MATH 400- HISTORY OF MATHEMATICS
Summer 2006 (1st. session)
Instructor: Dr. Alex Freire
COURSE LOG AND HANDOUTS
The course will be based on three texts
1- The development of Analysis:
Based on the TEXT: The Calculus Gallery: Masterpieces from Newton
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
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