Summer 2005

MTHS 640
A Mathematical Sampler


06/27/2005 - 08/10/2005
Monday & Wednesday 01:30 PM - 04:00 PM

Public Affairs Center 125

We will present a wide variety of topics from elementary mathematics, chosen for their striking beauty, but also for their bearing on issues of considerable importance. Some of the topics to be discussed are: the decomposition of integers into prime factors, the distribution of the prime numbers, countable and uncountable sets, combinatorial topology and geometry, irrational and transcendental numbers, constructions with straight-edge and compass and their limitations, geometric properties of curves and surfaces, and the isoperimetric inequality.

"Elementary" here means having few mathematical prerequisites. Our discussions will show that elementary arguments can yield startling and profound results. In addition, we will discuss problems which can be formulated in elementary terms, but whose only known solutions are quite sophisticated, and others for which no solution has yet been found.

The course is an attempt to enable students to experience mathematics as a creative enterprise by using examples of imaginative discoveries in mathematics, and by giving them a chance to explore subjects on their own.

The source for most of the course material is a book, an enchanting masterpiece of exposition, called The Enjoyment of Mathematics, which was written first in the 1920s by two distinguished mathematicians, Hans Rademacher and Otto Toeplitz, and which remains absolutely fresh and lively.

Grades will be based on written work, which will be regularly assigned throughout the term.

Adam Fieldsteel (A.B. Brown University; Ph.D. University of California, Berkeley) is professor of mathematics. His research focuses on ergodic theory and topological dynamics, and his recent publications include: (with A. Blokh), "Sets that force recurrence," Proceedings of the American Mathematical Society (2002); (with K. Dajani), "Equipartition of interval partitions and an application to number theory," Proceedings of the American Mathematical Society (2001); (with R. Hasfura), "Dyadic equivalence to completely positive entropy," Transactions of the American Mathematical Society (1998). Click here for more information about Adam Fieldsteel.


Consent of Instructor Required: No

Format: Seminar

Level: GLSP Credits: 3 Enrollment Limit: 18

Texts to purchase for this course:
Rademacher & Toeplitz, THE ENJOYMENT OF MATHEMATICS (Dover), Paperback


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