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Session 3265

Theoretical Issues in Computer Engineering

Feodor Vainstein, Mark Rajai Georgia Institute of Technology/ University of Memphis

Abstract

In this paper, we present our experience on teaching Theoretical Issues in Computer Engineering. We emphasize the importance of abstract algebra for practical applications. In particular we show that algebra is the appropriate mathematical tool for many problems in minimization, fault tolerance, digital communications, random number generators etc.

Introduction

Computer engineering has been formed as a distinct discipline only recently. It is significantly different from traditional engineering areas like mechanical, chemical or electrical engineering. By its nature, computer engineering is discrete and structural.

We believe that the maturity of a research area is mostly defined by the level at which mathematics is used in this area. There is an opinion that mathematics is 300 years ahead of other sciences, since most mathematical tools that are used now have been developed in 17th century. Computer engineering to some extent challenges this point of view. It is only 100-200 years behind mathematics (in some cases the gap is only 50 years wide).

In this paper, we present our experience on teaching Theoretical Issues in Computer Engineering. We emphasize on the importance of abstract algebra for practical applications. In particular we shall show that algebra is the appropriate mathematical tool for many problems in minimization, fault tolerance, digital communications, random number generators etc. Some textbooks on discrete mathematics cover abstract algebra superficially. There can be two explanations of this. First, it is believed that this subject is too tough for an engineering student. Second, many authors, being professional mathematicians, are not aware of all numerous applications of algebra in computer engineering and do not realize the importance of teaching it. We strongly disagree with these points of view.

We give the list of topics that should be, in our opinion, covered in a course on Theoretical Issues in Computer Engineering. Two versions, undergraduate and graduate are considered. For the undergraduate course the leading applications are minimization of finite state machines, Myhill Nerode theory, capabilities of computers, and linear machines. For a graduate level course the leading applications are error correcting codes, fault tolerant computing, and cryptography.

Proceedings of the 2003 American Society for Engineering Education Annual Conference & Exposition Copyright © 2003, American Society for Engineering Education

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Vainstein, F., & Rajai, M. (2003, June), Theoretical Issues In Computer Engineering Paper presented at 2003 Annual Conference, Nashville, Tennessee. 10.18260/1-2--12076