Math 300 A Concise History of Mathematics

**Instructor:** Ali Sinan Sertöz

**Homepage: **http://www.fen.bilkent.edu.tr/~sertoz**
Phone: **290 1490

Office:

Schedule:

Thursday 14:40-16:30 SBZ-04

Text Book:

Undergraduate Texts in Mathematics, Springer-Verlag 1994.

**Syllabus**: Numbers in brackets denote the chapters from
the book around which the discussions will proceed.

24-27 September 2001: (1,2)

General discussion about methods. Given a certain era, what is known then? Which civilization is attributed with the discovery? What are the other civilizations doing then? What is the significance of that knowledge then, and now?

What are the evidences on which we build all these discussions?

The Moscow papyrus, the Rhind papyrus, Plimpton 322 tablet.1-4 October 2001: (3,4,5,6,7)

Thales, Pythagoras and Euclid

*Elements*.8-11 October 2001: (8,9)

More on*Elements*.

Concept of infinity in ancient times.15-18 October 2001: (10,11,12)

Plato, Aristotle, Eudoxus.22-25 October 2001: (13,14,15)

Ruler and compass constructions.

More on*Elements*.1 November 2001: (16,17)

Archimedes, Apollonius.5-8 November 2001: (18,19,20,21)

Early Medieval mathematics.12-15 November 2001: (22,23)

Late Medieval mathematics.19-22 November 2001: (24,25)

Finding roots of polynomials; cubics and quartics.26-29 November 2001: (26,27,28)

Napier, Galileo, Kepler, Desargues, Descartes, Fermat.3-6 December 2001: (29,30,31)

Pascal, Newton, Leibniz.10-13 December 2001: (32,33)

Euler, Lagrange.20 December 2001: (34,35)

Nineteenth century algebra and analysis.24-27 December 2001: (36,37)

Nineteenth century geometry and number theory.2 January 2002: (38,39,40)

Twentieth century: Hilbert's problem list.

**Grading: **Each student is required to prepare two term-projects; one on
an ancient and one on a more recent mathematical concept or a mathematician. The grading
will then depend on the creative approach and the depth and breadth of the final
work. There will be a written final exam where students will be able choose from a set of
questions those which are akin to their interests and will have a chance of demonstrating
their understanding and interpretation of this concise history of mathematics. No other
homework or quizzes are planned. Assesment: Term projects are 35% each, final exam is 30%.

**Optional: **There will be optional extra hours where we may view videos
from the department library about more recent topics of popular interest, or listen to
extracurricular topics of interest presented by participating students.

There are numerous internet sources for the history of mathematics. One such link is the Index of Biographies.

A Sample Answer Paper for the Final Exam is available here in two
formats:

DVI File PDF File