# CSE 261 Discrete Structures Total Credits (3)

**Instructors:**

Xiaolei Huang, Shahida Parvez (Spring 2016)

**Current Catalog Description**

Topics in discrete structures chosen for their applicability to computer science and engineering. Sets, propositions, induction, recursion, combinatorics; binary relations and functions; ordering, lattices and Boolean algebra; graphs and trees; groups and homomorphisms. Various applications. Prerequisite:MATH 21 or MATH 31 or MATH 51 or MATH 76

**Textbook**

Kenneth H. Rosen, "Discrete Mathematics and its Applications", 7th Ed., McGraw-Hill, 2011, ISBN 978-0073383095

**COURSE OUTCOMES:**

**Students will:**

- Know how to think logically and mathematically
- Have the ability to construct formal proofs in propositional and predicate logic
- Have the ability to judge the validity of arguments
- Have the ability to construct algorithms
- Have the ability to assess the complexity of algoithms
- Have the ability to use abstract structures to represent discrete objects and their interrelationships
- Have the abiltiy to model using sets, functions, relations, trees, and graphs.

**RELATIONSHIP BETWEEN COURSE OUTCOMES AND STUDENT ENABLED CHARACTERISTICS:**

**CSE 261 substantially supports the following student enabled characteristics:**

**A.** An abiltiy to apply knowledge of computing and mathematics appropriate to the discipline

**Prerequisites by Topic:**

- Math 21/ Calculus 1
- Functions and graphs
- Limits and continuity
- Derivative, differential, and applications
- Indefinite and definite integrals
- Trigonometric, logarithmic, exponential, and hyperbolic functions
- Growth and decay

**Major Topics Covered in the Course**

- Propositional Logic
- Logical Equivalences
- Quantifiers and Predicate Logic
- Rules of Inference
- Varieties of Formal Proofs
- Proof Methods and Strategies
- Sets and Set Operations
- Functions
- Sequences
- Summations
- Matrices
- Algorithms
- Growth of Functions -Big O, Big Omega, Big Theta
- Complexity of Algorithms
- Integers and Division
- Prime Numbers and Euclidean Algorithm for GCD
- Applications of Number Theory
- Emnumerations
- Permutations and combinations
- Mathematical Induction
- Recursive Definitions and Algorithms
- Relations and their Properties
- Graphs
- Trees

**Assessment Plan for the Course**

The students are given 10 medium-length homework assignments, two one-hour and fifteen minute tests, and a three-hour final examination. Each homework assignment typically covers two topics, and each test has seven questions. The final examination typically has eighteen questions and covers the whole range of topics. The performance of each student on each assignment and test and the final is rigorously tracked. Mean scores are computed for each assignment.

**How Data in the Course are Used to Assess Program Outcomes:(unless adequately already in the assessment discussion under Criterion 4)**

Each semester I include the above data from the assessment plan for the course in my self-assessment of the course. This report is reviewed by the Curriculum Committee of the CSE Department.