in the history of mathematics, discussed in full technical detail
but with stress on the underlying ideas, their evolution and
The course will trace the evolution of various areas of mathematics, such
as analysis, algebra, and geometry. While it will involve a great deal of
technical mathematics, the course will also explore issues closely bound up
with its progress, such as the changing standards of rigor in mathematics,
the cultural context of mathematics, the roles of problems and crises in
the development of mathematics, and the roles of intuition and logic in its
Students will be expected to write a major paper depicting the evolution of
a given problem, general principle, concept, or subfield of mathematics;
for example, function, the real numbers, distribution of primes, the
arithmetization of analysis, fashions in mathematics, the rise of rigorous
proof, or Fermat's Last Theorem.
The course will not follow a prescribed text, but the following book is
recommended: V.J. Katz, A History of Mathematics
(2nd Ed.), Addison-Wesley, 1998.
Many references, on various topics, will be given in class.
The final grade will be based on a major paper (20%), other assignments
(30%), two tests (20%), and a final exam (30%).
Prerequisite:36 credits from MATH courses without second digit
5, including at least 12 credits at or above the 3000 level. (12
of the 36 credits may be taken as corequisites.)
Coordinator: Israel Kleiner