Spring 2009

MTHS 638
Euclidean and Non-Euclidean Geometries

Fieldsteel,Adam

01/29/2009 - 05/07/2009
Thursday 06:00 PM - 08:30 PM

Science Tower 139

In the 19th century, it was discovered that the classical geometry of Euclid does not preclude other geometries of very different character. In the 20th century, it was realized that non-Euclidean geometries are essential to understanding the nature of the space we inhabit. This course will give a rigorous axiomatic development of Euclidean (planar) geometry and contrast it with the geometries that result from alterations in the axioms. We will pay particular attention to the important geometry of the hyperbolic plane. In addition, as time permits, we will discuss topics such as the introduction of coordinates into Euclidean and non-Euclidean planes and the theory of area.

We will read the book, Geometry: Euclid and Beyond by Robin Hartshorne.

Students need not have background in geometry beyond the high-school level, but will be expected to appreciate the logical development of the subject and to write carefully-reasoned geometrical proofs. This course is open to auditors.


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.


ENROLLMENT INFORMATION

Consent of Instructor Required: No

Format: Seminar

Level: GLSP Credits: 3 Enrollment Limit: 18

Texts to purchase for this course:
Robin Hartshorne, GEOMETRY: EUCLID AND BEYOND (Springer), Hardcover

READING MATERIALS ARE AVAILABLE AT BROAD STREET BOOKS, 45 BROAD STREET, MIDDLETOWN, 860-685-7323 Order your books online

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