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.

Teaching Assistant: Louis-Philippe Thibault, lp.thibault@mail.utoronto.ca.

Texts

Lang's Algebra, Selick's lecture notes for this class, Dummit and Foote's Abstract Algebra, Hungerford's Abstract Algebra. My son Assaf (a math student in another university) recommends also Harry Potter and the Methods of Rationality.