You've been "reforming" mathematics for some years now. You've been trying to balance the opportunities of new technology, the changing audience and the exciting new material accessible to undergraduates. You're under pressure to the needs of other departments, and faced with the intransigence of College Curriculum Committees that won't let you require ten mathematics courses of every undergraduate, twenty of our mathematics majors. You've heard a hundred conference presentations, and read other books in the MAA Notes Series: the classic "Toward a Lean and Lively Calculus" (#6 in the Series), the five volumes of the "Resources for Calculus Collection (#27-31), and all the rest.
You're just bubbling with ideas for enriching and improving your mathematics courses and curricula. The problem is, where can all these changes fit into your curriculum? It's already full. Cramming more material can't work, no matter how spectacular the material or talented you are as a teacher.
This book addresses these problems: How do we find room in the curriculum for modernization and improvement? How do we service other departments, especially Engineering and Physics, more efficiently?
For decades, we have been "weeding" the curriculum, removing material that is less useful, obsolete, or, some would say, too difficult. Analytic geometry and Euclidean geometry are both gone from most programs. Involutes and evolutes are long gone from calculus courses. Many believe that there isn't much left that can be left out. The curriculum is already cut to the bone. We probably can't require more courses for our programs without bringing down the wrath of the other departments. Nor could we lengthen classes or extend the semester (even if we wanted to) for the sake of including more material. And it is a "fact of life" that students aren't all excellent, so we can't cover more material simply by covering the material faster.
This book, "Confronting the Core Curriculum" presents the proceedings of a 1994 conference at the US Military Academy at West Point to discuss and study the relatively radical approach being used at the Military Academy. They call the program "Seven into four."
The organizers point out that this innovation is not the first to come out of the Military Academy. They claim to have been the first in America to use blackboards as the primary tool to teach mathematics, in the 1820's, and in 1944 they required slide rules of every student.
The West Point idea is to take the content of seven "introductory" mathematics courses, the ones that form the core of the mathematics major curriculum and the bulk of the mathematics courses that other departments require of their students, and squeeze the material into just four courses. They accomplish this squeeze partly by omitting some material, but mostly by reorganizing the material so that it is better coordinated.
It is a little tricky to figure out just what the "seven" courses are, but they seem to be Calculus I, II and III, Linear Algebra, Differential Equations, Probability and Statistics, and Discrete Mathematics. They compress and reorganize this material into four courses, Discrete Dynamical Systems, two Calculus courses, and Probability and Statistics.
The proceedings report on each of the four courses, how they work at West Point, and at other institutions that have tried similar innovations, as well as a good deal of lively discussion.
While this book should not be the only book on mathematics reform you ever read, it does address issues that the others tend to gloss over, and it proposes solutions to some of those issues. The discussions make clear the strengths and weaknesses of those solutions, and they might not work everywhere. However, if your department is under pressure to cover mathematics for other departments in less time, or if you need more room in your curriculum to cover other more modern material, then this book will provide valuable ideas.
Ed Sandifer (firstname.lastname@example.org) is a professor of mathematics at Western Connecticut State University and has run the Boston Marathon 26 times.