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.
|1||Map of mathematics. Timeline of important math events and people. General questions about math.||, [5, Part I, VIII.7]||PDF file|
|2||Math in Egypt, Babylon and ancient China. Egyptian fractions and the Chinese Reminder Theorem.||, , ||PDF file|
|3||Big names: Math of Ancient Greece and Hindu-Arabic math.||, , |
|4||More math from Ancient Greece: The problems of Diophantus and the paradoxes of Zeno.||, , |
|5||The peculiar story of the solution of the cubic. Cardano, Tartaglia and others.||, this Quanta article|
|6||The development of Calculus. John Wallis and the Newton-Leibniz rivalry.||, , The book of A. Alexander|
|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.||, |
|10||The development of Probability and Statistics: The correspondence between Pascal and Fermat.||The book of K. Devlin,
The paper of G.Shafer
|11||The seven giants of statistics and some main theorems: LLN, CLT, the method of least squares.||Article 1 , Article 2|
|12||The development of Algebra.||||13||The development of Combinatorics and Algorithms.||, |
|14||Walk through math events in the 19th and 20th: Hilbert’s problems, Cantor and Godel. Big proofs and famous conjectures.|||
|15||Presentations of the biographical papers (i.e., the final exam)|
[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.
[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.
HALL OF FAME (Top scorers in the class):
[TO BE COMPLETED] >