphs and Graph Isomorphism

11. Trees

# 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 2011 - Exam 1 (Exam, Solution)

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