This course will present an overview of the development of mathematics from ancient civilizations to the 19th century. Selected topics from the history of mathematics including number systems; Euclidean geometry; the development of algebra in India, Arabia, and the West; and calculus. Special emphasis will be placed on some recurrent themes, e.g., calculation of areas, progressive enlargement of number systems, changing concepts of rigorous proof.
Besides lectures, part of the course will be devoted to presentations of selected topics by participants, either in class or in the form of papers. The goal is to expose students to the historical development of mathematical ideas, over time and across cultures, and to acquaint them with some of the basic techniques, as they were historically developed.
Your paper will be graded on
1) your success in establishing a central, unifying theme;
2) how well it is supported by concrete material, drawn from your sources;
3) the overall quality of your writing and paper organization.
Week | Lecture dates | Sections | topics | ||
---|---|---|---|---|---|
1-2 | 1/16, 19, 23 | Chapter 1 | Egypt, Babylonian and Mesopotamian Mathematics | ||
3 | 1/26, 1/30 | Chapter 2 (brief version) | Early Greek Mathematics (Euclid) | ||
4 | 2/2, 2/6 | Chapters 2 & 3 (brief) | Greek Mathematics (Euclid & Archimedes) | ||
5 | 2/9 | Chapter 4 (ch.5&6 long version) | Post-Euclid Greek Math (Classic Greek Problems) | ||
6 | 2/13, 2/16 | Chapter 5 (ch.7 long) | Ancient Chinese Mathematics | ||
7 | 2/20, 2/23, 2/27 | Chapter 6 (8 long) | Indian Mathematics | ||
8 | 2/27, 3/2 | Chapter 7 (9 long) | Islamic Mathematics — and paper topic | ||
9 | 3/6, 3/9 | Review, Midterm | The Midterm on Friday covers ch. 1-6 (brief) viz. ch.1-8 (long) |
||
9+ | 3/13, 3/16 | R&R | SPRING BREAK | ||
10 | 3/20, 3/23 | Chapters 8&9 (10&12 long) | Medieval and Early Renaissance Europe | ||
11 | 3/27, 3/30, 4/2 | Chapter 10 (12-13 long) | Late Renaissance, and the Pre-Calculus Era | ||
12 | 4/3, 4/6 | Chapter 11 (15-16 long) | The discovery of Calculus; paper outline due 3/30 and paper draft due 4/6 |
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13 | 4/10, 4/13 | Ch. 12 & 14 (17&18 long) | Euler, the 18th Century, Probability | ||
14 | 4/17, 4/20 | Ch.14,16.4,17.1 (19&21 long) | Linear Algebra, Matrices & Continuity | ||
15 | 4/24, 4/27 | Chapters 13,15 (21-22 long) | Probability, Linear Algebra, Review | ||
16+ | 5/9 | Cumulative (tbd) | Final Exam (8-11AM on May 9) | ||
Useful reference:
MacTutor History of Mathematics archive
Charles Weibel / weibel@math.rutgers.edu / Spring 2018