The following is an estimate only - if you must miss a day please contact me or another student to find out what was covered.
- Week 1: Introduction to axiomatic systems and axioms of groups
- Week 2: Permutations and examples of groups
- Week 3: Subgroups, Cosets, Lagrange's Theorem
- Week 4: Homomorphisms, Kernel, Image, etc.
- Week 5: Quotient groups, Isomorphism Theorems
- Week 6: Group actions, orbits, conjugacy classes, etc.
- Week 7: Finite groups, Sylow theorems, counting
- Week 8: Review and Midterm Oct. 22
- Week 9: Axioms for Commutative rings, examples
- Week 10: Fields and Polynomial Rings
- Week 11: Homomorphisms and Ideals
- Week 12: Euclidean domains / properties of polynomials over a Field
- Week 13: Quotient rings, Isomophism theorems
- Week 14: Basic theory of fields
- Week 15: Construction/classification of finite fields
- Final Exam: Tues, Dec 11 8-10am, room TBA
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