Abstract Algebra I
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Here is is a textbook that I wrote for MTH 561 and 562.
Office Hours: via Zoom, Wed and Thurs at 3-4pm Here is the syllabus. This course has an optional writing credit. | ||
| Assignment | Due Date | Topics |
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Homework 1 Solutions |
Thurs, Aug 31 |
Introduction: Abel-Ruffini Theorem Axioms of Groups Permutations Old Notes on Matrices Old Notes on Determinants |
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Homework 2 Solutions |
Thurs, Sept 14 |
Meet and Join of Subgroups Cyclic Groups Isomorphism of Groups Dihedral Groups Othogonal Groups |
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Exam 1: Thurs, Sept 21 Exam Solutions | ||
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Homework 3 Solutions |
Tues, Oct 10 |
Posets and Lattices Kernel and Image of a Homomorphism Correspondence Theorem for Groups Fundamental Theorem of Cyclic Groups The Euler-Fermat Theorem |
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Homework 4 Solutions |
Thurs, Oct 19 |
Equivalence Modulo a Subgroup Cosets and Lagrange's Theorem Direct Products Chinese Remainder Theorem Normal Subgroups |
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Exam 2: Thurs, Oct 26 Exam Solutions | ||
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Homework 5 Solutions |
Tues, Nov 14 |
First Isomorphism Theorem Group Actions Burnside's Lemma Euler's Totient Function |
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Homework 6 Solutions |
Tues, Dec 12 |
"Hard" vs "Soft" Group Theory Cauchy's Theorem Second Isomorphism Theorem Groups of Size p^2 Unsolvability of S_n |