SYLLABUS: Math 30 Spring, 1998 Professor J. V. Grabiner



Times: MWF 11 (lectures), Tu 11-12:15 (required lab), all in Scott 230.
Office: Fletcher 222, phone 7-3160, secretary 7-3061;
Email: jgrabiner@pitzer.edu
Office Hours: M Tu W F, 10 - 11 AM, and by appointment
Text: James Callahan et al, Calculus in Context, W. H. Freeman, 1995 (available at Huntley)
Topics: Mathematical modeling, functions, limits, derivatives, differential equations, Euler's method, integrals, and the Fundamental Theorem of Calculus. We'll do most of the first 6 chapters of the text.

Graphing Calculator: ESSENTIAL. Any brand is acceptable. I'm using a TI-85. The new TI-86 is similar and not much more expensive; it has more memory and some advanced features. Bring your calculator to class. The back of the textbook (p. 749ff) has every step of the relevant programs written out, in sections for the TI-81, 82, 85 (will also work for the TI-86), Casio fx-7700G and 9700GE, and Sharp EL-9200/9300 graphing calculators.
You need to learn, as fast as possible, to do normal calculations (arithmetic, x5, ex, sin x, etc.) on your calculator. We will work together in lab to help you learn each of the following. (Bring your CALCULATOR INSTRUCTION BOOK to labs with you.)
(a) how to enter, edit, and run programs
(b) how to enter and graph functions, zoom in on part of the graph, and identify points on the graph using the cursor and "trace" utilities
PUT YOUR NAME ON YOUR CALCULATOR and INSTRUCTION BOOK!
Programs can be sent from one TI-85 to another, or from a TI-85 to a TI-86. To avoid having to type the originals in on your own, you can use mine if you have a TI-85 or TI-86.

Prerequisite: Math 23 (C or better), or placement score. This will be enforced. See me if you have any questions.

Approach : This course differs from standard courses in involving students immediately with large, open-ended problems taken from the sciences and social sciences, using powerful calculators to help solve the equations which model such problems. Group work will enhance students' abilities to deal with the material by asking questions and articulating conjectures. We aim for understanding of the concepts by working through problems. You have to be actively involved in thinking about what you're doing. We'll start off slowly so you become used to the general approach, and so you get used to reading the textbook. By the beginning of the second week you'll see how this course differs from other math courses you've taken.

Homework policies: Homework will be collected at the start of class, usually each Wednesday. If it's one class late it will be docked 10%; if more than one class late, 50%. Exceptions (for instance, illness) must be okayed by the instructor IN WRITING; the grader cannot make exceptions.
In addition, there will be lab assignments and/or group assignments during any given week. Lab work will be due at the start of class Wednesday. Group work will have deadlines specified. The same policies will apply.
Please type homework if at all possible. It must be legible; messy or illegible work will be returned without being graded.
Homework will count 1/3 of the total course grade.
You are encouraged to discuss the homework with each other and, to that extent, to work together. But do your actual write-up alone unless you are doing a group problem. If you don't understand the homework, your exam scores will suffer.
The purpose of homework is not to produce a set of written-on pages, but for you to understand how to do these and similar problems through having actually done them.

Thought Problems: I will organize groups of 3-4 students to work on thought problems. There will be one (or a sequence of related ones) each week. Each group must submit one written answer to the problem in essay form. The responsibility for the final write-up will be rotated through the group. (Who goes first can be determined by the group.) Like all real-world work in mathematics and its applications to the sciences, homework should be clearly written. You should explain the steps used in solving the problems. Lengthy verbiage isn't necessary, grammar and spelling won't be chewed over, but clarity of exposition is required. Occasionally there will be a "write this up individually and perfectly" problem to see whether you can write up a (relatively easy) problem solution clearly and on your own.

Grabiner's First Law of Group Work: Talk with each other! Questions are signs, not of ignorance, but of being engaged with the material. Discussion and debate are signs, not of hostility, but of learning to learn from each other's different perspectives.

Labs: In lab I'll assign a problem, give you each a copy, and you will work on it in groups, with me around as a resource. These labs are an essential part of the course. Problem solutions will be handed in. The deadline will be at the start of the next Wednesday's class.

The use of graphing calculators : Modern technology has transformed the way the calculus is actually used by scientists. We can do computations in a few seconds that took people like Newton and Gauss weeks. The simple symbolic computations that used to consume half of introductory calculus courses can now be done by the touch of a button. Therefore, the parts of the subject "calculus" that require human intelligence -- understanding the concepts, being able to translate real-world situations into mathematics -- have become much more important than they used to be.

Nuts and bolts of graphing calculators for this course:
This course will use very simple programs for your calculator; you will easily be able to understand how they work and how to modify them. The calculator will not be used as a magician, but simply to calculate faster and more accurately, or to produce and manipulate graphs to enhance your understanding of how functions vary. The programs for various types of calculators appear at the end of the textbook. If you have a TI-85 or TI-86, I can transmit my copies of these programs to your machine. If you have another calculator, you can type them in EXACTLY as they appear in the text. Typing them in is a drag, but there's not that much, and you only have to do it once. This is NOT a course in how to program calculators; the calculator is a means, not an end. If you have ANY difficulty with the calculator, deal with it IMMEDIATELY.

Grabiner's First Law of Computing and Calculating : Nothing ever works exactly the way you expect the first time. Learn to laugh, and then ask for help. With the programs we're using, the most likely explanation for difficulties is that somebody has made a typographical error. Check this first.

Tests: There will be two or three midterms and a final. Dates will be determined as the course progresses, but Friday, February 6 or 13, seem likely first candidates. Exams may have take-home components. If so, you'll be asked to sign a pledge that you have done the work entirely on your own.
Final Exam: Saturday, May 16, 1998, 8 A.M.

First week's reading and assignments:
First, read and know the policies in this syllabus. Read all of section 1.1; start 1.2 for the second Monday. Problems to hand in Wednesday, January 28: Section 1.1, 1-7, 15-17, 18-22. (Don't try to do them all at once. This is a long assignment.)
Thought Problems for your group: Section 1.1, 23-28. You'll need to have already worked on the individual problems in order to contribute to your group solution.
Individual perfect write-up problem: Section 1.1, problem 16. Put it on a separate piece of paper, please.

Grading algorithm: Homework 1/3 (includes labs and all thought problems as well as ordinary homework), midterms 1/3, final 1/3. If your final is much better than your earlier work I will take this into account.

A final word: Advanced mathematics rests upon more elementary mathematics. If you don't understand something early in the course, you will find it hard to understand the topics that follow, and you may not even know why you are having difficulties. So if there is something you don't understand, come see me as soon as possible or send me an e-mail. I'll be happy to help you.