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Welcome to Math 1100!
(additions to this web site no longer count towards good deed points)
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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.Domain PID, 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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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.
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Teaching Assistant: Louis-Philippe Thibault, lp.thibault@mail.utoronto.ca.
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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
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Dror's notes above / Student's notes below
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Notes for midterm studying - Summaries of topics covered in the lectures. File:Checklist for Topics covered in the lectures.pdf
Summary of the major results covered Media:MAT1100Summary.pdf
