Discrete Mathematics for Computer Science: What, How Much, Who, When

Notes by Henry M. Walker
Department of Mathematics and Computer Science
Grinnell College

Presentation to Iowa Undergraduate Computer Science Consortium

Saturday, October 12, 2002




Talk Outline






Sources of Information/Reports

Conferences/Workshops

Reports

Correspondence/Dialog with Groups and Individuals









Areas of Widespread Agreement

Goals of a Mathematics Curriculum

The work of CRAFTY/CUPM with client disciplines has led to a nice statement of goals for undergraduate mathematics.

Importance of Discrete Mathematics in the First Two Years

Topics Desired in the Discrete Mathematics Sequence (at least for CS)

Need for Computer Science Students to Take an Additional Semester of Math









Issues

Several questions arise in considering discrete mathematics in the mathematics curriculum. Some basic questions are:







Approaches for Including Discrete Mathematics in the Mathematics Curriculum

The basic problem is that mathematicians and various client disciplines have diverse needs.

Three basic approaches

Realistically, there seem to be three curricular approaches to address the needs of diverse audiences.
  1. Integrate continuous and discrete mathematics in a common [2-year] sequence
  2. Offer independent/disjoint courses in continuous mathematics, statistics, and discrete mathematics
  3. Organize separate courses in continuous mathematics, statistics, and discrete mathematics to take advantage of common approaches [and topics]

Each approach seems to have its own advantages and disadvantages.

An Integrated Continuous/Discrete Mathematics Sequence

Basic Idea: Combine continuous and discrete mathematics in a highly integrated sequence (perhaps including some probability and statistics) Variation: Add some discrete mathematics topics to existing courses

Independent and Disjoint Courses

This approach seems quite common in many colleges and universities. Separate tracks of courses are offered for continuous mathematics, statistics, and discrete mathematics. One such variation follows.
Separate Introductory Math Tracks

Separate Continuous/Discrete Courses With Some Sequencing

Difficulties in advising incoming students can be deferred if all students begin with the same mathematics courses, but with possible branching in a second year.

Approach 1: Tony Ralston et al in early 1980s

Approach 2: Currently in Use at Grinnell

Grinnell's current curriculum moves discrete mathematics to the second semester of the sophomore year, with a calculus/linear algebra prerequisite.


Conclusions









This document is available on the World Wide Web as

http://www.cs.grinnell.edu/~walker/curriculum/discrete-math-iowa.html

created October 7, 2002
last revised October 9, 2002
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For more information, please contact Henry M. Walker at walker@cs.grinnell.edu.