Welcome to Math 1100! (additions to this web site no longer count towards good deed points)
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#
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Week of...
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Notes and Links
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1
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Sep 8
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About This Class; Monday - Non Commutative Gaussian Elimination; Thursday - the category of groups, automorphisms and conjugations, images and kernels.
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2
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Sep 15
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Monday - coset spaces, isomorphism theorems; Thursday - simple groups, Jordan-Holder decomposition series.
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3
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Sep 22
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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.
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4
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Sep 29
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Monday - Cauchy's Thm, Sylow 1; Thursday - Sylow 2.
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5
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Oct 6
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Monday - Sylow 3, semi-direct products, braids; HW2; HW 2 Solutions; Thursday - braids, groups of order 12, Braids
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6
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Oct 13
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No class Monday (Thanksgiving); Thursday - groups of order 12 cont'd.
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7
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Oct 20
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Term Test; Term Test Solutions on Monday, HW3; HW 3 Solutions; Thursday - solvable groups, rings: defn's & examples.
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8
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Oct 27
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Monday - functors, Cayley-Hamilton Thm, ideals, iso thm 1; Thursday - iso thms 2-4, integral domains, maximal ideals, One Theorem, Three Corollaries, Five Weeks
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9
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Nov 3
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Monday - prime ideals, primes & irreducibles, UFD's, Euc.DomainPID, Thursday - Noetherian rings, PIDUFD, Euclidean Algorithm, modules: defn & examples, HW4, HW 4 Solutions
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10
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Nov 10
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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.
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11
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Nov 17
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Monday-Tuesday is UofT's Fall Break, HW5, Thursday - 1t3c5w handout cont'd, JCF Tricks & Programs handout
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12
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Nov 24
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Monday - JCF Tricks & Programs cont'd, tensor products, Thursday - tensor products cont'd
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13
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Dec 1
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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
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F
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Dec 15
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The Final Exam
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Register of Good Deeds
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Add your name / see who's in!
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See Non Commutative Gaussian Elimination
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See The Simplicity of the Alternating Groups.
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Dror's notes above / Student's notes below
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I've texted up the handout for proving the simplicity of An. Enjoy!
File:Simplicity of An.pdf
A few of these photos are a bit blurry. If anyone has suggestions for how to take better photos, I'd be very happy to hear them! (I haven't been using flash because I believe it would disrupt the class.)