History of Mathematics
Mathematics 436 — Spring 2018

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. 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.

Term Paper

This course satisfies either of the SAS Writing and Communicating requirements (WCr and WCd).
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.
The finished paper is due by May 1.

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.


The course grade will be determined by the assigned homework (30%), the term paper (30%) and the two exams (40%).
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

Tentative Course Syllabus

Week Lecture dates Sections topics
1-21/16, 19, 23 Chapter 1 Egypt, Babylonian and Mesopotamian Mathematics
31/26, 1/30 Chapter 2 (brief version) Early Greek Mathematics (Euclid)
42/2, 2/6 Chapters 2 & 3 (brief) Greek Mathematics (Euclid & Archimedes)
52/9 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, 3/9Review, Midterm The Midterm on Friday covers
ch. 1-6 (brief) viz. ch.1-8 (long)
9+3/13, 3/16 R&R SPRING BREAK
103/20, 3/23 Chapters 8&9 (10&12 long)Medieval and Early Renaissance Europe
113/27, 3/30, 4/2 Chapter 10 (12-13 long)Late Renaissance, and the Pre-Calculus Era
124/3, 4/6 Chapter 11 (15-16 long)The discovery of Calculus;
paper outline due 3/30 and paper draft due 4/6
134/10, 4/13 Ch. 12 & 14 (17&18 long)Euler, the 18th Century, Probability
144/17, 4/20 Ch.14,16.4,17.1 (19&21 long) Linear Algebra, Matrices & Continuity
154/24, 4/27 Chapters 13,15 (21-22 long)Probability, Linear Algebra, Review
16+5/9Cumulative (tbd) Final Exam (8-11AM on May 9)

First Assignment, due January 19

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 this assignment is to give me a sample of your writing style.

Homework Assignments

due January 26: Chapter 1, #3,5,6,9 (In the longer book it is #7,9,13 and: compute 5/13,6/13,8/13 using 2/13=1/8+1/52+1/104.)
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