Intro to Higher Math

Spring 2003

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Instructor: Dr. Art Duval

Please feel free to come by my office any time during scheduled office hours. You are welcome to come at other times, but in that case you might want to make an appointment, just to make sure that I will be there then. You can make an appointment simply by talking to me before or after class, by calling me at my office or at home, or by sending e-mail.

You may also ask any questions directly via phone or e-mail. If I'm not in when you call, please leave a message on the voice-mail or answering machine with your name, number, and a good time for me to call you back. I will try to respond to your phone or e-mail message as soon as possible.

Course Philosophy and Objectives:

This course is built on the proposition that you learn mathematics, and how to construct mathematical proofs, better when you formulate the questions and discover the answers yourself. Upon successful completion of the course, you will be able to investigate mathematical questions, big and small, both experimentally and theoretically.

This is very different from courses like pre-calculus, calculus and differential equations, which are primarily focused on computations. Although there are computations in this course, they are a tool for discovering, and proving, more general mathematical truths.

Textbook: Laboratories in mathematical experimentation: A Bridge to higher mathematics, by Mount Holyoke College.

This book consists of 16 mathematical "labs". We will go through the following labs, at the rate of two weeks per lab:

You will also go through one additional lab, or another topic of your choosing (with my approval), on your own, at the end of the semester.


Class time will be devoted exclusively to labs. Each lab will start with a brief explanation of the question or problem to be explored. You will perform experiments (usually with a computer or programmable calculator) and gather data. The data will lead you to make your own conjectures, which you will then test and refine by further experimentation. Finally, when you are more certain of your conjectures, you will prove them carefully. (In practice, this process is rarely as straightforward and linear as outlined here. You will often revisit earlier steps as you carry out later steps.)

You may work in small groups of your choosing in class (as well as out of class). There will also be whole-class discussions about your experimental and theoretical discoveries.

After two weeks of work in class (and while you are starting the next lab), you will have a week to write up your discoveries, both experimental and theoretical, into a clearly-written report. (Grading criteria are below.) Although you may work with other students during the lab, you must write your report yourself. After each report is graded and returned to you, you will have approximately one more week to revise your report for a better grade, if you like. Revised reports must be complete; in other words, it should be possible to understand your revised report without reading your original report.


Each lab will be graded on the following criteria: Experimental design; Organization and presentation of data; Analysis of data; Statement of conjectures; and Mathematical analysis (including proofs) of conjectures (see p. xvii of the text).

The final grade for each lab will be the average of the grades you receive on your initial report, and on your revision. If you do not turn in a revision, it will simply be the grade of your initial report. Your grade for the course will be the average of the final grades for each of the seven labs.

Drop date:

The deadline for student-initiated drops with a W is Friday, March 7. After this date, you can only drop with the Dean's approval, which is granted only under extenuating circumstances.

I hope everyone will complete the course successfully, but if you are having doubts about your progress, I will be happy to discuss your standing in the course to help you decide whether or not to drop. You are only allowed three enrollments in this course, so please exercise the drop option judiciously.