To the Curriculum Foundations Planning Committee, Participants in the Bowdoin Workshop, and all other Supporters of the Project:

The message below from Charles Kelemen describes the first large scale effort by the computer scientists from the Bowdoin Workshop to disseminate their report and to solicite responses. This is an impressive effort --- it establishes a sterling model for all subsequent workshop groups to follow.

On behalf of CRAFTY and the CUPM I thank the CS workshop members for the quality of their report and the speed with which they have taken it to the wider computer science community.

I look forward to hearing the responses to the report.

Bill Barker

-------- Original Message --------
Subject: Mathematics for Computer Science
Date: Wed, 16 Feb 2000 10:58:04 -0500
From: Charles Kelemen <cfk@cs.swarthmore.edu>

Dear Friends,

The purpose of this posting is to invite members of the computer education community to discuss the first two years of college level mathematics for computer science, information systems, information technology and software engineering education.  This is in response to an initiative by the Mathematical Association of  America (MAA), through its Committee on the Undergraduate Program in Mathematics (CUPM), to carefully analyze the undergraduate mathematics curriculum and its implications for client disciplines (see Item B below).  We are opening this discussion to SIGCSE members in hopes of stimulating continued discussion at the SIGCSE meeting in Austin and in Curriculum 2001 committees.  We plan to accumulate and eventually summarize all postings on this thread for both the CS and mathematics (eg, MAA and CUPM group) educational communities.

As part of the CUPM effort, a number of disciplinary workshops were/are being held.  Computer scientists who participanted in the "CUPM Curriculum  Foundations Workshop in Physics and Computer Science" held at Bowdoin College October 28-31, 1999 were Owen Astrachan, Doug Baldwin, Kim Bruce, Peter Henderson, Charles Kelemen, Dale Skrien, Allen Tucker, and Charles Van Loan.

The full CS workshop report is available at:  http://www.cs.swarthmore.edu/~cfk/cupm2.pdf

The key points of this report are summarized in Item A below.
We invite you to read the full report and post comments to the SIGCSE mailing list or to either Peter Henderson or Charles Kelemen.
For further discussion at SIGCSE in Austin, attend the panel "CS1 and CS2: Foundations of Computer Science and Discrete  Mathematics"
Thursday 10:30 A.M. - 12:00 P.M.  An alternate forum for discussion is the math-thinking discussion group
 http://www.cs.geneseo.edu/~baldwin/math-thinking/math-thinking.html

Respectfully submitted by:

 Peter B. Henderson              Charles F. Kelemen, Professor
 Dept of Computer Science        Computer Science Program
 Butler University               Swarthmore College
 4600 Sunset Avenue              500 College Avenue
 Indianapolis, IN 46208          Swarthmore, PA  19081
 phenders@butler.edu             cfk@cs.swarthmore.edu

==== Item A ================

Our general conclusion is that undergraduate computer science majors need to acquire mathematical maturity and skills, especially in discrete mathematics, early in their college education. The following topics are likely to be used in the first three courses for CS majors:
logical reasoning, functions, relations, sets, mathematical induction, combinatorics, finite probability, asymptotic notation, recurrence/difference equations, graphs, trees, and number systems.
Ultimately, calculus, linear algebra, and statistics topics are also needed, but none earlier than discrete mathematics. Thus, such a discrete mathematics course should be offered in the first semester and the prerequisite expectations and conceptual level should be the same as for the Calculus I course offered to mathematics, science
and engineering majors. Our detailed recommendations respond directly to the series of questions of direct relevance to the CUPM Initiative posed by the Workshop hosts (see Item C below).

The report focuses on the needs of computer science from the first two years of college mathematics instruction.  While the authors have all been involved in computer science curriculum design in the past, this report does not represent the position of any official ACM or IEEE sanctioned curriculum committee.  As ususal, it is a compromise that does not even reflect the exact opinions of any particular member of the workshop.  We hope that it will be informative to the mathematics
community and taken together with other input from the CS community (e.g. a record of the SIGCSE postings on this issue) and other client disciplines help the mathematicians in their planning.

Here is an abridged version of what we received from the mathematics folks.

===== Item B  ======================================================

This is the first in a series of disciplinary-based workshops, all part of the CUPM Curriculum Initiative for the Mathematical Sciences. The Workshop at Bowdoin is designed to seek guidance from physicists and computer scientists on the design of modern and effective programs in the mathematical sciences.

The specific goal of the Workshop will be to provide responses to a series of questions of direct relevance to the CUPM Initiative. The current versions of the questions are enclosed with this letter.
...

The primary focus of the Workshop will be on the first two years of undergraduate mathematics education. This is the most influential portion of the mathematics curriculum and is the central concern of CRAFTY ("Calculus Reform And the First Two Years"), the CUPM Subcommittee which is organizing this series of  workshops. However, discussions will not be limited to the first two years - we hope valuable suggestions will be made for the full spectrum of mathematics courses as it affects physics and computer science.
...

The Mathematical Association of America (MAA), through its Committee on the Undergraduate Program in Mathematics (CUPM), is beginning a major analysis of the undergraduate mathematics curriculum. Historically CUPM curriculum recommendations have had a significant influence in the design of undergraduate Mathematics programs. Last revised in 1982, these important and influential guidelines need to be reconsidered.

Given the impact of mathematics instruction on the sciences and quantitative social sciences - especially instruction during the first two years - there is a need for significant input from these partner disciplines. CUPM will gather much of this necessary information over the next year-and-a-half through a series of invitational disciplinary workshops, culminating in a curriculum conference to analyze and synthesize the workshop findings.

The first of these CUPM workshops will be sponsored and hosted by Bowdoin College on October 28-31, 1999. The focus will be on the needs of physics and computer science from the first two years of college mathematics instruction.
...

After the disciplinary workshop papers have been circulated and commented upon, an invitational curriculum conference will be convened. This conference, working primarily from the workshop papers, will produce detailed curricular recommendations for the first two years of undergraduate mathematics instruction.  This culminating event should take place in 2001.
...

====== Item C =====================================

A primary goal of the Workshop is to obtain responses from physicists and computer scientists to the following series of questions. The responses will help guide the CUPM as it formulates recommendations for programs in the mathematical sciences for the 21st century. These questions may not cover all of the issues you believe important and relevant to our goal - if so, please suggest additional questions or rewordings of those we have given.
 

Understanding and Content.

   What conceptual mathematical principles must students master in the first two years?  What mathematical problem solving skills must students master in the first two years?  What broad mathematical topics must students master in the first two years?  What priorities exist between these topics?  What is the desired balance between theoretical understanding and computational skill?  How is this balance achieved?  What are the mathematical needs of different student populations and how can they be fulfilled?
 

Technology.

   How does technology affect what mathematics should be learned in the first two years?  What mathematical technology skills should students master in the first two years?  What different mathematical technology skills are required of different student populations?

Instructional Interconnections.

   What impact does mathematics education reform have on instruction in your discipline?  How should education reform in your discipline affect mathematics instruction?  How can dialogue on educational issues between your discipline and mathematics best be maintained?
 

Instructional Techniques.

   What are the effects of different instructional methods in mathematics on students in your discipline?  What instructional methods best develop the mathematical comprehension needed for your discipline?  What guidance does educational research provide concerning mathematical training in your discipline?

The CUPM would also appreciate having examples of the important types of mathematical problems students should be able to solve after two years of undergraduate mathematics."