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MAT 6500: Point-Set Topology - Fall 2018 by Dan Isaksen, Wayne State University, Exercises of Topology

National Intelligence University (NIU)Topology

A course description for mat 6500: point-set topology offered at wayne state university in fall 2018 by dan isaksen. The course focuses on abstract topological spaces and continuous functions, with learning outcomes including manipulation of open sets, analysis of connectedness and compactness, and construction of topological spaces using products and quotient constructions. Students have three options for participation: in-person, videoconference, or recorded classes. Prerequisites include mat 5610 or instructor consent, and students should be confident with writing proofs and working with abstract mathematical objects. The course covers armstrong: basic topology, springer, and includes exams, homework, and essays.

What you will learn

  • What text is required for MAT 6500: Point-Set Topology?
  • What are the learning outcomes of MAT 6500: Point-Set Topology?
  • What options does the instructor provide for participating in MAT 6500: Point-Set Topology?

Typology: Exercises

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Course Description
MAT 6500
Fall 2018
Dan Isaksen
Wayne State University
Learning Outcomes: The main objective of the course is to study point-set topology from an
abstract perspective. After completing this course, students will be able to:
•manipulate abstract topological spaces and continuous functions, from first principles
involving open sets.
•analyze and interpret specific properties of topological spaces, such as connectedness and
compactness.
•construct topological spaces using products and quotient constructions.
•compute and use fundamental groups of topological spaces.
•classify compact surfaces.
Student Expectations:
With the goal of making the course more accessible, students have three options for partic-
ipating in this course:
1. Attend classes on Tuesday and Thursday mornings in State Hall.
2. Attend classes on Tuesday and Thursday mornings by videoconference from a remote
location.
3. Watch recorded versions of the classes at another time.
In my experience, in-person attendance provides the best overall experience for students
because they are able to interact with the instructor and with other students. This is the best
way to master the subject matter of the class.
Live attendance by videoconference provides some limited opportunity to interact.
Watching recorded classes makes it more difficult for students to succeed. I recommend this
only for students who do not have another viable option.
Here are instructions for participating by option (2). We use the Zoom videoconference
platform. You must install the free Zoom client on your own computer or tablet or smartphone.
The regular meeting link is https://zoom.us/j/735879490
In addition to more traditional homework problems, I will also assign short essays on a
regular basis. These essays must be typeset using LaTeX. Homework and essays will be due
each Thursday. Assignments are posted on Canvas.
Exams will also include take-home essay questions.
Prerequisites: MAT 5610 or consent of instructor. Students should already be confident with
writing proofs and working with abstract mathematical objects.
Class Meetings: The class meets on Tuesdays and Thursdays 10:00–11:15am in State Hall
211, except for official university holidays. There will be no class on Thursday November 22.
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Course Description

MAT 6500

Fall 2018

Dan Isaksen

Wayne State University

Learning Outcomes: The main objective of the course is to study point-set topology from an abstract perspective. After completing this course, students will be able to:

  • manipulate abstract topological spaces and continuous functions, from first principles involving open sets.
  • analyze and interpret specific properties of topological spaces, such as connectedness and compactness.
  • construct topological spaces using products and quotient constructions.
  • compute and use fundamental groups of topological spaces.
  • classify compact surfaces.

Student Expectations: With the goal of making the course more accessible, students have three options for partic- ipating in this course:

  1. Attend classes on Tuesday and Thursday mornings in State Hall.
  2. Attend classes on Tuesday and Thursday mornings by videoconference from a remote location.
  3. Watch recorded versions of the classes at another time.

In my experience, in-person attendance provides the best overall experience for students because they are able to interact with the instructor and with other students. This is the best way to master the subject matter of the class. Live attendance by videoconference provides some limited opportunity to interact. Watching recorded classes makes it more difficult for students to succeed. I recommend this only for students who do not have another viable option. Here are instructions for participating by option (2). We use the Zoom videoconference platform. You must install the free Zoom client on your own computer or tablet or smartphone. The regular meeting link is https://zoom.us/j/ In addition to more traditional homework problems, I will also assign short essays on a regular basis. These essays must be typeset using LaTeX. Homework and essays will be due each Thursday. Assignments are posted on Canvas. Exams will also include take-home essay questions.

Prerequisites: MAT 5610 or consent of instructor. Students should already be confident with writing proofs and working with abstract mathematical objects.

Class Meetings: The class meets on Tuesdays and Thursdays 10:00–11:15am in State Hall 211, except for official university holidays. There will be no class on Thursday November 22.

The midterm examinations are on Tuesday October 9 and Tuesday November 6. The final examination is on Tuesday December 18 at 8:00–10:00am. At the instructor’s discretion, students may be granted alternative exam times. In any case, students must take exams on campus in a proctored environment.

Text: The required text is Armstrong: Basic Topology, Springer. We will cover Chapters 2– thoroughly. If time allows, we will cover selected material from Chapters 6–8.

Contacting Me: E-mail: isaksen@wayne.edu.

Office Hours: FAB 1195, Mondays, Wednesdays, and Fridays at 12:30-1:00pm. Online meet- ings can be arranged during these times. I am happy to schedule appointments outside of regular office hours. Appointments are not strictly necessary, but there is no guarantee that I will be in my office if you just stop in.

Online information: All information, including the contents of this sheet, will be posted on the Blackboard site.

Grading:

First exam 25% Second exam 25% Final exam 25% Homework 15% Essays 10%

Homework: Homework assignments will be posted on the course Blackboard site. These assignments are due each Thursday, and they may be submitted electronically.

Student Disability Services: If you have a documented disability that requires accommoda- tions, you should register with Student Disability Services. I will be happy to discuss this further with you in private.