Spring 2004–05Ma 5c - Introduction to
Abstract Algebra |
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The third term of Ma 5 will cover field theory, Galois theory, and finish with representations of finite groups. The first two are found in Part IV of Dummit and Foote; the third is in Part VI. We will not cover all the material but selected portions. In the field theory and Galois theory portion we study field extensions, algebraic elements, Galois groups, and the connection between subgroups of the Galois group and subfields. We show not all angles can be trisected by straight edge and compass and some quintics cannot be solved by radicals alone. The topics in representation theory will be covered as time permits. Text: Dummit and Foote, Abstract Algebra. Class lectures will sometimes cover slightly different material and may cover material from a different point of view. In particular, exams and homework may involve material covered in lectures but not in Dummit-Foote. Grades: The grade will be determined on the basis of homework (60%) and a midterm (40%). There will be no final exam. Homework Policy: Students may work together on homework as long as each student writes up solutions individually in his or her own words. In solving homework problems, you should quote theorems and lemmas from class and the text. Results from the text in sections not yet covered will not receive credit unless the proof is supplied. One homework set may be turned in up to one week late. Other late homework will not be accepted for credit except in exceptional circumstances such as illness (in which case a note from the Dean will be expected) or other personal emergency.
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