14-1100

DBN: Classes: 2014-15: 14-1100/Navigation Welcome to Math 1100! (additions to this web site no longer count towards good deed points) # Week of... Notes and Links 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 Register of Good Deeds Add your name / see who's in! 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.

Further Resources

• Graduate Studies at the UofT Math Department. In particular, Graduate Course Descriptions.

• My 14-1100 notebook.

• My 2011 Class.

• My 2010 Class.

• Paul Selick's 2007 class (Errata).

• Some (mostly complete) notes from last year's class: 10-1100-Notes.

Dror's notes above / Student's notes below