Math 30810 Honors Algebra III (Fall 2021)
Groups and Rings

 

Date Lecture Topics Recording
08/23 Overview
08/25 Matrices
08/27 Zorn's lemma and vector space bases
08/30 Composition laws
09/01 Examples of groups
09/03 Operations on subgroups, subgroups of the integers
09/06 Bezout's identity, cyclic groups, orders
09/08 Homomorphisms, examples, homs of Q
09/10 Homomorphisms, conjugation, Im and ker
09/13 Normal subgroups, equivalence relations, quotients
09/15 Equivalence relations, equivalence classes
09/17 Group cosets
09/20 Applications of cosets
09/22 Groups quotients
09/24 Modular arithmetic, correspondence theorem Recording
09/27 Chinese Remainder Theorem Recording
09/29 The multiplicative group structure of modular arithmetic, Euler's theorem, Fermat's little theorem Recording
10/01 Euler's phi, CRT for multiplicative groups Recording
10/04 In-class Midterm
10/06 Wilson's theorem, orders of elements Recording
10/08 Primitive elements mod p Recording
10/11 Isomorphisms theorems Recording
10/13 Automorphism groups Recording
10/15 Automorphism groups and generators Recording
10/25 Generators, dihedral groups, SL_2(Z) Recording
10/27 Normal subgroups, symmetric groups Recording
10/29 Symmetric groups, inversions, generators, sign of a permutation Recording
11/01 Sign of permutation, normal subgroups of S_n Recording
11/03 Conjugation and semidirect products Recording
11/05 Group actions Recording
11/08 Group actions, orbits, stabilizers Recording
11/10 Class equation (Take-home Midterm due) Recording
11/12 The Sylow theorems Recording
11/15 Rings Recording
11/17 Polynomials Recording
11/19 Fraction fields Recording
11/22 Ideals, homomorphisms of rings Recording
11/29 Isomorphism theorems Recording
12/01 Prime ideals, maximal ideals Recording
12/03 Euclidean ringsa and unique factorization Recording
12/06 Unique factorization and Gaussian integers Recording

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