Course Description
A survey of the fundamental mathematical tools used in computer engineering: sets, relations, and functions; propositional and predicate logic; proof writing strategies, such as direct, contradiction and induction; summations and recurrences; counting and discrete probability; undirected and directed graphs with applications in computer engineering.
Athena Title
Discrete Mathematics for Engr
Equivalent Courses
Not open to students with credit in CSCI 2610, CSCI 2610E
Prerequisite
MATH 1113
Semester Course Offered
Offered spring
Grading System
A - F (Traditional)
Course Objectives
This course presents a survey of those topics in discrete mathematics most relevant to students studying computer engineering. At the end of the semester, all students should be able to do the following: 1. Build truth tables for propositional expressions. 2. Prove properties using a variety of proof strategies, including direct proofs, proofs by contradiction, proofs by cases and inductive proofs. 3. Convert a number from one base to another (e.g., from decimal to binary). 4. Perform arithmetic operations on binary numbers. 5. Use permutations and combinations to count the number of elements in large sets. 6. Apply the pigeonhole principle. 7. Determine conditional probabilities. 8. Determine if a function is an injection, a surjection, a bijection or none of these. 9. Use bijections to prove if a given set is countable. 10. Use diagonalization to prove a given set is uncountable. 11. Given an equivalence relation R over a domain D, partition D into subsets (equivalence classes) according to R.
Topical Outline
Propositional logic Predicate logic Proofs: types of proofs Sets, set logic and set operations Functions Sequences and summations Integer algorithms Modular arithmetic Mathematical induction Counting The pigeonhole principle Permutations and combinations Finite probabilities Relations Using graphs to represent relations
Syllabus
Public CV