Math 200: Introduction to Algebraic Structures

Topics:	The course is unevenly divided into three parts: basic arithmetic in the integers and definitions, examples and first properties of groups, Sylow theorems; theory of rings and modules with application of (non)-unique factorization in rings and to classification of modules over a Euclidean domain, which is in turn used to derive rational canonical form of matrices and the classification of finitely-generated abelian groups; theory of fields, finite extensions of the rationals, with application to non-trisectability of angles using straightedge and compass
Prerequisites:	A course in linear algebra that includes Gaussian elimination, determinants and their properties and some theory of abstract vector spaces (basis, dimension, linear transformation); and the ability to write clear and correct proofs.
Text:	Abstract Algebra by D. Dummitt and R. Foote
Professor:	William Pardon 219 Physics 660-2838 wlp@math.duke.edu
Office Hours:	Monday, 1-3 and by appointment
Lectures:	Tuesdays and Thursdays, 8:30-9:45, Physics 205
Requirements and Grading:	There will be a midterm exam, a final exam and weekly homework. Some problems from the homework will reappear on exams. Your final letter grade will be based on these components weighted as follows: homework 15%, midterm exam 25%, final exam 40%.
Collaboration:	You may (and are encouraged to) discuss issues raised in class or the homework problems with your fellow students and both offer and receive advice. However all your homework must be written up by you and you alone. For the midterm and the final exam, you will work entirely on your own. With this understood, you must reaffirm your committment to the Duke Community Standard on all submitted work.
Links:	Syllabus

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