Abstract Algebra I
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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: Mondays 4-5pm and Wednesdays 1-2pm Here is the syllabus. | ||
| Course Notes | ||
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| Item | Date | Information |
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Homework 1 Solutions in the Notes |
Fri Aug 31 |
Quadratic and Cardano Formulas Lagrange's Method Permutations Definition of Group and Subgroup |
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Homework 2 Solutions in the Notes |
Fri Sept 14 |
Subgroup Generated by a Subset Intersection and Join Examples of Cyclic Groups Definition of Isomorphism |
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Exam 1 Solutions |
Fri Sept 21 |
Total = 21 Average = 16.8 Median = 17 St Dev = 4.8 |
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Homework 3 Solutions in the Notes |
Fri Oct 5 |
Posets and Lattices Subgroups of Z Galois Connections Fundamental Theorem of Cyclic Groups |
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Homework 4 Solutions in the Notes |
Mon Oct 22 |
Equivalence Modulo a Subgroup Lagrange's Theorem Normal Subgroups and Quotients First Isomorphism Theorem Definition of Group Actions |
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Exam 2 Solutions | Fri Oct 26 |
Total = 24 Average = 18.5 Median = 20.5 St Dev = 4.6 |
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Homework 5 Solutions in the Notes |
Fri Nov 16 |
Multiplication of Groups Direct and Semidirect Products Isometries of Euclidean Space Simple and Solvable Groups The Orbit-Stabilizer Theorem |
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Homework 6 Solutions in the Notes |
Thurs Nov 29 |
Free and Transitive Group Actions The Class Equation Groups of Size p and p^2 S_n is Not Solvable A_5 is Simple |
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Exam 3 Solutions | Mon Dec 3 |
Total = 24 Average = 18.1 Median = 29.0 St Dev = 5.2 |