Spring semester 2015

Why is differential and integral calculus, developed in the 17th century by Newton and Leibniz (and substantial fragments of which were developed much earlier) considered one of humankind’s great intellectual, scientific, cultural, and aesthetic achievements?

That is what students ought to find out from a calculus course when it is included within a broad liberal education for those without a pre-identified need to apply the subject in later work. The purpose of an honest course is not to provide students with an opportunity to show that they can do challenging things so that they can be rewarded with a grade.

The conventional course is designed for students who already understand that mathematics is an intellectual and aesthetic endeavor, a science in which new discoveries are being made as much as in physics or biology, and mathematics does not consisting only of mathematical skills.  Students taking the conventional calculus course must learn everything in a list of technical topics (e.g. computing every sort of limit, derivative, and integral), but nothing about the answer to the questions in the first paragraph above.  It is expected that they will learn what calculus is used for in later courses in physics, engineering, statistics, etc.  Anything about what it all means or why it is an important intellectual or aesthetic achievement must be excluded because the obligatory list of technical skills leaves no time for that.

That kind of course, when taken by students who do not yet know the answer to the question in the first paragraph above, sweeps conceptual ideas under the carpet. Universities encourage thousands of such students to take calculus and to regard learning calculus as merely the price of a grade that will impress potential employers and graduate and professional schools rather than as the thing they show up for.  That is not education.  Students emerge thinking that those technical skills are what mathematics is. That is a lie. Students who really want to understand the answer to the question in the first paragraph above get left behind. But universities collect lots of tuition money.

This course in the spring of 2015 is for students who are actually students, who are there because learning is what they want, rather than a price they pay for a grade. This course will enable you to understand applications of calculus in physics, chemistry, biology, economics, statistics, and other subjects.

The course has no affiliation with any university or institution and no academic credit will be earned. The cost is the same as that of the University of Minnesota’s math 1271.

Content will be adapted to interests and abilities of students.

Prerequisites are those for math 1271 except that you should, to some substantial extent, have understood the prerequisite material, as opposed to merely getting grades of “A+” in courses.

The textbook is Calculus in Context by Calahan, Cox, Hoffman, O’Shea, Pollatsek, and Senechal, which can be downloaded from the web for free. This book emphasizes applications of calculus in the sciences.

I will be your instructor. I am Michael J. Hardy, Ph.D. I earned my doctorate at the University of Minnesota in 1997 with a major in statistics and a minor in mathematics. I have taught at the Massachusetts Institute of Technology, the University of North Carolina, the Woods Hole Oceanographic Institution, the University of Minnesota, and elsewhere.

Specifically how will “calculus made honest” differ from conventional calculus courses? The following is a list of some contrasts: contrasting syllabi (a pdf document).

A paradox resides at the base of differential calculus.  Here is an explanation of the paradox and a fairly easy way to resolve it: instantaneous rates12.2.14

And another link: On the absurdities of some aspects of the conventional calculus course.

The course begins on Monday afternoon, January 26.  If interested, contact me before then:

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