History of Mathematics
Mathematics 436 — Spring 2009

Prof. Weibel ( Office hours)



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.

Term Paper

As part of the SAS core curriculum writing requirement, 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, approved by the professor, and write about how it has evolved over the course of history.

Examinations

Midterm examination: Tuesday, March 10 in class covering through week 7.

FINAL EXAM: Friday, May 8, 2009 12-3 PM in SERC 211

Readings

January 20-29
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 .
February 3-10
Read Chapter 2 in the text.
Euclid's Elements (Editing done by R. Fitzpatrick)
13 transparancies about Euclid's Elements
February 10-17
Read Chapters 3 & 4 in the text. (Late Greek Math)
Archimedes and Mathematics (287-212 BC)
Late Greek Math (Diophantus, Hypatia)
Read Deakin's Article on Hypatia (355-415 AD)
February 19-24
Read Chapters 5 & 6 in the text. (Math in Ancient China and India)
Math in China (100BC-1100AD)
Math in India (800BC-700AD)
February 26-March 3
Read Chapter 7 in the text. (Islamic Math)
Math in the Islamic World (800-1400)
March 25-31
Read Chapters 8 and 9.1 in the text, and handout about Fibonacci.
Medieval Europe
April 1-7
Read Chapter 10 and the rest of chapter 9 in the text.
Math in the early Renaissance (1300-1500
Math in the late Renaissance (1500-1650)
April 8-14
Read Chapter 11 in the text. (The invention of Calculus 1n 1600s.)
Calculus in the 1600s
Analysis in the 1700s
April 14-20
Read Chapters 12, 13 and 17.1 in the text. (Calculus 1700-1900.)
Differential Equations in the 1700s
Probability origins
April 21-27
Read Chapters 14, 16.4, 17.1 (Algebra 1700-1870)
Algebra transparencies
Cauchy: Limits and Continuity
April 27
Read Chapters 15.1, 19.1 (Euclid's Parallel Axiom, Hyperbolic Geometry)
Geometry transparencies

Homework Assignments

First Assignment, due January 22, 2009

Write a mathematical autobiography and email it to me. Be sure to include the words "math 436" in the subject line. Include your name, recent mathematics courses you have taken, and reflect on which were your favorites and which were hardest. Describe your mathematical interests, and your post-graduation plans. Explain why you have chosen to register for this course and what you expect from it.
Be creative and tell your story in complete sentences. One of the purposes of the assignment is to give me a sample of your writing style.

Tentative Course Syllabus

Week Lecture dates Sections topics
11/20, 1/22 Chapter 1 Egypt and Mesopotamian Mathematics
21/27, 1/29 Chapters 1 & 2 Babylonian and Early Greek Mathematics (Euclid)
32/3, 2/5 Chapters 2 & 3 Greek Mathematics (Euclid & Archimedes)
42/10, 2/12 Chapter 3 & 4Post-Euclid Greek Mathematics (Classic Greek Problems)
52/17, 2/19 Chapters 4 & 5Late Greek and Ancient Chinese Mathematics
62/24, 2/26 Chapter 6Indian Mathematics
73/3, 3/5 Chapter 7Islamic Mathematics
83/10, 3/12Review, Midterm The Midterm on Thursday covers chapters 1-7
93/17, 3/19 R&R SPRING BREAK
103/24, 3/26 Chapters 8 & 9Medieval and Renaissance Europe
113/31, 4/2 Chapter 10The Pre-Calculus Era
124/7, 4/9 Chapter 11The discovery of Calculus
134/14, 4/16 Chapters 12 & 13Euler and the 18th Century; Probability Theory
144/21, 4/23 Chapters 14 & 16Algebra & Linear Algebra
154/28, 4/30 Chapter 15Non-Euclidean Geometry, Review



Return to Top of page Last updated: April 2009; C. Weibel

Charles Weibel / weibel@math.rutgers.edu / Spring 2009