01:640:437 HISTORY OF MATHEMATICS (Spring 2023)

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 these branches and notable people in mathematics, as well as to understand some key motivational ideas.

Time and Place: Monday and Thursday 10:20 AM - 11:40 AM; Busch Campus, SEC-207, Rutgers University.

Lecturer: Stoyan Dimitrov (emailТoStoyan {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	The peculiar story of the solution of the cubic. Cardano, Tartaglia and others.	[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, The paper of G.Shafer	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]	PDF file
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 a subject to slight changes.

Grading:

[35%] Topic paper on famous mathematicians at a given university or from a given country, or on the historical development of a mathematical branch.

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 or 8. The due date to submit the paper is the Thursday class of week 8. 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 the Thursday class of week 15. The biographical papers must be between 3 and 4 pages excluding bibliography (font 11, don't use huge or tiny margins). A good biographical paper should discuss one or more 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 Thursday class of week 13. Access the Homework problems

[15%] Weekly quizes.
Every week (except when we have presentations), a short 10-minutes quiz will be given, at the end of our Monday class.

Additional comments:

• This is the official site of the course. The Canvas page of the class will be used only for announcements and to enter grades.
• Keep in mind the due dates for the Topic paper and the Homework (the Thursday sections of Week 8 and Week 13, respectively), and the Biographical paper (the Thursday sections of Week 15). Please, print your assignments out and bring them to class.
• Attendance is not mandatory. However, if you miss a class, you will have 0 points on the quiz given at the end. During finals' week, you will have a short, but more difficult test (than the quizzes), allowing you to compensate the missed quizzes or get bonus points.
• Contact me via email if you have any questions or objections to any of your grades. I am always happy to increase your grade if you can motivate yourself and if you are not afraid from discussion.
• I expect a respectful behaviour during our classes. Cell phones should not necessarily be turned off, but they can be used only by exclusion.
• Plagiarism and cheating in any form is strongly prohibited, when working on all of your assignments! All students in the course are expected to be familiar with and abide by the academic integrity policy
• Rutgers is fully committed to compliance with the Americans with Disabilities Act; policies and procedures are indicated at http://ods.rutgers.edu. Students who wish to request special accommodations must present a Letter of Accommodations to the instructor as early in the terms as possible.

HALL OF FAME (Top scorers in the class):
Mehraaj Tawa: 98%, Eran Abeysekera: 97%, Anastasiya Chuchkova: 95%.

Selected presentations:

1. Little-known facts about Ramanujan by Rajas Chordiya
2. The value created by hedge funds by Pranay Doshi
3. The Universities of Berlin by Mehraaj Tawa
4. Physicist and Mathematician - Joseph-Louis Lagrange by Mehraaj Tawa
5. Biography of Andrei Kolmogorov by Anastasiya Chuchkova

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