10-327/About This Class

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 ${\mathbb {R} }$, HW4, HW4 Solutions, Thursday - connectedness, path-connectedness and products 7 Oct 25 Monday - Compactness of $[0,1]$, 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 - $T_{3.5}$ and $I^{A}$, 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 Add your name / see who's in! See Hilbert's 13th

In Preparation

The information below is preliminary and cannot be trusted! (v)

Crucial Information

Agenda: Understand "continuity" in the most abstract, learn about "the fundamental groups" and maybe touch "surfaces".

Instructor: Dror Bar-Natan, drorbn@math.toronto.edu (Wiki before Email!), Bahen 6178, 416-946-5438. Office hours: by appointment.

Classes: Mondays 2-3 and Thursdays 2-4 in Sydney Smith 1070.

Teaching Assistant: David Reiss, david.reiss@utoronto.ca, SS 622.

URL: https://drorbn.net/drorbn/index.php?title=10-327.

Abstract

Taken from the Faculty of Arts and Science Calendar:

Metric spaces, topological spaces and continuous mappings; separation, compactness, connectedness. Topology of function spaces. Fundamental group and covering spaces. Cell complexes, topological and smooth manifolds, Brouwer fixed-point theorem.

• Prerequisite: MAT257Y1/(MAT224H1, MAT237Y1, MAT246H1 and permission of the instructor)

Text Book(s)

Our main text book will be Topology (second edition) by James Munkres, ISBN 978-0131816299. It is a required reading.

Wiki

The class web site is a wiki, as in Wikipedia - meaning that anyone can and is welcome to edit almost anything and in particular, students can post notes, comments, pictures, whatever. Some rules, though -

• This wiki is a part of my (Dror's) academic web page. All postings on it must be class-related (or related to one of the other projects I'm involved with).
• You must login to edit. To get an account, email me your preferred login name, your real name and your email address if different from the address you are writing from.
• Criticism is fine, but no insults or foul language, please.
• I (Dror) will allow myself to exercise editorial control, when necessary.
• The titles of all pages related to this class should begin with "10-327/" or with "10-327-", just like the title of this page.
• Some further editing help is available at Help:Contents.

Marking Scheme

There will be one term test (25% of the total grade) and a final exam (50%), as well as about 9 homework assignments (25%).

The Term Test

The term test will take place in class on Thursday October 28th, 2-4PM. A student who misses the term test without providing a valid reason (for example, a doctor’s note) within one week of the test will receive a mark of 0 on the term test. There will be no make-up term test. If a student misses the term test for a valid reason, the weight of the problem sets will increase to 35% and the weight of the final exam to 65%.

Homework

Assignments will be posted on the course web page and distributed in class (usually on Tuesdays) approximately on the weeks shown in the class timeline. They will be due a week later at the tutorials (on Thursdays) and they will be (at least partially) marked by the TAs. All students (including those who join the course late) will receive a mark of 0 on each assignment not handed in; though in computing the homework grade, your worst two assignments will not count. I encourage you to discuss the assignments with other students or even browse the web, so long as you do at least some of the thinking on your own and you write up your own solutions. Remember that cheating is always possible and may increase your homework grade a bit. But it will hurt your appreciation of yourself, your knowledge and your exam grades a lot more.

Good Deeds

Students will be able to earn up to 25 "good deeds" points throughout the year for doing services to the class as a whole. There is no pre-set system for awarding these points, but the following will definitely count:

• Drawing a beautiful picture to illustrate a point discussed in class and posting it on this site.
• Taking class notes in nice handwriting, scanning them and posting them here.
• Typing up or formatting somebody else's class notes, correcting them or expanding them in any way.
• Writing an essay on expanding on anything mentioned in class and posting it here; correcting or expanding somebody else's article.
• Doing anything on our 09-240/To do list.
• Any other service to the class as a whole.

Good deed points will count towards your final grade! If you got $n$ of those, they are solidly yours and the above formula for the final grade will only be applied to the remaining $100-n$ points. So if you got 25 good deed points (say) and your final grade is 80, I will report your grade as $25+80(100-25)/100=85$. Yet you can get an overall 100 even without doing a single good deed.

Important. For your good deeds to count, you must do them under your own name. So you must set up an account for yourself on this wiki and you must use it whenever you edit something. I will periodically check Recent changes to assign good deeds credits.

Class Photo

To help me learn your names, I will take a class photo on Thursday of the third week of classes. I will post the picture on the class' web site and you will be required to send me an email and identify yourself in the picture or to identify yourself on the Class Photo page of this wiki.

Accessibility Needs

The University of Toronto is committed to accessibility. If you require accommodations for a disability, or have any accessibility concerns about the course, the classroom or course materials, please contact Accessibility Services as soon as possible: disability.services@utoronto.ca or http://studentlife.utoronto.ca/accessibility.

How to Succeed in this Class

• Keep up! Don't fall behind on reading, listening, and doing assignments! University goes at a different pace than high school. New material is covered once and just once. There will be no going over the same thing again and again - if you fall behind, you stay behind. Unless you are an Einstein, there is no way to do well in this class merely by attending lectures - you must think about the material more than 3 or 5 hours a week if you want it to sink in. And if you are planning on not attending lectures, well, think again. Most people find it very hard to pace their own studies without a human contact; if you'll try, you are likely to discover the hard way that you belong to the majority.
• If in high school you were the best in your class in math, now remember that everybody around you was the same. You may find that what was enough then simply doesn't cut it any more. Try to catch that early in the year!
• Math is about understanding, not about memorizing. To understand is to internalize; it is to come to the point where whatever the professor does on the blackboard or whatever is printed in the books becomes yours; it is to come to the point where you appreciate why everything is done the way it is done, what does it mean, what are the reasons and motivations and what is it all good for. Don't settle for less!
• Keep asking yourself questions; many of them will be answered in class, but not all. Remember the old Chinese proverb:

"Teachers open the door, but you must enter by yourself"

"师傅领进门,修行靠个人!"

The saddest that can happen to you in this class is if you won't notice the door being opened.