# : Mathematical Foundations for Computer Engineering -- ENEE 641, Fall 2010

## Instructor:

Dr. Uzi Vishkin
Telephone: 301-405-6763
E-mail: last name at umiacs.umd.edu
Office: AVW 2365
Office hours: M 2:00--3:00. By appointment.

E-mail: sbahrami@umd.edu

## Course web site:

www.umiacs.umd.edu/~vishkin/TEACHING/ENEE641-F10/index.html

Homework 1
Homework 2
Homework 3
Homework 4
Homework 5
Homework 6
Homework 7
Homework 8

## Introduction:

The evolving discipline of computer engineering requires increasing mathematical knowledge and sophistication. Electronic design needs efficient computational methods, and its verification a high level of mathematical rigor. More specifically, computer aided design of digital systems and their verification are heavily based on mathematical computational methods and requires profound understanding of their efficiency a nd apparent hardness concepts. Layout, logic, and architectural-level synthesis are almost entirely based on computational techniques. Compilers are playing a dominant role in computing systems in general including the embedded systems area. Compilers must be correct and should be efficiently implemented. Insuring correctness and efficiency require profound mathematical understanding. Communication networks is another electrical and computer engineering domain where the understanding of mathematical computational methods and their efficiency is important.

## Course Goals:

Mathematical modeling, design, analysis, and proof techniques related to computer engineering. Probability, logic, combinatorics, set theory, and graph theory, as they pertain to the design and performance of computer engineering systems. Techniques for the design and analysis of efficient computational methods from graph theory and networks. Understanding of the limits on the efficiency of such computational methods. Translation from mathematical theory to actual programming. The course emphasizes mathematical rigor.

None.

## Topics Prerequisite(s):

Properties of functions and counting principles, relations, equivalence relations, partial orders and related topics, asymptotic notation and recurrences, elementary sorting methods, knowledge of C, and basic calculus.

## Textbook(s)

Introduction to Algorithms, T.H. Cormen, C.E. Leiserson, R.L. Rivest and C. Stein, McGraw-Hill, Third Edition, 2009, ISBN 978-0-262-03384-8.

## Core Topics:

- Growth of functions.
- Propositional and predicate logic.
- Counting and probability.
- State machines and automata.
- Recursion and recursive descriptions.
- Organizations of data.
- Computational methods: Dynamic programming and the greedy approach.
- Graph theory and computational methods.
- Uses of randomization.
- Combinatorial optimization.
- Apparent hardness of problems; practical ways for proving apparent hardness; heuristics and other approaches for coping with apparent hardness.
- Parallel algorithms (optional topic).
- Pattern matching (optional topic).
- Geometry computations (optional topic).
The presentation will provide computer engineering context to the core topics covered.

Homework 10%
Project 5%
Midterm 30%