This course is designed to prepare math, computer science, and engineering majors for a

background in abstraction, notation, and critical thinking for the mathematics most directly

related to computer science. Topics include: logic, relations, functions, basic set theory,

countability and counting arguments, proof techniques, mathematical induction, combinatorics,

discrete probability, recursion, sequence and recurrence, elementary number theory, graph

theory, and mathematical proof techniques.

**Prerequisite:** MATH 2313 or 2413 Calculus I

**Learning Outcomes**Upon successful completion of this course, students will:

- Construct mathematical arguments using logical connectives and quantifiers.
- Verify the correctness of an argument using propositional and predicate logic and truth

tables. - Demonstrate the ability to solve problems using counting techniques and combinatorics in

the context of discrete probability. 4. Solve problems involving recurrence relations and

generating functions. - Use graphs and trees as tools to visualize and simplify situations.
- Perform operations on discrete structures such as sets, functions, relations, and sequences.
- Construct proofs using direct proof, proof by contraposition, proof by contradiction, proof by

cases, and mathematical induction. - Apply algorithms and use definitions to solve problems to prove statements in elementary

number theory.

**Required Reading**

“Discrete Mathematics and Its Applications” by Kenneth Rosen, McGraw Hill, 8th edition

**Recommended Reading**

1. Schaum’s Outline of Discrete Mathematics, Third Edition (Schaum’s Outlines) 3rd Edition by

Seymour Lipschutz (Author)

2. Discrete Mathematics: An Open Introduction

By Oscar Levin (Author)

3. Introductory Discrete Mathematics by V. K. Balakrishnan

4. Mathematical Maturity via Discrete Mathematics (Dover Books on Mathematics)

by Vadim Ponomarenko (Author)

List of discussion/lecture topics

1: The Foundations: Logic and Proofs

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

3: Algorithms

4: Number Theory and Cryptography

5: Induction and Recursion

6: Counting

7: Discrete Probability

8: Advanced Counting Techniques

9: Relations

10: Graphs

11: Trees

12: Boolean Algebra

13: Modeling Computation

The ADA of 1990 provides civil rights protection for individual with disabilities. It guarantees equal

opportunities for “qualified individuals” with disabilities in all public facilities, educational programs,

activities, services and benefits. The ADA upholds and maintains compliance standards to ensure

institutions of higher education policies, procedures and practices are non-discriminatory. Students

needing academic accommodations should contact the Office of Disability Services at 713-313-7691