Summer 2006 (1st. session)
Instructor: Dr. Alex Freire


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