Colorado State University, Pueblo
Math 411 — Introduction to Topology — Summer 2015

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Lectures: MW 3-5:30pm in PM 116      Office Hours: MW1-3pm (usually), or by appointment

Instructor: Jonathan Poritz     Office: PM 248     E-mail: jonathan.poritz@gmail.com
Phone: 549-2044 (office — any time); 357-MATH (personal;please use sparingly)

Text: No text! We will be using various freely available texts on the Internet plus some supplements written for the course by your instructor.

Prerequisites: A satisfactory grade (C or higher) in Math 320 (Introductory Discrete Mathematics). The point of this prerequisite is to ensure that you have started the process of becoming comfortable with a certain level of abstraction in mathematics, such reading and writing proofs.

Postrequisites: This course is required for anyone who wants to understand topology.

Course Content/Objective: The Catalog is rather terse:

An introduction to topological spaces, homeomorphisms, topological properties, and separation axioms.
Topology is a beautiful subject of pure mathematics. At this point in human history, there are very few applications of topology to other disciplines. It is important in some very abstract areas of theoretical physics and to a small extent in some ares of computer science (e.g., one talks about the "network topology", although that is pretty much never followed by any sophisticated results from topology, the mathematical discipline).

Despite the lack of application, topology has many beautiful, powerful, surprising, fascinating results. It is also a field undergoing significant growth in recent years, since the Poincaré Conjecture was proven.

During the first part of the course (about two weeks) we will talk about basics including point-set topology and the fundamental group, including at least the following

At that point we will go in one of the following directions, depending upon student interest:

Class [dis]organization:

  • There will be regular homework assignments, which will consist each of only a few problems — but they will be fairly challenging problems! One part of this HW which be new to many students is the importance of the quality of exposition.
  • If you absolutely have to miss a class, please inform me in advance and I will video the class and post the video on the 'net. You can then watch the class you missed in the comfort of you home and (hopefully) not fall behind. Classes I have videoed will have the icon Black and white camera icon next to that day's entry on the schedule/homework page to remind you of the available video. (But you must e-mail me for a link to the video, you will not be able to search for it.)

    • Exams: We will have one midterm exam on a dates to be determined (and announced at least a week in advance). It may have a take-home portion in addition to the in-class part. We will also have a final exam, on Wednesday, July 1st, 3-5:30pm, in our usual classroom.

    Grades: In each grading category, the lowest n scores of that type will be dropped, where n is the value in the "# dropped" column. The total remaining points will be multiplied by a normalizing factor so as to make the maximum possible be 100. Then the different categories will be combined, each weighted by the "course %" from the following table, to compute your total course points out of 100. Your letter grade will then be computed in a manner not more strict than the traditional "90-100% is an A, 80-90% a B, etc." method. [Note that the math department does not give "+"s or "-"s.]

      pts each # of such # dropped revision % course %
    Classroom participation: 3/class ≈14 classes 7 classes 0% 10%
    Homework: 3/prob ≈36 probs 3 probs 75% 30%
    Midterm: >100 1 0 50% 30%
    Final Exam: >200 1 0 0% 30%

    Academic integrity: Mathematics is more effectively and easily learned — and more fun — when you work in groups. However, all work you turn in must be your own, and any form of cheating is grounds for an immediate F in the course for all involved parties. In particular, some assignments, such as take-home portions of tests, will have very specific instructions about the kinds of help you may seek or resources you may use, and violations of of these instructions will not be tolerated.

    Students with disabilities: The University abides by the Americans with Disabilities Act and Section 504 of the Rehabilitation Act of 1973, which stipulate that no student shall be denied the benefits of education "solely by reason of a handicap." If you have a documented disability that may impact your work in this class for which you may require accommodations, please see the Disability Resource Coordinator as soon as possible to arrange accommodations. In order to receive accommodations, you must be registered with and provide documentation of your disability to: the Disability Resource Office, which is located in the Library and Academic Resources Center, Suite 169.