***This is a course guideline. Students should contact instructor for the updated information on current course syllabus, textbooks, and course content***
Prerequisites: MATH 2331
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 ED. ISBN: 9781259676512)
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*
Chapter 8: Advanced Counting Techniques
- 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
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