|Welcome to Math 1100!|
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||Notes and Links
||About This Class; Monday - Non Commutative Gaussian Elimination; Thursday - the category of groups, automorphisms and conjugations, images and kernels.
||Monday - coset spaces, isomorphism theorems; Thursday - simple groups, Jordan-Holder decomposition series.
||Monday - alternating groups, group actions, The Simplicity of the Alternating Groups, HW1, HW 1 Solutions, Class Photo; Thursday - group actions, Orbit-Stabilizer Thm, Class Equation.
||Monday - Cauchy's Thm, Sylow 1; Thursday - Sylow 2.
||Monday - Sylow 3, semi-direct products, braids; HW2; HW 2 Solutions; Thursday - braids, groups of order 12, Braids
||No class Monday (Thanksgiving); Thursday - groups of order 12 cont'd.
||Term Test; Term Test Solutions on Monday, HW3; HW 3 Solutions; Thursday - solvable groups, rings: defn's & examples.
||Monday - functors, Cayley-Hamilton Thm, ideals, iso thm 1; Thursday - iso thms 2-4, integral domains, maximal ideals, One Theorem, Three Corollaries, Five Weeks
||Monday - prime ideals, primes & irreducibles, UFD's, Euc.DomainPID, Thursday - Noetherian rings, PIDUFD, Euclidean Algorithm, modules: defn & examples, HW4, HW 4 Solutions
||Monday - R is a PID iff R has a D-H norm, R-modules, direct sums, every f.g. module is given by a presentation matrix, Thursday - row & column reductions plus, existence part of Thm 1 in 1t3c5w handout.
||Monday-Tuesday is UofT's Fall Break, HW5, Thursday - 1t3c5w handout cont'd, JCF Tricks & Programs handout
||Monday - JCF Tricks & Programs cont'd, tensor products, Thursday - tensor products cont'd
||End-of-Course Schedule; Monday - tensor products finale, extension/reduction of scalars, uniqueness part of Thm 1 in 1t3c5w, localization & fields of fractions; Wednesday is a "makeup Monday"!; Notes for Studying for the Final Exam Glossary of terms
||The Final Exam
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See Non Commutative Gaussian Elimination