MATH 394
Galois Theory Spring 2024
Division III Quantitative/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 finite combinations of 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: Format: lecture
Limit: 30
Expected: 15
Class#: 3507
Grading: no pass/fail option, yes fifth course option
Requirements/Evaluation: problem sets and oral exams
Prerequisites: MATH 355
Enrollment Preferences: Juniors and seniors
Distributions: Division III Quantitative/Formal Reasoning
QFR Notes: This is a math class

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