MATH 484
Galois Theory Spring 2020
Division III Quantative/Formal Reasoning

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Some equations–such as x^5 – 1 = 0–are easy to solve. Others–such as x^5 – x – 1 = 0–are very hard, if not impossible (using standard mathematical operations). Galois discovered a deep connection between field theory and group theory that led to a criterion for checking whether or not a given polynomial can be easily solved. His discovery also led to many other breakthroughs, for example proving the impossibility of squaring the circle or trisecting a typical angle using compass and straightedge. From these not-so-humble beginnings, Galois theory has become a fundamental concept in modern mathematics, from topology to number theory. In this course we will develop the theory and explore its applications to other areas of math.
The Class: Type: lecture
Limit: 15
Expected: 10
Class#: 3550
Grading: no pass/fail option, yes fifth course option
Requirements/Evaluation: evaluation will be based primarily on written homeworks, oral presentations, and exams
Prerequisites: MATH 355
Enrollment Preferences: discretion of the instructor
Unit Notes: this course is not a senior seminar, so it does not fulfill the senior seminar requirement for the Math major
Distributions: Division III Quantative/Formal Reasoning

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