14-1100/Classnotes for Monday November 10: Difference between revisions

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{{14-1100/Navigation}}
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Here are some handwritten notes about direct sums in a bit more detail:
{|
|[[File:MAT1100 Lec_17, 14-11-10M - direct sums, small p1.pdf]]
|[[File:MAT1100 Lec 17, 14-11-10M - direct sums, small p2.pdf]]
|}
Handwritten notes about presentation matrices for finitely generated modules in a bit more detail:
''Apologies''! I had found a few mistakes my notes: there are a few places where I'd flipped <math>R^n</math> with X, and other similar errors.

Here are some jpg's with corrections, although there may still be other mistakes...
{|
|[[File: 14-1100 Lec 17, 14-11-10M - module gen by a matrix, small p1.jpg|200px|thumb|left|page 1]]
|[[File: 14-1100 Lec 17, 14-11-10M - module gen by a matrix, small p2.jpg|200px|thumb|left|page 2]]
|}
{|
|[[File: 14-1100 Lec 17, 14-11-10M - module gen by a matrix, small p3.jpg|200px|thumb|left|page 3]]
|}


{|
{|
Line 38: Line 55:


'''Here are some handwritten notes:'''
'''Here are some handwritten notes:'''

{|
|[[File:14-1100 Lec 17 page 1.JPG|200px|thumb|left|Lec 15 page 1]]
|[[File:14-1100 Lec 17 page 2.JPG|200px|thumb|left|Lec 15 page 2]]
|[[File:14-1100 Lec 17 page 3.JPG|200px|thumb|left|Lec 15 page 3]]
|[[File:14-1100 Lec 17 page 4.JPG|200px|thumb|left|Lec 15 page 4]]
|}
{|
|[[File:14-1100 Lec 17 page 5.JPG|200px|thumb|left|Lec 15 page 5]]
|}

Latest revision as of 13:16, 10 December 2014

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.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 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
Class Photo
Add your name / see who's in!
10-1100-Splash.png
See Non Commutative Gaussian Elimination

Here are some handwritten notes about direct sums in a bit more detail:

File:MAT1100 Lec 17, 14-11-10M - direct sums, small p1.pdf File:MAT1100 Lec 17, 14-11-10M - direct sums, small p2.pdf

Handwritten notes about presentation matrices for finitely generated modules in a bit more detail: Apologies! I had found a few mistakes my notes: there are a few places where I'd flipped with X, and other similar errors.

Here are some jpg's with corrections, although there may still be other mistakes...

page 1
page 2
page 3
Lec 17 board 1
Lec 17 board 2
Lec 17 board 3
Lec 17 board 4
Lec 17 board 5
Lec 17 board 6
Lec 17 board 7
Lec 17 board 8
Lec 17 board 9
Lec 17 board 10
Lec 17 board 11
Lec 17 board 12
Lec 17 board 13
Lec 17 board 14
Lec 17 board 15
Lec 17 board 16
Lec 17 board 17

Here are some handwritten notes:

Lec 15 page 1
Lec 15 page 2
Lec 15 page 3
Lec 15 page 4
Lec 15 page 5
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