Abstract Algebra (WI21)
Course Info:
- Lectures: Monday, Wednesday, Friday, block E (1:10 - 2:15 p.m. EST)
- Course type: Remote with synchronous components (RSC)
- x-period: Tuesday, block EX (1:40 - 2:30 p.m. EST)
- Dates: 7 January 2021 - 10 March 2021
- Zoom Link: Use navigation bar. Send me an email if you have any problems.
- Instructor: John Voight
- E-mail: jvoight@gmail.com
- Office hours: during x-hour, or please make an appointment by email!
- Course Web Page: https://canvas.dartmouth.edu/courses/44838 (or http://www.math.dartmouth.edu/~m81w21/ redirects)
- Prerequisites: Math 71, or Math 31 and permission. If you are unsure about your preparation, please talk to the instructor!
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Required Texts:
- David Dummit and Richard Foote, Abstract Algebra, 3rd edition, 2004. [Roughly chapters 13-14.]
- Juliusz Brzeziński, Galois Theory Through Exercises, 1st edition, 2018.
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Recommended Texts:
- J.S. Milne, Fields and Galois theory, version 4.60.
- Serge Lang, Algebra, Graduate Texts in Mathematics, vol. 211, Third edition, 2005. [Roughly chapters IV-VI.]
- Ian Stewart, Galois Theory, Fourth edition, 2015.
- Grading: Grade will be based on weekly homework and a takehome final exam (see Grading).
Course Catalogue Description:
This course provides a foundation in core areas in the theory of rings and fields. Specifically, it provides an introduction to commutative ring theory with a particular emphasis on polynomial rings and their applications to unique factorization and to finite and algebraic extensions of fields. The study of fields continues with an introduction to Galois Theory, including the fundamental theorem of Galois Theory and numerous applications.
Learning Outcomes:
By the end of this course, you should be able to:
- Understand of the basic structures of Galois theory: define terms, explain their significance, and apply them in context;
- Solve mathematical problems: utilize abstraction and think creatively, using Magma for computation.
Additional Pages:
Course Summary:
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