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 outline, and references, are due March 30. 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: Wednesday, May 9, 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 about Late Greek Math (Chapter 3 in the brief text, or chapters 4-5 in the long text)
- Archimedes: Palimpsest & Math (287-212 BC)
- Late Greek Math (Diophantus, Hypatia)
- Read Deakin's Article
on
*Hypatia*(355-415 AD) - February 13-23
- Read about Math in Ancient China and India (Chapters 5 & 6 in the brief text, chapters 7-8 in the long text)
- Math in China (100BC-1100AD)
- Math in India (800BC-700AD)
- February 27 - March 9
- Read about Islamic Math (Chapters 7 in the brief text, ch. 9 in the long text).
- Math in the Islamic World (800-1400)
- March 20-23
- Read about Medieval Europe (chapter 8 in brief text, ch.10-11 in long text).
- Math in the early Renaissance (1300-1500
- Math in the late Renaissance (1500-1650)
- April 3-6
- Read about the invention of Calculus in the 1600s. (Ch. 11 in the brief text, 15-16 in the long text)
- Calculus in the 1600s
- April 10-13
- Read about Calculus, Algebra & Number Theory in the 1700s. (Ch.12 & 14 brief, ch. 14.4&17 in the long text)
- Analysis in the 1700s
- Algebra in the 1700s
- April 17-20
- Read about Algebra and Number Theory in 1700-the late 1800s. (chapters 14, 16.1-4, 17.1 in the brief text; 19 & 21 in long text)
- Cauchy: Limits and Continuity
- Analysis in France
- April 24-27
- Read Chapters 12--22

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 |
||

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) | ||

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

due March 23: Ch.7 (brief) #3,5,7,13,18,26; or Ch.9 (long) #4,6,10,16,29,41

due March 30: Brief: Ch.8 #3,12,16,18 and Ch.9 #1,5,15,18; or Long: Ch.10 #4,21,31,35 and Ch.12 #4,10,28,31

Paper outline and references due March 30.

due April 6: Draft due. ALSO Brief: Ch.10 #1,6,16,23 and Ch.11 #4,8

Long: Ch.14 #5, 15(use Fig.14.7), 30,39 and Ch.15 #6,10

due April 13: Brief: Ch.11 #12,20, 26, 28, 35, 42;

Long: Ch.15 #17,28 and Ch.16 #9,16,31,39

due April 20: Brief: Ch.12 #3,11,27,36 and Ch.13 #7,16;

Long: Ch.17 #5,13,35,50 and Ch.18 #11,31

due April 27: Brief: ch.14 #4,13,15; ch.16 #2,36a,38 -OR- Long: Ch.19 #17,26,31; ch.21 #2,49a,55

due by May 1: Finished term paper.

Useful reference:
MacTutor History of Mathematics archive

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

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