14-1100

DBN: Classes: 2014-15: 14-1100/Navigation

#	Week of...	Notes and Links
Welcome to Math 1100! (additions to this web site no longer count towards good deed points)
1	Sep 8	About This Class; Monday - Non Commutative Gaussian Elimination; Thursday - the category of groups, automorphisms and conjugations, images and kernels.
2	Sep 15	Monday - coset spaces, isomorphism theorems; Thursday - simple groups, Jordan-Holder decomposition series.
3	Sep 22	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.
4	Sep 29	Monday - Cauchy's Thm, Sylow 1; Thursday - Sylow 2.
5	Oct 6	Monday - Sylow 3, semi-direct products, braids; HW2; HW 2 Solutions; Thursday - braids, groups of order 12, Braids
6	Oct 13	No class Monday (Thanksgiving); Thursday - groups of order 12 cont'd.
7	Oct 20	Term Test; Term Test Solutions on Monday, HW3; HW 3 Solutions; Thursday - solvable groups, rings: defn's & examples.
8	Oct 27	Monday - functors, Cayley-Hamilton Thm, ideals, iso thm 1; Thursday - iso thms 2-4, integral domains, maximal ideals, One Theorem, Three Corollaries, Five Weeks
9	Nov 3	Monday - prime ideals, primes & irreducibles, UFD's, Euc.Domain $\Rightarrow$ PID, Thursday - Noetherian rings, PID $\Rightarrow$ UFD, Euclidean Algorithm, modules: defn & examples, HW4, HW 4 Solutions
10	Nov 10	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.
11	Nov 17	Monday-Tuesday is UofT's Fall Break, HW5, Thursday - 1t3c5w handout cont'd, JCF Tricks & Programs handout
12	Nov 24	Monday - JCF Tricks & Programs cont'd, tensor products, Thursday - tensor products cont'd
13	Dec 1	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
F	Dec 15	The Final Exam
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See Non Commutative Gaussian Elimination

Core Algebra I

Department of Mathematics, University of Toronto, Fall 2014

Agenda: Groups, rings, modules.

Course Highlights: We'll solve the Rubik's cube! We'll understand many groups of small order! We'll understand "Modules over PIDs"! We'll know that the quintic can't be solved!

Instructor: Dror Bar-Natan, drorbn@math.toronto.edu, Bahen 6178, 416-946-5438. Office hours: by appointment.

Classes: Mondays 1-3 and Thursdays 1-2 in Bahen 6183.