MATH 250C Spring 2017

Course Information

Lectures: MWF 4:10 in 1128 Bainer.
Final: Friday, June 9 from 3:30 to 5:30.
Text: Advanced Modern Algebra second edition by Joseph Rotman.
Syllabus: Department Syllabus.

Course Outline: The course will cover representation theory from sections 7.3 to 7.5, categories from sections 6.2 to 6.3 and possibly 7.8 to 7.9 and homology from sections 9.4 and 9.6 and possibly 9.5, 9.7 and 9.8.

This is a rough and optimistic outline of when topics will be covered and will be edited as the term progresses. The exam scheduling will not change. Homework problems will also be added with assignments collected on Friday s.

 Day Date Section(#s) covered Homework Monday April 3 7.3-7.5: Finite group representations Wednesday April 5 7.3: semisimplicity Friday April 7 7.4: Artin-Wedderburn Monday April 10 7.4: Maschke Wednesday April 12 7.4: KG examples Friday April 14 7.4: 6.7, 6.14, 6.21, 7.19, 7.22, 7.25 Monday April 17 7.5: Characters Wednesday April 19 7.5: Characters Friday April 21 7.5: Characters inner product 7.20, 7.23, 7.27, 7.32. Monday April 24 7.5 Character tables Wednesday April 26 7.5 Restriction/Induction Friday April 28 7.5 Frobenius Reciprocity 7.29, 7.30, 7.34, 7.35, 7.38, 7.39. Monday May 1 Midterm Wednesday May 3 Thurston Lecture Friday May 5 6.2: Categories Monday May 8 6.3: Functors 7.41, Midterm Problems Wednesday May 10 6.9: Limits Friday May 12 6.9: Limits Monday May 15 6.10: Adjoints 6.35, 6.41, 6.43, 6.46, 6.47, 6.53, 6.54, 6.56. Wednesday May 17 6.10: Adjoints Friday May 19 6.9: Additive Categories Monday May 22 7.8: Abelian Categories 6.102, 6.103, 6.105, 6.109, 6.111, 6.112. Wednesday May 24 7.9: Module Categories Friday May 26 9.4: Homological Algebra Monday May 29 no class Wednesday May 31 9.4: Resolutions 7.67, 7.74, 7.77, 7.79, 7.84. Friday June 2 9.5: Derived Functors Monday June 5 9.6: Ext Wednesday June 7 9.6: ext and extensions Do not turn in: 9.23, 9.37, 9.38, 9.46, 9.52. Friday June 9 final 3:30-5:30