MATH 400- HISTORY OF MATHEMATICS

Summer 2006 (1st. session)

Instructor: Dr. Alex Freire

SYLLABUS (PDF)

COURSE LOG AND HANDOUTS

PLAN:

The course will be based on three texts

1- The development of Analysis:

Based on the TEXT: The Calculus Gallery: Masterpieces from Newton to Lebesgue,

by William Dunham (Princeton U. Press, 2005). This book traces the development of Analysis from

Newton and Leibniz to the early 20th century, through the work of Newton, Leibniz, Bernouilli(s),

Euler, Cauchy, Liouville, Riemann, Weierstrass, Cantor, Volterra, Baire and Lebesgue. Some biography,

but emphasis on the mathematical development.

2- The Prime Number Theorem and the Riemann Hypothesis

Based on the TEXT: Prime Obsession: Bernhard Riemann and the Greatest Unsolved

Problem of Mathematics, by John Derbyshire (Penguin paperback, 2004). This is a "popular"

account, alternating historical and mathematical chapters. It is centered around Bernhard Riemann

and his 1859 paper on the `prime number theorem'. Also figuring prominently are Euler, Gauss, Dirichlet,

Chebyshev, Dedekind, Hadamard, Hilbert, Landau, Hardy and others.

Both texts have been ordered by the UTK bookstore, but if you want to get a head start

(and possibly save some $$$) , there is always Amazon.

The goal is to learn as much as possible of the historical/human context and the mathematics along

both axes. Of course, the depth of the mathematics presented will be tailored to the students taking

the class, but we should all (students and instructor) aim to learn both history and math.

3-TEXT: A concise history of mathematics, Dirk Struik