Math 441. Introductory Topology I
Fall 2010, Section 1
Time: Monday + Wednesday, 3:204:40
Place: ARC 110
Instructor: Michael Saks
Office hours
Text: Topology, by J. Munkres, 2nd edition.
Announcements and additional resources
Course objectives
Responsibilities of students
Grading
Exam schedule
Supplementary notes on writing proofs
Reading assignments
Homework requirements
Homework assignments
Announcements and Additional Resources
Posted 121510. Here are Supplementary notes on compactness
Posted 112110. Solutions to the first two problems of
HW 9 are posted (see the HW table below).
Posted 111110. The midterm will be Monday, 112210.
Posted 111110. Assignment 10 is now available. Contrary
to what was posted earlier, this assignment will be due on Wednesday,
111710.
Posted 102210 I will be away from the University during the
week of November 15. Professor Weibel will teach the class that week.
That week, you may attend
Professor Weibel's office hours TuesdayFriday 11:0012:00.
Also, during that week,
Professor Luo
is available for questions during his office hours on Tuesday 9:3011:30.
Posted 101810 I posted a new version of the practice problems
to correct an error on problem 7 that remained.
Posted 101710 I posted a new version of the practice problems
to correct an error on problem 7.
Posted 101410 I have posted practice problems for the midterm.
These are representative of what you'll see on the exam (but the
exam won't be as long). The practice problems are located
in the homework table (note there is no homework assignment due
Wednesday 10/20 because of the exam).
Posted 101410 Students had a lot of trouble with assignment 6, so
I posted solutions (see the homework table on this page).
Posted 101210 Assignment 6 has been modified. For problem 3
you have a choice to do either section 17:16 or section 17:17.
Posted 10610 The date of the first midterm is changed to Monday,
October 18.
Posted 9272010: I have posted comments on assignment 3 (see the
homework table on this page).
Posted 9272010:
Office hour for Tuesday October 12 is moved to 3:004:00
(instead of the usual 10:0011:00.)
Posted 9262010: I posted a revised version of Assignment 4.
I had incorrectly listed some problems as being from section 6, which
should have been from Section 5.
Posted 9152010: Assignment 3 is now available
Posted 982010: Assignment 2 is now available
Posted 972010: I posted a new version of Assignment 1 to correct
a typographical error on problem 4a. "then U is not a product set" was changed
to "then R is not a product set".
Posted 8252010: It will be very helpful for students to
read sections 1 to 4 of the book before the first class on September 1.
Posted 8252010: Here is a resource page devoted to The Axiom of Choice
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Course objectives
Topology is popularly referred to as "rubber sheet
geometry": it is the study of those properties of geometric figures that
don't don't change if we deform the figure without tearing it.
Topology is also an important
part of the foundations of mathematical analysis because it provides
a general notion of concepts such as continuity and convergence which
apply in many important settings.
The syllabus for the course will be somewhat flexible. We will cover all of the
unstarred sections from
sections 1 through 37, and perhaps some of the starred section.
Chapter 1 (Sections 111) is mostly a review of material that
you should have seen from Math 300 or Math 311, so I expect we won't spend much
time on it. Depending on time at the end of the semester, we will spend
some time on chapter 7 (sections 4347) and/or chapter 9 (sections 5160).
One of the main purposes of this course is to improve student's abilities
to deal with mathematical abstraction.
Students taking this course should already have had Math 300 and 311,
and should have experience with and mastery of the basic
language of mathematics, dealing with mathematical definitions,
reading, writing and understanding proofs.
This course will depend heavily on these skills and will develop them further.
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Responsibilities of students
Each student in this course is expected to be actively engaged in learning.
You are expected to:
to review the needed material from past courses, especially Math 300
and 311, as needed.
attend all classes, except in case of emergencies or special
circumstances. If you know in advance that you will miss a class,
notify me in advance. If you feel that you are not getting enough
out of class to make it worth your while to attend, then discuss
this with me.
let me know if the course is going too fast or too slow.
read the assigned portions of the text and any supplementary
notes.
do assigned homework following the
homework requirements, and let me know if you find the homework
too easy or too difficult.
participate in class, including: asking questions, answering questions,
correcting my errors, joining in discussions and making presentations
at the blackboard.
come to office hours. This is an opportunity to review
difficult material with me, discuss specific homework problems, or
to delve more deeply into material that we don't have time to cover.
When coming to discuss specific difficulties you are having
with the course material or homework, prepare in advance so that
you can be as clear and specific as possible in identifying
the difficulty you are having.
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Grading
Your grade in the course is based on two midterms, a final exam,
written homework, attendance and class participation.
A total score is computed according to the following formula:
Exams: Two midterms(20% each) and a final (40%).
Written homework (20%).
Your grade will mainly be based on this total, but I will temper this
with judgement. In particular,
your grade will be adjusted
based on some additional considerations, including:
If you have poor class attendance your grade may be lowered one notch.
If you have good attendance and participation and you are close to
the borderline, you may receive the higher grade.
To get an A: (1) your total score be above the A cutoff,
and (2) you must have a good performance on the HW.
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Exam schedule
Note: The dates of the midterms are subject to change.
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Supplementary notes on proof writing
Supplementary notes on writing proofs (which were used in 640:300)
can be found here
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Reading assignments
Most of the reading assignments will come from the textbook,
Munkres, Topology, 2nd Edition. There may be some supplementary
notes provided as well.
You should read the listed material before
the class for the given date.
Read by:

Assignment

9/1/10 
Sections 14 (Review of 300 and 311)

9/8/10 
Sections 57 (More review)

9/13/10 
Sections 57, cont'd

9/15/10

Sections 910.

9/20/10

Sections 1213.

9/22/10

Section 14

9/27/10

Section 1516

9/29/10

Sections 1718

10/4/10

Review Sections 1618

10/6/10

Sections 1718

10/11/10

Sections 1819

10/13/10

Sections 1920

10/18/10

Study for exam

10/20/10

Review section 18

10/25/10

Review Sections 1920

10/27/10

Section 21

11/1/10

Review Section 2021

11/3/10

Section 23

11/8/10

None

11/10/10

None

11/15/10

Section 24, 26

11/17/10

Section 27

11/22/10

To be announced

11/24/10

No class: Thanksgiving

11/29/10

None

12/1/10

None

12/6/10

Section 28

12/8/10

Section 29

12/13/10

Section 30,37

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Written Homework assignments
Homework is to be done according to the
homework requirements.
12/3/10
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Comments on this page should be sent to: saks@math.rutgers.edu
Last updated: August 22, 2010