Abstract Algebra II
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There is no required textbook. All lecture notes will be posted here. For further reading I recommend Michael Artin's Algebra and Charles C. Pinter's Book of Abstract Algebra.
Office Hours: Thurs 3:00-5:00pm on Zoom. Also by appointment. Here is the syllabus. | ||
| Course Notes | ||
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| Item | Date | Information |
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Homework 1 Solutions |
Fri, Feb 4 |
Intermediate Value Theorem Multivariable Polynomials Permutations Symmetric Polynomials Laplace's Proof of the FTA |
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Homework 2 Solutions |
Fri, Feb 18 |
Preview of Kronecker's Theorem Congruence Modulo a Subgroup Lagrange's Theorem Orbit-Stabilizer Theorem |
| Exam 1: Wed Feb 23, in class Solutions | ||
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Homework 3 Solutions |
Fri, Mar 11 |
Normal Subgroups Quotient Groups First Isomorphism Theorem |
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Homework 4 Solutions |
Mon, Mar 28 |
Isomorphism Classes of Groups Cyclic Groups Cyclotomic Polynomials |
| Exam 2: Fri Apr 1, in class Solutions | ||
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Homework 5 Solutions |
Fri, Apr 15 |
Ideals and Quotient Rings First Isomorphism Theorem for Rings Minimal Polynomials |
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Homework 6 Solutions |
Fri, Apr 29 |
Existence of Splitting Fields Existence of Finite Fields Uniqueness of Splitting Fields Uniqueness of Finite Fields |
| Exam 3: Mon May 2, in class Solutions | ||