Math 441. Introductory Topology I

Fall 2010, Section 1


Time: Monday + Wednesday, 3:20-4:40
Place: ARC 110
Instructor: Michael Saks

Office hours
Text: Topology, by J. Munkres, 2nd edition.

Contents of this page

  • 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 12-15-10. Here are Supplementary notes on compactness
  • Posted 11-21-10. Solutions to the first two problems of HW 9 are posted (see the HW table below).
  • Posted 11-11-10. The midterm will be Monday, 11-22-10.
  • Posted 11-11-10. Assignment 10 is now available. Contrary to what was posted earlier, this assignment will be due on Wednesday, 11-17-10.
  • Posted 10-22-10 I will be away from the University during the week of November 1-5. Professor Weibel will teach the class that week. That week, you may attend Professor Weibel's office hours Tuesday-Friday 11:00-12:00. Also, during that week, Professor Luo is available for questions during his office hours on Tuesday 9:30-11:30.
  • Posted 10-18-10 I posted a new version of the practice problems to correct an error on problem 7 that remained.
  • Posted 10-17-10 I posted a new version of the practice problems to correct an error on problem 7.
  • Posted 10-14-10 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 10-14-10 Students had a lot of trouble with assignment 6, so I posted solutions (see the homework table on this page).
  • Posted 10-12-10 Assignment 6 has been modified. For problem 3 you have a choice to do either section 17:16 or section 17:17.
  • Posted 10-6-10 The date of the first midterm is changed to Monday, October 18.
  • Posted 9-27-2010: I have posted comments on assignment 3 (see the homework table on this page).
  • Posted 9-27-2010: Office hour for Tuesday October 12 is moved to 3:00-4:00 (instead of the usual 10:00-11:00.)
  • Posted 9-26-2010: 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 9-15-2010: Assignment 3 is now available
  • Posted 9-8-2010: Assignment 2 is now available
  • Posted 9-7-2010: 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 8-25-2010: It will be very helpful for students to read sections 1 to 4 of the book before the first class on September 1.
  • Posted 8-25-2010: 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 1-11) 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 43-47) and/or chapter 9 (sections 51-60).

    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 cut-off, 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.
    Midterm 1 Monday, October 18
    Exam 2 Monday, November 22
    Final Exam Thurs, Dec. 16 8:00 AM to 11:00 AM

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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 1-4 (Review of 300 and 311)
    9/8/10 Sections 5-7 (More review)
    9/13/10 Sections 5-7, cont'd
    9/15/10 Sections 9-10.
    9/20/10 Sections 12-13.
    9/22/10 Section 14
    9/27/10 Section 15-16
    9/29/10 Sections 17-18
    10/4/10 Review Sections 16-18
    10/6/10 Sections 17-18
    10/11/10 Sections 18-19
    10/13/10 Sections 19-20
    10/18/10 Study for exam
    10/20/10 Review section 18
    10/25/10 Review Sections 19-20
    10/27/10 Section 21
    11/1/10 Review Section 20-21
    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
    Assignment # Last update Date due Comments (date posted)
    Assignment 1 9/7/10 9/8/10
    Assignment 2 9/8/10 9/15/10
    Assignment 3 9/15/10 9/22/10 Comments (9-27-2010)
    Assignment 4 9/26/10 9/29/10
    Assignment 5 10/4/10 10/6/10 Comments (10-11-2010)
    Assignment 6 10/6/10 10/13/10 Solutions
    Practice problems for midterm 10-17-10 not to be handed in
    Assignment 7 10/20/10 10/27/10
    Assignment 8 10/27/10 11/3/10
    Assignment 9 10/27/10 11/10/10 Selected Solutions
    Assignment 10 11/11/10 11/17/10
    Practice problems for midterm 2 11/17/10 not to be handed in
    Assignment 11 12/8/10
    Assignment 12 (optional) 12/9/10 Before the final 12/16/10

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    Comments on this page should be sent to: saks@math.rutgers.edu
    Last updated: August 22, 2010