Euclidean and Non-Euclidean Geometries
06/26/2006 - 08/10/2006
Monday & Wednesday 01:30 PM - 04:00 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.
There will be regular homework and exams.
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
|Level: GLSP||Credits: 3||Enrollment Limit: 18|
Texts to purchase for this course:
Robin Hartshorne, GEOMETRY: EUCLID AND BEYOND (Spring), Hardcover
READING MATERIALS AVAILABLE AT BROAD STREET BOOKS, 45 BROAD STREET, MIDDLETOWN, 860-685-7323
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