|Welcome to Math 257
||Notes and Links
||About This Class; Day 1 Handout (pdf, html); Monday, Wednesday, Friday, Day 2 Handout (pdf, html); First Week Notes.
||Monday, Wednesday, Tutorial 2 Handout, Friday, Second week notes, HW1, HW1 Solutions.
||Monday, Wednesday, Tutorial 3 Handout, Friday, Third week notes, Class Photo, HW2, HW2 Solutions.
||Monday, Wednesday, Friday, 4th week notes, HW3, HW3 Solutions.
||Monday is Thanksgiving, no class; Wednesday, Friday, 5th week notes, HW4, HW4 Solutions.
||Monday, Wednesday, Friday, 6th week notes, HW5, HW5 Solutions.
||Monday, Wednesday, Friday, 7th week notes
||Monday; Term test 1; Wednesday, HW6, HW6 pdf, HW6 Solutions, Friday, 8th week notes.
||Monday is last day to switch to MAT 237; Monday-Tuesday is UofT Fall Break; Wednesday, HW7, HW7 Solutions, Friday, 9th week notes.
||Monday, Wednesday, HW8, HW8 pdf, HW8 Solutions, Friday, Lecture recordings, 10th week notes.
||Monday, Wednesday, HW9, HW9 pdf, HW9 Solutions, Friday, Lecture recordings, 11th week notes.
||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.
||Monday, Wednesday, 13th week notes Semester ends on Wednesday - no class Friday.
||No classes: other classes' finals, winter break.
||Class resumes Friday at RS211, no tutorials or office hours this week, Friday, Friday notes.
||Monday, Wednesday, Friday, Weekly notes
||Monday, Term test 2; Wednesday, HW11, HW11 inline pdf,HW11 solutions, Friday, Weekly notes
||Monday; Hour 44 Handout (pdf, html); Wednesday, HW12, HW12 inline pdf, HW12 Solutions, Friday, Weekly notes
||Monday, Wednesday, HW13, HW13 inline pdf, HW13 Solutions,Friday, Weekly Notes
||Monday, Wednesday, HW14, HW14 inline pdf, Friday, Weekly Notes
||Monday, Wednesday, HW15, HW15 inline pdf, HW15 solutions, Friday,Weekly Notes, UofT examination table posted on Friday.
||Reading week - no classes; Tuesday is the last day to drop this class.
||Monday, Wednesday, HW16, HW16 inline pdf, Friday, Weekly Notes
||Monday, Wednesday, Friday, Weekly Notes
||Monday, Term test 3 on Tuesday at 5-7PM; Wednesday, HW17, HW17 inline pdf, Friday, Weekly Notes
||Monday, Wednesday, HW18, HW18 inline pdf, Friday
||No Monday class, Wednesday, Thursday (makeup for Monday, 5PM at MP 134), HW19, Friday
||Monday, Wednesday; Semester ends on Wednesday - no tutorials Wednesday and Thursday, no class Friday.
||The Final Exam.
|Register of Good Deeds
Add your name / see who's in!
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 3-4 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.
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 non-empty connected subsets of are single points").
Also, Add your name to the Class Photo page!
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.
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).