Welcome to Math 257

Edits to the Math 257 web pages no longer count for the purpose of good deed points.

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Week of...

Notes and Links

1

Sep 12

About This Class; Day 1 Handout (pdf, html); Monday, Wednesday, Friday, Day 2 Handout (pdf, html); First Week Notes.

2

Sep 19

Monday, Wednesday, Tutorial 2 Handout, Friday, Second week notes, HW1, HW1 Solutions.

3

Sep 26

Monday, Wednesday, Tutorial 3 Handout, Friday, Third week notes, Class Photo, HW2, HW2 Solutions.

4

Oct 3

Monday, Wednesday, Friday, 4th week notes, HW3, HW3 Solutions.

5

Oct 10

Monday is Thanksgiving, no class; Wednesday, Friday, 5th week notes, HW4, HW4 Solutions.

6

Oct 17

Monday, Wednesday, Friday, 6th week notes, HW5, HW5 Solutions.

7

Oct 24

Monday, Wednesday, Friday, 7th week notes

8

Oct 31

Monday; Term test 1; Wednesday, HW6, HW6 pdf, HW6 Solutions, Friday, 8th week notes.

9

Nov 7

Monday is last day to switch to MAT 237; MondayTuesday is UofT Fall Break; Wednesday, HW7, HW7 Solutions, Friday, 9th week notes.

10

Nov 14

Monday, Wednesday, HW8, HW8 pdf, HW8 Solutions, Friday, Lecture recordings, 10th week notes.

11

Nov 21

Monday, Wednesday, HW9, HW9 pdf, HW9 Solutions, Friday, Lecture recordings, 11th week notes.

12

Nov 28

Monday, Wednesday, HW10, HW10 Solutions, makeup class on Thursday at GB 120 at 5PM, no class and no DBN office hours Friday! 12th week notes.

13

Dec 5

Monday, Wednesday, 13th week notes Semester ends on Wednesday  no class Friday.

B

Dec 12,19,26

No classes: other classes' finals, winter break.

14

Jan 2

Class resumes Friday at RS211, no tutorials or office hours this week, Friday, Friday notes.

15

Jan 9

Monday, Wednesday, Friday, Weekly notes

16

Jan 16

Monday, Term test 2; Wednesday, HW11, HW11 inline pdf,HW11 solutions, Friday, Weekly notes

17

Jan 23

Monday; Hour 44 Handout (pdf, html); Wednesday, HW12, HW12 inline pdf, HW12 Solutions, Friday, Weekly notes

18

Jan 30

Monday, Wednesday, HW13, HW13 inline pdf, HW13 Solutions,Friday, Weekly Notes

19

Feb 6

Monday, Wednesday, HW14, HW14 inline pdf, Friday, Weekly Notes

20

Feb 13

Monday, Wednesday, HW15, HW15 inline pdf, HW15 solutions, Friday,Weekly Notes, UofT examination table posted on Friday.

R

Feb 20

Reading week  no classes; Tuesday is the last day to drop this class.

21

Feb 27

Monday, Wednesday, HW16, HW16 inline pdf, Friday, Weekly Notes

22

Mar 6

Monday, Wednesday, Friday, Weekly Notes

23

Mar 13

Monday, Term test 3 on Tuesday at 57PM; Wednesday, HW17, HW17 inline pdf, HW17 Solutions, Friday, Weekly Notes,Orientation_notes

24

Mar 20

Monday, Wednesday, HW18, HW18 inline pdf, Friday

25

Mar 27

No Monday class, Wednesday, Thursday (makeup for Monday), HW19, HW19 inline pdf, Friday, Weekly Notes

26

Apr 3

Monday, Wednesday; Semester ends on Wednesday  no tutorials Wednesday and Thursday, no class Friday.

F

Apr 1028

The Final Exam on Thursday April 20 (and some office hours sessions before).

Register of Good Deeds

Riddle Repository

Add your name / see who's in!



Reading
Read, reread and rereread your notes to this point, and make sure that you really, really really, really really really understand everything in them. Do the same every week! Also, read, reread and rereread sections 34 of Munkres' book to the same standard of understanding. Remember that reading math isn't like reading a novel! If you read a novel and miss a few details most likely you'll still understand the novel. But if you miss a few details in a math text, often you'll miss everything that follows. So reading math takes reading and rereading and rerereading and a lot of thought about what you've read. Also, preread sections 5 and 6, just to get a feel for the future.
Doing
Solve problems 1ab, 2, 3, 4ab in section 4, but submit only the underlined problems/parts. In addition, solve the following problems, though submit only your solutions of problems A and B:
Problem A. Let be a metric space. Prove that the metric itself, regarded as a function , is continuous.
Problem B. Let be a subset of a metric space . Show that the distance function to , defined by , is a continuous function and that iff .
Problem C. Prove the "Lebesgue number lemma": If is an open cover of a compact space , then there exists an (called "the Lebesgue number of ), such that every open ball of radius in is contained in one of the 's.
Problem D. The Cantor set is the set formed from the closed unit interval by removing its open middle third , then removing the open middle thirds of the remaining two pieces (namely then removing and ), then removing the open middle thirds of the remaining 4 pieces, and so on. Prove that is uncountable, compact and totally disconnected (the last property means "the only nonempty connected subsets of are single points").
Also, Add your name to the Class Photo page!
Submission
Here and everywhere, neatness counts!! You may be brilliant and you may mean just the right things, but if the teaching assistants will be having hard time deciphering your work they will give up and assume it is wrong.
This assignment is due in class on Friday October 7 by 2:10PM.
Important
Please write on your assignment the day of the tutorial when you'd like to pick it up once it is marked (Wednesday or Thursday).