Mathematics 436 — Spring 2018

**Lectures:**TF 2 (10:20-11:40 AM) in Tillet 207 (Livingston Campus); go to lecture table**Text:***Victor J. Katz*,**History of Mathematics: Brief Version.**Addison Wesley (ISBN: 0321161939), 2004.

*Victor J. Katz*,**History of Mathematics (3rd Edition)**Pearson 2009 or 2018 reissue.

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.

As part of these requirements, there will be a term paper consisting of at least 4,000 words. (This is about 8 single-spaced pages, or 16 double-spaced pages.)

Students are expected to select a branch of mathematics, and describe how it has evolved over the course of history.

The topic must be approved by the professor, before Spring Break. The first draft will be due April 6.

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.

Midterm examination: Friday, March 9 in class covering through week 7.

FINAL EXAM: Monday, May ?, 2018 8-11 AM in TIL 207

- January 16-26
- Read Chapter 1 in the text.
- Egyptian Mathematics (Rind Papyrus)
- Mathematics on Cuneiform tablets
- The Mathematics of Babylon
- Read about the Babylonian tablet Plimpton 322 and the representation of numerals.
- View the Babylonian tablet YBC 7289 to see how Babylonian mathematics displayed diagrams and numbers, and read the discussion .
- January 30 - February 2
- Read Chapter 2 in the brief History (or Chapters 2-3 in the long textbook).
- Euclid's Elements (Editing done by R. Fitzpatrick)
- 13 transparancies about Euclid's Elements
- February 6-9
- Read Chapter 3 in the text. (Late Greek Math)
- Archimedes: Palimpsest & Math (287-212 BC)
- Late Greek Math (Diophantus, Hypatia)
- Read Deakin's Article
on
*Hypatia*(355-415 AD) - February 13-23
- Read Chapters 5 & 6 in the text. (Math in Ancient China and India)
- Math in China (100BC-1100AD)
- Math in India (800BC-700AD)
- February 27 - March 9
- Read Chapters 7, 8 in the text. (Islamic Math)
- Math in the Islamic World (800-1400)
- March 20-30
- Read Chapters 9-10 in the text.
- Math in the early Renaissance (1300-1500
- Math in the late Renaissance (1500-1650)
- April 3-6
- Read Chapter 11 in the text. (The invention of Calculus in the 1600s.)
- Calculus in the 1600s
- April 10-13
- Read Chapters 12, 14 (Calculus, Algebra and Number Theory in the 1700s.)
- Analysis in the 1700s
- April 17-20
- Read Chapters 14, 16.1, 16.4 and 17.1 in the text.
- Algebra in the 1700s
- Cauchy: Limits and Continuity
- Analysis in France
- April 24-27
- Read Chapters 13 and 15

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 | Medieval and Renaissance Europe | ||

11 | 3/27, 3/30, 4/2 | Chapter 10 | The Pre-Calculus Era | ||

12 | 4/3, 4/6 | Chapter 11 | The discovery of Calculus | ||

13 | 4/10, 4/13 | Chapter 12 | Euler and the 18th Century | ||

14 | 4/17, 4/20 | Chapters 14, 16.4, & 17.1 | Linear Algebra, Matrices & Continuity | ||

15 | 4/24, 4/27 | Chapters 13, 15 | Probability, Non-Euclidean Geometry, Review | ||

16+ | 5/9 | Cumulative (tbd) | Final Exam (8-11AM on May 9) | ||

due January 30: Chapter 1 #16,18,29 (or #19,24,33 in the longer book)

due February 2: Chapter 2 #1,6,15,18,24,27 (or Ch.2 #5,12 and Ch.3 #17,18,34,37 in the longer book)

due Feb 9: Write proofs of Euclid VI-23, IX-14 and X-1 in modern language, AND

do problems #2.32, 3.3, 3.35 (brief) (or #3.44, 4.6, 4.38 in the long book)

due February 16: #3.21, 3.24, 3.33, 4.2, 4.3, 4.18 (brief); or #5.1, 5.11, 5.18, 6.8, 6.9, 6.27 (long)

due February 23: Ch.5 #1,2,7,16,20,24 (brief); or Ch.7 (long) #1,2,16,22,26,30

due March 2: Ch.6 (brief) #4,20,7,9,25,28; or Ch.8 (long) #5,10,15,17,32,35

Useful reference:
MacTutor History of Mathematics archive

Return to Top of page Last updated: Febuary 2018; C. Weibel

Charles Weibel / weibel@math.rutgers.edu / Spring 2018