Linear Algebra through Geometry
09/12/2005 - 12/17/2005
Monday 07:00 PM - 09:30 PM
Science Tower 139
Special Schedule: July 4th Holiday makeup class will be held Friday, July 8 from 9:00-12:00
Linear algebra is a subject with a dual nature; the central ideas are both algebraic and geometric. While the power of the subject comes from the algebra, the ideas are perhaps best understood by emphasizing their geometric content, which is the geometry of lines, planes, and their higher dimensional analogues.
In this course, we will develop the subject first in two dimensions, where the geometry and algebra are simplest, and then in three dimensions, where it is still possible to visualize the geometry. Once the subject is understood in these settings, we will see how (and how easily) the subject extends to higher dimensions. In particular, we will see how the algebra we develop with the aid of geometry can then be used to investigate geometric objects that we are unable to visualize.
Regular homework will be assigned and will be an essential part of the learning process.
No mathematical background is required beyond high school algebra and geometry.
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:
Banchoff and Wermer, LINEAR ALGEBRA THROUGH GEOMETRY (Springer), Hardcover
READING MATERIALS AVAILABLE AT BROAD STREET BOOKS, 45 BROAD STREET, MIDDLETOWN, 860-685-7323
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