COURSE AIMS AND OBJECTIVES: To give a unified view of undergraduate mathematics by approaching the subject through its history
COURSE DESCRIPTION AND SYLLABUS:
1. Babylonian and Egyptian mathematics.
2. The beginnings of mathematics in Greece. The theorem of Pythagoras. Perfect numbers. Incommensurable quantities.
3. Eudoxus' theory of proportion and method of exhaustion.
4. Euclid's Elements. Apollonius' Conic sections.
5. Archimedes, Aristarchus and Eratosthenes.
6. Hipparchus, Ptolemy, Diophantes.
7. Medieval mathematics of India and Islam. Mathematics in medieval Europe.
8. Algebra in the Renaissance.
9. Early infinitesimal methods (Galileo, Kepler, Cavelieri)
10. Analytic geometry of Fermat and Descartes.
11. Newton's calculus of series and the calculus of Leibniz.
12. Euler's analysis.
13. Arithmetization of analysis (Weierstrass, Dedekind, Cantor)
14. Twentieth century mathematics. Set theory, topology, measure theory.
15. New ideas in algebra. Logic and computability.