01:640:437 HISTORY OF MATHEMATICS course (Fall 2022)


Main goals: During this course, we will study about ideas and people who were among the most important for the development of the different branches of mathematics. A major goal will be to stimulate further interest in learning about some of these branches and about the life and work of notable people in the subject.


Time and Place: Monday and Thursday 8:30 AM - 9:50 AM; Busch Campus, SEC-216, Rutgers University.

Lecturer: Stoyan Dimitrov (ЕmailТoStoyan {at} gmail [dot] com).
Office Hours: Friday, 3:40pm - 5pm via Zoom (write me an email some time before 3:40pm and I will send you a Zoom link)

Syllables:

Week Topic Sources Presentation
1 Map of mathematics. Timeline of important math events and people. General questions about math. [4], [5, Part I, VIII.7] PDF file
2 Math in Egypt, Babylon and ancient China. Egyptian fractions and the Chinese Reminder Theorem. [1], [3], [4] PDF file
3 Big names: Math of Ancient Greece and Hindu-Arabic math. [2], [3], [5] PDF file
4 More math from Ancient Greece: The problems of Diophantus and the paradoxes of Zeno. [1], [3], [5] PDF file
5 Cardano and the solution of the cubic. [2], this Quanta article PDF file
6 The development of Calculus. John Wallis and the Newton-Leibniz rivalry. [1], [4], The book of A. Alexander PDF file
7 Presentations of the topic papers (i.e., the midterm exam).
8 Presentations of the topic papers (i.e., the midterm exam).
9 Some results of Euler and Gauss. [2], [4] PDF file
10 The development of Probability and Statistics: The correspondence between Pascal and Fermat. The book of K. Devlin,
Wiki link 1, Wiki link 2
PDF file
11 The seven giants of statistics and some main theorems: LLN, CLT, the method of least squares. Article 1 , Article 2 PDF file
12 The development of Algebra. [1] PDF file
13 The development of Combinatorics and Algorithms. [1], [6] PDF file
14 Walk through math events in the 19th and 20th: Hilbert’s problems, Cantor and Godel. Big proofs and famous conjectures. [5]
15 Presentations of the biographical papers (i.e., the final exam)

Bibliography:

  1. „A history of mathematics“, C. Boyer, U. Merzbach.
  2. „Journey through genius, The great theorems of mathematics“, W. Dunham.
  3. „A Concise History of Mathematics: Fourth Revised Edition“, D. Struik.
  4. „The Mathematical Experience“, P. Davis, R. Hersh.
  5. „The Princeton Companion of Mathematics“, T. Gowers.
  6. "History of mathematics: An introduction", V. Katz, 2nd edition
Disclaimer: The schedule of topics is subject to change.

Grading:

[35%] Topic paper on the historical development of a mathematical field or on another topic related to history of mathematics.

Go to this link and select a topic from the list there. You can also suggest your own topic (more details in the link itself). I advise you to select your topic by the end of the 3rd week of classes. Each student will present his paper during week 7. The due date to submit the paper is the end of week 7 (Sunday, 11:59pm). The paper must be between 4 and 5 pages excluding bibliography (font 11, don't use huge or tiny margins). A good paper should discuss in details some mathematical results and explain them in accessible form to the reader. The evaluation criteria include: quality of the content and the included information, the quality of the mathematical explanation, writing style and clarity.

[25%] Biographical paper on the life and work of a famous mathematician.

Go to this link and select one name of a mathematician for your biographical paper from the list there. You can also suggest a name not in the list (more details in the link itself). I advise you to select your mathematician by the end of the 8th week of classes. Each student will present his biographical paper during week 15 (the last week). The due date to submit your biographical paper is the end of week 14 (Sunday, 11:59pm). The biographical papers must be between 2 and 3 pages excluding bibliography (font 11, don't use huge or tiny margins). A good biographical paper should discuss one of the mathematical results of the person the paper is about. The evaluation criteria include: quality of the content and the included information, how much math is explained and how well, writing style and clarity.

[25%] Homework on mathematical problems.

This will be a written homework over some problems related to the mathematics discussed during lectures. The due date to submit your homework is the end of week 13 (Sunday, 11:59pm).

Access the Homework problems

[15%] Weekly quizes.
Every week (except in weeks 1,7 and 15), a short 10-minutes quiz will be given, at the end of our first class for the week (i.e., the Monday section). Your 10 best quizzes will be part of your final grade.

Additional comments: