10-327/Classnotes for Thursday October 14: Difference between revisions

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Here are some lecture notes..

[http://katlas.math.toronto.edu/drorbn/images/5/51/10-327-lec09p01.jpg Lecture 9 page 1]

[http://katlas.math.toronto.edu/drorbn/images/7/76/10-327-lec09p02.jpg Lecture 9 page 2]

[http://katlas.math.toronto.edu/drorbn/images/e/e3/10-327-lec09p03.jpg Lecture 9 page 3]

[http://katlas.math.toronto.edu/drorbn/images/9/95/10-327-lec09p04.jpg Lecture 9 page 4]

[http://katlas.math.toronto.edu/drorbn/images/8/84/10-327-lec09p05.jpg Lecture 9 page 5]

[http://katlas.math.toronto.edu/drorbn/images/9/97/10-327-lec09p06.jpg Lecture 9 page 6]

==Riddles==
===The Dice Game===
Two players A and B decide to play a game.
Player A takes 3 blank dice and labels them with the numbers 1-18.
Player B then picks one of the three die.
Then Player A picks one of the remaining two die.
The players then roll their dice, and the highest number wins the round.
They play 10,023 rounds.
Who would you rather be Player A or B?

===Almost Disjoint Subsets===
Find an uncountable collection of subsets of <math>\mathbb{N}</math> such that any two subsets only contain a finite number of points in their intersection. Don't cheat by using the axiom of choice!

[[10-327/Solution to Almost Disjoint Subsets]]

*I wasn't there for this riddle but it sounded interesting, though I might have the phrasing wrong - John.
* Feel free to cheat and use the axiom of choice - I don't see how it would help anyway. [[User:Drorbn|Drorbn]] 17:40, 18 October 2010 (EDT)

=== Solutions ===
4 Solutions to problems in Munkre's book regard to Metrics and Metric topology. -Kai [[User:Xwbdsb|Xwbdsb]] 16:47, 28 October 2010 (EDT)

[http://katlas.math.toronto.edu/drorbn/images/e/ef/10-327metric_exercise1.jpg page1]
[http://katlas.math.toronto.edu/drorbn/images/c/c0/10-327metric_exercise2.jpg page2]
[http://katlas.math.toronto.edu/drorbn/images/8/82/10-327metric_exercise3.jpg page3]
[http://katlas.math.toronto.edu/drorbn/images/e/ec/10-327metric_exercise4.jpg page4]
[http://katlas.math.toronto.edu/drorbn/images/8/8e/10-327metric_exercise5.jpg page5]

Latest revision as of 19:43, 28 October 2010

DBN: Classes: 2010-11: 10-327/Navigation
Additions to the MAT 327 web site no longer count towards good deed points
# Week of... Notes and Links
1 Sep 13 About This Class, Monday - Continuity and open sets, Thursday - topologies, continuity, bases.
2 Sep 20 Monday - More on bases, Thursdsay - Products, Subspaces, Closed sets, HW1, HW1 Solutions
3 Sep 27 Monday - the Cantor set, closures, Thursday, Class Photo, HW2, HW2 Solutions
4 Oct 4 Monday - the axiom of choice and infinite product spaces, Thursday - the box and the product topologies, metric spaces, HW3, HW3 Solutions
5 Oct 11 Monday is Thanksgiving. Thursday - metric spaces, sequencial closures, various products. Final exam's date announced on Friday.
6 Oct 18 Monday - connectedness in , HW4, HW4 Solutions, Thursday - connectedness, path-connectedness and products
7 Oct 25 Monday - Compactness of , Term Test on Thursday, TT Solutions
8 Nov 1 Monday - compact is closed and bounded, maximal values, HW5, HW5 Solutions, Wednesday was the last date to drop this course, Thursday - compactness of products and in metric spaces, the FIP
9 Nov 8 Monday-Tuesday is Fall Break, Thursday - Tychonoff and a taste of Stone-Cech, HW6, HW6 Solutions
10 Nov 15 Monday - generalized limits, Thursday - Normal spaces and Urysohn's lemma, HW7, HW7 Solutions
11 Nov 22 Monday - and , Thursday - Tietze's theorem
12 Nov 29 Monday - compactness in metric spaces, HW8, HW8 Solutions, Thursday - completeness and compactness
13 Dec 6 Monday - Baire spaces and no-where differentiable functions, Wednesday - Hilbert's 13th problem; also see December 2010 Schedule
R Dec 13 See December 2010 Schedule
F Dec 20 Final exam, Monday December 20, 2PM-5PM, at BR200
Register of Good Deeds
10-327-ClassPhoto.jpg
Add your name / see who's in!
10-327-Splash.png
See Hilbert's 13th

See some blackboard shots at BBS/10_327-101014-142707.jpg.

Dror's notes above / Student's notes below

Here are some lecture notes..

Lecture 9 page 1

Lecture 9 page 2

Lecture 9 page 3

Lecture 9 page 4

Lecture 9 page 5

Lecture 9 page 6

Riddles

The Dice Game

Two players A and B decide to play a game. Player A takes 3 blank dice and labels them with the numbers 1-18. Player B then picks one of the three die. Then Player A picks one of the remaining two die. The players then roll their dice, and the highest number wins the round. They play 10,023 rounds. Who would you rather be Player A or B?

Almost Disjoint Subsets

Find an uncountable collection of subsets of such that any two subsets only contain a finite number of points in their intersection. Don't cheat by using the axiom of choice!

10-327/Solution to Almost Disjoint Subsets

  • I wasn't there for this riddle but it sounded interesting, though I might have the phrasing wrong - John.
  • Feel free to cheat and use the axiom of choice - I don't see how it would help anyway. Drorbn 17:40, 18 October 2010 (EDT)

Solutions

4 Solutions to problems in Munkre's book regard to Metrics and Metric topology. -Kai Xwbdsb 16:47, 28 October 2010 (EDT)

page1 page2 page3 page4 page5

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