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| MA 45401 - Galois Theory Honors |
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Credit Hours: 3.00. This course will give a thorough introduction to Galois theory. Galois theory is a fundamental tool in many areas of mathematics, including number theory and algebraic geometry. This course will increase students' mathematical maturity and prepare them for graduate school. Topics include finite extension fields and their symmetries, ruler and compass constructions, complex roots of unity, solvable groups, and the solvability of polynomial equations by arithmetic and radical operations. This course is intended for third- or fourth-year students who have taken MA 45000 (Algebra Honors) or MA 45300 (Elements of Algebra I). Typically offered Spring.
3.000 Credit hours Syllabus Available Levels: Undergraduate, Graduate, Professional Schedule Types: Distance Learning, Lecture Offered By: College of Science Department: Mathematics Course Attributes: Honors, Upper Division May be offered at any of the following campuses: West Lafayette Learning Outcomes: 1. Know the historical background of Galois theory. 2. Know the classical version which addresses questions about roots of polynomials and the modern formulation in terms of abstract algebra. 3. Know about finite extension fields and their symmetries. 4. Know how Galois theory answers ancient questions about ruler and compass constructions. 5. Know about cyclotomic fields generated by complex roots of unity. 6. Know how Galois theory answers questions about the solvability of polynomial equations by arithmetic and radical operations. Prerequisites: Undergraduate level MA 45000 Minimum Grade of B- or Undergraduate level MA 45300 Minimum Grade of B- |
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