Grad Algebra II
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Textbook: None. All lecture notes will be posted right here. You might notice that the lectures borrow heavily from Paolo Aluffi's Algebra: Chapter 0. | ||
| Item | Date | Information |
|---|---|---|
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Homework 1 Solutions |
Thurs Feb 4 |
Course Notes Differences between Ab and Grp Concrete vs. Abstract Rings The category Rng The category R-Mod The definition of "Abelian Category" |
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Homework 2 Solutions |
Thurs Mar 3 |
Course Notes Field => Euclidean => PID => UFD Free Modules Modules over a field have dimension Modules over a domain have rank Key Lemma for PIDs: submodule of free is free F.T.F.G.M.P.I.D., Part I |
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Midterm Exam
Review Notes Solutions |
Tues Mar 15 |
Total = 32 Average = 24.5 Median = 26 St Dev = 6.1 |
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Homework 3 Solutions |
Tues, Apr 12 |
Course Notes The Category/ies R-Alg Matrix Notation RREF, Hermite Normal Form Smith Normal Form F.T.F.G.M.P.I.D., Part II |
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Homework 4 Solutions |
Wed, Apr 27 |
Course Notes Fundamental Theorem of f.g. Abelian Groups K[x]-Modules Rational & Jordan Canonical Forms Minimal & Characteristic Polynomials Epilogue: Restriction & Extension of Scalars |
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Final Exam
Review Notes Solutions |
Wed May 4 |
Total = 34 Average = 25.4 Median = 26 St Dev = 6.6 |
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Qualifying Exam List of Topics Solutions |
Thurs May 26 |
Total = 43 Average = 35.6 Median = 35.8 St Dev = 4.7 |