# Math 240

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

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Syllabus

# Textbook

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

# Lecture Notes

0. Introductory Lecture

1. The Foundations: Logic and Proofs

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

2.1 Sets

2.2 Set Operations

2.3 Functions

2.4 Sequences and Summations

2.5 Cardinality of Sets

2.6 Matrices

3. Algorithms

3.1 Algorithms

3.2 The Growth of Functions

3.3 Complexity of 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

4.4 Solving Congruences

5. Induction and Recursion

5.1 Mathematical Induction

5.2 Strong Induction and Well-Ordering

5.3 Recursive Deﬁnitions and Structural Induction

5.4 Recursive Algorithms

6. Counting

6.1 The Basics of Counting

6.2 The Pigeonhole Principle

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

9.3 Representing Relations

9.5 Equivalence Relations

9.6 Partial Orderings

10. Graphs

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. Trees

11.1 Introduction to Trees

# 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 (ExamSolution)

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

Spring 2011 – Final (ExamSolution)

Spring 2015 – Exam 2

Spring 2016 – Exam 2