Course Identification

1. Mathematics in ancient Egypt.
2. Mathematics in Mesopotamia (mostly Babylonia).
3. The Greek Revolution.
4. Greek mathematics slightly later .
5. Archimedes.
6. Late Greek mathematics.
7. The five problems.
8. The middle ages.
9. Renaissance and the sixteenth century.
10. Infinitesimal calculus.
11. Leibniz.
12. The eighteenth century.
13. The nineteenth century (in the extended sense) and its revolutions.
14. Gauss.
15. Riemann.
16. Hilbert and Poincare.
17. Set theory.
18. Logic, Goedel and foundations of mathematics.
19. Various philosophical approaches.
20. Influence of events and fashions in mathematics on math teaching and on textbooks.
21. Abraham Robinson and his contributions.
22. Development of mathematics in the second half of the second half of the twentieth century and earlier twenty-first century. In particular the influence of computers and the solutions of long-standing problems.

Upon successful completion of the course students will be able to:

1. Demonstrate at least a superficial understanding of the problems of the philosophy of mathematics
2. Demonstrate acquaintance with the development of mathematical ideas, concepts and methods from antiquity to the present.

ישראל קליינר (ISRAEL KLEINER) מאמרים נבחרים בהסטוריה של המתמטיקה : בעריכת נצה
מובשוביץ-הדר, חיפה: מעלות, תשנ"ה 1994.

The mathematical experience , by Philip J. Davis, Reuben Hersh, Elena Anne Marchisotto ; with an introduction by Gian-Carlo Rota.: Springer, 1995, 2003 3rd printing.

A concise history of mathematics, by Dirk J. Struik, Dover, 1987.

http://www.math.cuhk.edu.hk./course_builder/1718/math1010a/university_math_intro.pdf