MATH 4030: History of Mathematics

MATH 4030 History of Mathematics Spring 2014

Lectures: MWF 11:15-12:05, Malott 406

Lecturer: Prof. Steven Strogatz
533 Malott Hall, 255-5999, shs7@cornell.edu

TA: Drew Zemke, drew.zemke@gmail.com

Office hours:
Strogatz, 1:30-3:30, Mondays, 533 Malott
Zemke, Mon 3:30-4:30 and Tues, 12:30-1:30, Malott 218

Topics:
1. Greek geometry, number theory, and infinity (Pythagoras, Euclid, Diophantus, Archimedes)
2. Quadratic, cubic and quartic equations (Tartaglia, Cardano, Viète)
3. Analytic geometry (Fermat, Descartes, Newton)
4. Projective geometry (Desargues, Pascal)
5. Calculus and infinite series (Wallis, Newton, Leibniz, Euler, Gregory)
6. Complex numbers in algebra (d’Alembert, Gauss)
7. Hypercomplex numbers: Quaternions and octonions (Hamilton)
8. Group theory and unsolvability of the quintic (Galois)
9. Non-Euclidean geometry (Bolyai, Lobachevsky, Gauss)
10. Differential geometry - a very brief look (Gauss)

Textbook: Mathematics and Its History, John Stillwell, 3rd ed.
You can buy a hardcover copy of the book at the Cornell Store.
An electronic version of the book is available free online at
https://catalog.library.cornell.edu/cgi-bin/Pwebrecon.cgi?BBID=7038199&DB=local
From the Springer page for the e-book, the Buy Now button allows anyone at Cornell to buy an on-demand paper copy for $24.99.

Course Website: https://piazza.com/cornell/spring2014/math4030/home

Reading and Quizzes: Please read the book by Stillwell. It’s wonderful (much better than most textbooks) and contains terrific insights of all types: mathematical, conceptual, and historical. You should do the reading assigned for each lecture before you come to class. For example, on Jan 22 and 23 you should read—and think about—the assigned material for Jan 24 (which you can see from the syllabus is Sections 1.4–1.7 in Stillwell; note that this includes historical material about Pythagoras). To nudge you to do the reading, I will be giving unannounced 5-minute quizzes from time to time, roughly every week or two. If you have done the reading and thought about it, the quizzes should be easy.

Participation: Piazza is a great place to ask questions and to answer them. Tell your classmates (anonymously) what you're finding interesting or confusing in the reading, lectures, or homework. You will get participation points for raising good questions, following up on other students' questions, or answering questions. Sharing links or doing anything else that contributes to the class will also count. At the end of the course, we'll compute a participation score for you. This will be used to provide some insurance against a low score on the final.

Examinations:
There are two Preliminary Exams and a comprehensive Final Exam. The prelims are in class on Friday, Feb 14 and on Weds, April 9. The date and time of the final exam are still to be announced. Please mark these dates and do not schedule anything that conflicts with them. Prelim 1 covers chapters 1–3. Prelim 2 covers chapters 4 and 6–10. The final exam covers the whole course.

Homework:
Weekly homework assignments will be collected in class on Wednesdays. Late homework will not be accepted. If you know you have to miss a Weds class for whatever reason, you are responsible for getting your homework to the TA before the Weds class. Please write up your solutions clearly and neatly; illegible homework will not be graded. All the assigned homework problems and reading are listed in the syllabus and daily schedule, which is posted on Piazza. Homework problems for the material covered in lecture the previous M,W,F will be due the following Wednesday. For example, HW1 covers material from Chapter 1 discussed in lecture on Weds 1/22 and Fri 1/24, and is due the next week, on Weds 1/29. (The two exceptions to the HW being due on Weds are HW4 and HW10, which are due on Friday 2/17 and 4/11 because of February break and the prelim on 4/9.)

Grading:
Each student’s grade will be determined by the quizzes, two prelims, homework, the final exam, and possibly by participation points earned on Piazza -- see below for further explanation. Your two lowest quiz grades and two lowest homework grades will be dropped.
Quizzes: 20%
Prelims: 20%
Homework: 30%
Final exam: 30%
Participation insurance: We will compute 30% final and compare it to 20% final + 10% participation. We'll use whichever number is higher. Thus participation on Piazza offers some "insurance" against a low score on the final. Note that if your participation is weak or absent, it doesn't hurt you; it just means you will have to rely on your score on the final. Still, I hope you will participate as much as you can -- many of you have really good ideas and questions to share … and it will make the class more fun!

Academic Integrity:
Each student is expected to abide by the Cornell University Code of Integrity, http://cuinfo.cornell.edu/Academic/AIC.html. You may work together on homework, but you must write your own solutions and you must list the names of anyone you worked with. You may not use any answer manuals from the Internet or elsewhere. Each student is responsible for his or her own work on all examinations. Violations will be dealt with swiftly and justly.

Contacting us:
You are encouraged to use the Piazza site to post and to answer questions, particularly as they pertain to the course matter. This has the advantage of letting others see your questions and answers, and may often result in a faster response than email. If you still feel the need to use email, please include “Math4030” in the subject line , along with a short description of your question or issue. Keep the body of your message short and to the point. We will respond as promptly as possible, but not instantaneously.