MATH 2305 - Discrete Mathematics - University of Houston
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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*

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


Grading: Please consult your instructor's syllabus regarding any and all grading guidelines. 

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