MATH 2305 - Discrete Mathematics - University of Houston

# MATH 2305 - Discrete Mathematics

***This is a course guideline.  Students should contact instructor for the updated information on current course syllabus, textbooks, and course content***

Prerequisites: MATH 2413

Course Description: Topics selected from logic, set theory, combinatorics, and graph theory.

Textbook: Discrete Mathematics and Its Applications, Kenneth H. Rosen , McGraw-Hill Publishing Co.  (Fall 2019 and thereafter: 8th Edition. ISBN: 9781259676512)

Core Material:

Chapter I. The Foundations: Logic and Proofs

• 1.1 Propositional logic
• 1.2 Applications of propositional logic
• 1.3 Propositional equivalence
• 1.4 Predicates and quantifiers
• 1.5 Nested quantifiers
• 1.6 Rules of inferences
• 1.7 Introduction to proofs
• 1.8 Proof methods and strategy

Chapter 2. Basic Structures: Sets, Functions, Sequences, Sums an Matrices

• 2.1 Sets
• 2.2 Set operations
• 2.3 Functions
• 2.4 Sequences and summations

Chapter 3. Algorithms

• 3.1 Algorithms
• 3.2 The growth of functions

Chapter 4: Number Theory and Cryptography

• 4.1 Divisibility and modular arithmetic
• 4.2 Integer representation and algorithms
• 4.3 Primes and greatest common divisors
• 4.4 Solving congruencies
• 4.6 Cryptography*

Chapter 5: Induction and Recursion

• 5.1 Mathematical induction
• 5.2 Strong induction and well-ordering
• 5.3 Recursive definitions and structural induction

Chapter 6: Counting

• 6.1 The basics of counting
• 6.2 The Pigeonhole principle
• 6.3 Permutations and combinations
• 6.5 Generalized permutations and combinations*

• 8.1 Application of recurrence relations
• 8.2 Solving linear recurrence relations (* optional sections, cover as time allows)

Additional material (at least one of the following topics must be included in the syllabus)

• 7. Discrete Probability
• 9. Relations
• 10. Graphs
• 11. Trees
• 12. Boolean Algebra