MATH 3336 - Discrete Mathematics - University of Houston

# MATH 3336 - 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 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)

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

CSD Accommodations:

Accommodation Forms: Students seeking academic adjustments/auxiliary aids must, in a timely manner (usually at the beginning of the semester), provide their instructor with a current Student Accommodation Form (SAF) (paper copy or online version, as appropriate) from the CSD office before an approved accommodation can be implemented.

Details of this policy, and the corresponding responsibilities of the student are outlined in The Student Academic Adjustments/Auxiliary Aids Policy (01.D.09) document under [STEP 4: Student Submission (5.4.1 & 5.4.2), Page 6]. For more information please visit the Center for Students with Disabilities Student Resources page.

Additionally, if a student is requesting a (CSD approved) testing accommodation, then the student will also complete a Request for Individualized Testing Accommodations (RITA) paper form to arrange for tests to be administered at the CSD office. CSD suggests that the student meet with their instructor during office hours and/or make an appointment to complete the RITA form to ensure confidentiality.

*Note: RITA forms must be completed at least 48 hours in advance of the original test date. Please consult your counselor ahead of time to ensure that your tests are scheduled in a timely manner. Please keep in mind that if you run over the agreed upon time limit for your exam, you will be penalized in proportion to the amount of extra time taken.

UH CAPS

Counseling and Psychological Services (CAPS) can help students who are having difficulties managing stress, adjusting to college, or feeling sad and hopeless. You can reach (CAPS) by calling 713-743-5454 during and after business hours for routine appointments or if you or someone you know is in crisis. No appointment is necessary for the "Let's Talk" program, a drop-in consultation service at convenient locations and hours around campus.