E-Book Overview
The Conference/Workshop of which these are the proceedings was held frcm 28 June to 1 July, 1982 at Williams College, Williamstown, MA. The meeting was funded in its entirety by the Alfred P. Sloan Foundation. The conference program and the list of participants follow this introduction. The purpose of the conference was to discuss the re-structuring of the first two years of college mathematics to provide some balance between the traditional ca1cu1us linear algebra sequence and discrete mathematics. The remainder of this volume contains arguments both for and against such a change and some ideas as to what a new curriculum might look like. A too brief summary of the deliberations at Williams is that, while there were - and are - inevitable differences of opinion on details and nuance, at least the attendees at this conference had no doubt that change in the lower division mathematics curriculum is desirable and is coming.
E-Book Content
The Future of College Mathematics Proceedings of a Conference/Workshop on the First Two Years of College Mathematics Edited by Anthony Ralston Gail S . Young [I Springer-Verlag New York Heidelberg Berlin Anthony Ralston SUNY at Buffalo Department of Computer Science 4226 Ridge Lea Road Amherst, N.Y. 14226 U.S.A. Gail S. Young University of Wyoming Department of Mathematics Laramie, Wyoming 82071 U.S.A. AMS Subject Classifications: OOA to, OOA25, OOA99, 01A80 Library of Congress Cataloging in Publication Data Main entry under title: The Future of College Mathematics Bibliography: p. Includes index. 1. Mathematics-Study and teaching (Higher)Congresses. I. Ralston, Anthony. II. Young, Gail S. III. Alfred P. Sloan Foundation. QAll.AIF84 1983 510'7'11 82-19447 Conference/Workshop held at Williams College, Williamstown, MA from June 28 to July 1, 1982. Sponsored by the Alfred P. Sloan Foundation. With 3 Illustrations © 1983 by Springer-Verlag New York Inc. Softcover reprint of the hardcover 1st edition 1983 All rights reserved. No part of this book may be translated or reproduced in any form without written permission from Springer-Verlag, 175 Fifth Avenue, New York, New York 10010, U.S.A. Printed and bound by R.R. Donnelley & Sons, Harrisonburg, VA. 987654321 ISBN-13: 978-1-4612-5512-3 DOl: 10.1007/978-1-4612-5510-9 e-ISBN-13: 978-1-4612-5510-9 v Contents Introduction List of participants Program viii ix Papers An Overview of the Arguments Concerning the Development of a New Curriculum 1 Anthony Ralston Who Takes Elementary Mathematics Courses? Why? A Guess, and Some Problems for Change 13 Gail S. Young Symbolic Manipulation and Algorithms in the Curriculum of the First Two Years 27 Herbert S. Wilf Problem Solving and Modeling in the First Two Years 43 William F. Lucas The Mathematical Needs of Students in the Physical Sciences 55 Jack Lochhead Engineering Needs and the College Mathematics Core 71 Isaac Greber The First Two Years of Mathematics at a University as It Relates to the Mathematical Needs of Students in the Social Sciences 75 Robert Norman Mathematics in Business and Management 81 Stanley Zionts Mathematics Curriculum and the Needs of Computer Science 89 William L. Scherlis and Mary Shaw Developing Mathematical Maturity 99 Lynn Arthur Steen A Two-Year Lower-Division Mathematics Sequence III Donald Bushaw How to Cure the Plague of Calculus (or Revisions in the Introductory Mathematics Curriculum) Fred S. Roberts 121 vi Principles for a Lower-Division Discrete-Systems-Oriented Mathematics Sequence 135 Alan Tucker Statistics in the