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.
|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.||, , ||PDF file|
|4||More math from Ancient Greece: The problems of Diophantus and the paradoxes of Zeno.||, , ||PDF file|
|5||Cardano and the solution of the cubic.||, this Quanta article|
|6||The development of Analysis. John Willis and the Newton-Leibniz rivalry.||, , The book of A. Alexander|
|7||Presentations of the topic papers (i.e., the midterm exam).|
|8||Some results of Euler and Gauss.||, ||9||The development of Probability and Statistics: The correspondence between Pascal and Fermat. The works of Ronald Fisher.||The book of K. Devlin,
Wiki link 1, Wiki link 2
|10||The development of Algebra, Combinatorics and Algorithms.||to be added||11||Euclidian and Non-Euclidian Geometries.||, , |
|12||Cantor and the infinity paradoxes.||to be added||13||Hilbert’s problems. The results of Kurt Godel and their implications.||to be added|
|14||Walk through 20th century math events. Bourbakism, Grothendieck, Shannon and others. Big proofs and open problems.||to be added|
|15||Presentations of the biographical papers (i.e., the final exam)|
[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).
[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.