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ABSTRACT ALGEBRA I

INSTRUCTOR: Greg Naber
OFFICE: Korman Center 255
OFFICE HOURS: MTWR 9:00‐9:50, or by appointment
TEXT: Algebra: Abstract and Concrete , Frederick M. Goodman

“Abstract” means “disassociated from any specific instance”. Abstract mathematical structures are essentially what is left when all of the superficial, cosmetic features are pruned away from various specific instances, that is, from the examples. These come in a number of flavors (algebraic, topological, analytic, etc.) and their great virtue is that they allow one to learn something about all of the examples by studying just one object. Understanding the properties of linear transformations on abstract vector spaces, for example, provides concrete information about systems of linear equations, linear ordinary and partial differential equations, and linear integral equations, etc. The objective of this course is to examine a few such algebraic structures (groups, rings, fields, modules) in whatever depth our time constraints will allow. Presumably, everyone in the class has been exposed to these ideas before, in an undergraduate class, but no assumption will be made that you have brought with you any of the theorems that you learned there. We will start from scratch, but will assume that many of the more elementary arguments can be left for you to read on your own. The text is quite a good one; very detailed and very readable and, best of all, available free online (although Professor Goodman asks that, in lieu of an author’s royalty, everyone make a contribution to some humanitarian organization such as ). Course grades will be based on two tests, one about halfway through the course and one at the end, both weighted equally.

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