## ECEN 2703 - Discrete Mathematics for Computer Engineers

Catalog Data ECEN 2703 (3). Discrete Mathematics for Computer Engineers. Emphasizes elements of discrete mathematics appropriate for computer engineering. Topics: Logic, proof techniques, algorithms, complexity, relations, and graph theory.
Credits and Design 3 credit hours. Required core course for ECE program, elective course for EE program.
Prerequisite(s) APPM 1360, Calculus 2 for Engineers
ECEN 1030, C Programming for EE/ECE (or CSCI 1300)
Corequisite(s) None.
Instructor(s) Aaron Bradley, Jeremy Siek, Fabio Somenzi.
Textbook Douglas E. Ensley and J. Winston Crawley, Discrete Mathematics, Mathematical Reasoning and Proof with Puzzles, Patterns, and Games, Wiley, 2006, ISBN-13 978-0-471-47602-3.

Course Objectives For students to:
1. To understand how to think and write about mathematics, logic, and numbers.
2. To appreciate the power of abstract mathematics through the study of sets and functions.
3. To understand and be able to apply the connections between combinatorics, counting, and probability.
Learning Outcomes After taking this course students will be able to recognize and use the following concepts, ideas, and/or tools:
1. Sets, logic, functions, and proofs, including induction, recursive definitions, relations, the pigeonhole principle, boolean algebra, and the growth of functions.
2. Combinatorics, counting, and algorithms, including combinations, permutations, probability of discrete events, and expected value.
3. Graphs and trees, including Eulerian and Hamiltonian paths, shortest paths, minimum spanning trees, proofs about graphs and trees, isomorphic graphs, planar graphs, connections to matrices and relations, binary trees.
Student Outcomes
 3a 3b 3c 3d 3e 3f 3g1 3g2 3h 3i 3j 3k Math/Sci Exper-iments Design Teams EngrProblems Respon-sibility Oral Written Engr SolnsImpact LLLearning Contem-porary Tools H L
Topics Covered
1. Overview of discrete mathematics
2. Propositional logic and truth tables
3. Predicate logic and valid arguments (proofs)
4. Induction
5. Pigeonhole principle
6. Modular arithmetic
7. Sets, element-wise proofs, and Boolean algebra
8. Functions and relations
9. Counting, combinations, binomial theorem
10. Permutations, binary sequences, recursive counting
11. Probability, expected value
12. Graphs, paths, connectivity, trees
13. Graph algorithms such as breadth-first search, minimum spanning tree
14. Graph isomorphism, planar graphs
15. Connection between graphs, relations, and matrices
16. Graph representations of games
17. Binary trees

Last revised: 05-17-11, PM, ARP.