Welcome to Math 1100! (additions to this web site no longer count towards good deed points)

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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, JordanHolder 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, OrbitStabilizer Thm, Class Equation.

4

Sep 29

Monday  Cauchy's Thm, Sylow 1; Thursday  Sylow 2.

5

Oct 6

Monday  Sylow 3, semidirect 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, CayleyHamilton Thm, ideals, iso thm 1; Thursday  iso thms 24, integral domains, maximal ideals, One Theorem, Three Corollaries, Five Weeks

9

Nov 3

Monday  prime ideals, primes & irreducibles, UFD's, Euc.DomainPID, Thursday  Noetherian rings, PIDUFD, Euclidean Algorithm, modules: defn & examples, HW4, HW 4 Solutions

10

Nov 10

Monday  R is a PID iff R has a DH norm, Rmodules, 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

MondayTuesday 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

EndofCourse 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


This assignment is due at class time on Thursday, November 20, 2011.
Solve the following questions
Problem 1. (Klein's 1983 course)
 Show that the ideal inside the ring is not principal.
 Is a domain?
Problem 2. Prove that a ring is a PID iff it is a UFD in which for every nonzero .
Problem 3. (Lang) Show that the ring is a PID and hence a UFD. What are the units of that ring?
Problem 4. (Dummit and Foote) In , find the greatest common divisor of and , and express it as a linear combination of these two elements.
Problem 5. (Klein's 1983 course) Show that is not a UFD.
Problem 6. (Hard!) Show that the quotient ring is not a UFD.