MATH 394
Galois Theory Spring 2018 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#: 3684
Requirements/Evaluation: evaluation will be based primarily on written homeworks, oral presentations, and exams
Extra Info: may not be taken on a pass/fail basis
Prerequisites: MATH 355
Enrollment Preference: discretion of the instructor
Distributions: Division III; Quantative/Formal Reasoning;

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