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:

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 (An introduction to topological spaces, homeomorphisms, topological properties, and separation axioms.

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

*metrics**open*and*closed sets**subspace*and*product topologies**continuous functions**connected*and*compact sets**separation axioms*- definition of the
*fundamental group* *covering spaces*, including the*universal covering space*- the
*Van Kampen Theorem*

*(co)homology*or*differential topology*and*Morse Theory*or*geometric structures*or*group actions*or*elements of differential geometry*.

**Class ***[dis]***organization:**

**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 1 ^{st}, 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.