History of Mathematics
Mathematics 436 — Spring 2009
TTh 6 (5:00-6:20AM) in SERC 211 (Busch Campus);
go to lecture table
Victor J. Katz, History of Mathematics: Brief Version.
Addison Wesley (ISBN: 0321161939), 2004.
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.
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.
Midterm examination: Tuesday, March 10 in class covering through week 7.
FINAL EXAM: Friday, May 8, 2009 12-3 PM in SERC 211
- 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
- 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
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
||Egypt and Mesopotamian Mathematics
||Chapters 1 & 2
||Babylonian and Early Greek Mathematics (Euclid)
||Chapters 2 & 3
||Greek Mathematics (Euclid & Archimedes)
| 4||2/10, 2/12
||Chapter 3 & 4||Post-Euclid Greek Mathematics
(Classic Greek Problems)
| 5||2/17, 2/19
||Chapters 4 & 5||Late Greek and Ancient Chinese Mathematics
| 6||2/24, 2/26
||Chapter 6||Indian Mathematics
| 7||3/3, 3/5
||Chapter 7||Islamic Mathematics
| 8||3/10, 3/12||Review, Midterm
||The Midterm on Thursday covers chapters 1-7
| 9||3/17, 3/19
|| SPRING BREAK
||Chapters 8 & 9||Medieval and Renaissance Europe
||Chapter 10||The Pre-Calculus Era
||Chapter 11||The discovery of Calculus
||Chapters 12 & 13||Euler and the 18th Century;
||Chapters 14 & 16||Algebra & Linear Algebra
||Chapter 15||Non-Euclidean Geometry, Review
Return to Top of page
Last updated: April 2009; C. Weibel
Charles Weibel / firstname.lastname@example.org /