General Topology
MA366 Fall 2021: Northern Michigan University

This is the syllabus for Topology Math 366. Here you'll find information on prerequisites, grading policy, homework, study resources, exam dates and a tentative course schedule.

Classroom

Class will be held, unless otherwise noted, at the following days & times.

  • Math 366 :: JAMR 3311 :: 2:00 - 2:50 pm :: MWF

    • Your daily attendance is required. You are expected to come to class daily, to be fully awake, to pay attention to and participate in the class discussion. I will do my part to make class something you look forward to rather than dread.

    Prerequisites

    You need either:

  • C or better in MA211 & MA265

    • Course Webpage

  • http://euclid.nmu.edu/~joshthom/Teaching/MA366

    • Textbook

    The (required) textbook we will use for this course is

    Introduction to Topology - Pure and Applied by Adams & Franzosa.

    Office Hours

  • Tuesday: 2pm - 3pm
  • Thursday: 12pm - 2pm
  • Friday: 12pm - 1pm

    • Grading

    There are 200 possible points which constitute your grade. You may earn them as follows.

  • Problem Sets - 80 points (40%)
  • Quizzes - 20 points (10%)
  • Midterm - 50 points (25%)
  • Course Summary - 20 points (10%)
  • Final Paper - 30 points (15%)

    • Problem Sets

    There will be eight problem sets. In most of the problems your will be writing proofs. As in any higher-level mathematics class, your proofs should be written in complete sentences. The goal of the proof should be to explain not to verify. Pictures and diagrams are encouraged. A selection of problems will be graded. If a problem is to be graded, it will be graded as follows.

  • 0 - left blank
  • 3 - question copied, nothing else written
  • 4 - something written apart from the question, but it appears to be written only to take up space
  • 6 - substantially incomplete; does not really answer the main question; major errors; poor writing
  • 8 - mostly complete; maybe a few minor errors
  • 9 - complete; no errors; some personal insight; well-written
  • 10 - wonderful

    • You are welcome to work with your classmates on problem sets but your final writeup must be your own. Do not look up solutions to the problem in any written form, including the internet. You are encouraged to ask me questions about the problem sets.

    Quizzes will be given frequently. These will be closed book but easy if you read and know the basic definitions and examples.

    Midterm

  • October 18

    • The midterm examination will be in class during our usual time. The exam will be closed book, closed notes, closed friends and open-brained.

    Course Summary

    This will consist of a stream-lined summary of our course.
  • Important definitions
  • Important theorems
  • No proofs neccessary
  • Typesetting in Latex is encouraged but not required. I recommend Overleaf.

    • Final Paper

  • You choose the topic. Find sources online, in textbooks or from this list of possible topics
  • Your goal is to summarize the topic and give details as if you are explaining it to your classmates.
  • You can work alone or in pairs. Single-author: 4-5 pages. Co-authored: 8-10 pages.
  • You may talk to anyone about the paper but the writing must be your own.
  • The writing center may be helpful.
  • Grades for co-authored papers will adjusted by a "partner evaluation coefficient".
  • Deadline to submit topic: November 1
  • Deadline to submit annotated bibliography: November 14
    (A list of sources (at least two), with descriptions of why you're using them)
  • Deadline to submit final paper: December 11

    • The final paper will be worth 30 points (15% of your grade). Grading will be based as follows:
  • 2 points : Submitted paper topic on time
  • 3 points : Submitted annotated bibliogrphy on time
  • 10 points: Paper exposition
  • 15 points: Paper content

    • Laptops & Phones

    Do not use your laptop, phone or electronic media device in class unless instructed to do so.

    Other Resources

  • Three-Dimensional Geometry and Topology - Bill Thurston & Silvio Levy
  • Topology Now! - Bill Messer & Philip Straffin
  • The Geometry Junkyard

    • Both free and paid tutoring is available, in the tutoring lab on the 2nd floor of Jamrich.

    Learning Outcomes

    Upon successful completion of this course students will be able to:

  • Distinguish spaces from one another using homeomorphisms, compactness and connectedness.
  • Create topological spaces using products, quotients and subspaces.
  • Apply fundamentals of topology to solve problems.

    • Evaluation of these learning outcomes will be done through a mix of assignments, class exercises, projects, research papers, group work, written & oral quizzes and exams.

    Course Description

    We will cover the first 7 chapters of the textbook, and various parts of chapters 8-14.

  • Chapter 1 :: Topological Spaces :: Week 1 & 2
  • Chapter 2 :: Interior, Closure, and Boundary :: Weeks 3 & 4
  • Chapter 3 :: Creating New Topological Spaces :: Weeks 5,6 & 7
  • Chapter 4 :: Continuous Functions and Homeomorphisms :: Weeks 8 & 9
  • Chapter 5 :: Metric Spaces :: Weeks 10 & 11
  • Chapter 6 :: Connectedness :: Weeks 12 & 13
  • Chapter 7 :: Compactness :: Weeks 12 & 13
  • Chapters 8-14 :: Research Paper Topics :: Week 14

    • Natural Sciences Requirement

    This course satisfies the Foundation of Natural Sciences/Mathematics requirement. Students who complete this course should be able to demonstrate a basic understanding of mathematical logic; use mathematics to solve scientific or mathematical problems in college classes; express relationships in the symbolic language of mathematics; and appreciate the role of mathematics in analyzing natural phenomena.

    University Policies

    Academic Honesty: Cheating is not only unethical and pathetic, but is a violation of the Northern Michigan University Student Code and University Policy and grounds for your dismissal from the University.

    Discrimination & Harassment: Northern Michigan University does not unlawfully discriminate on the basis of race, color, religion, national origin, gender, age, height, weight, martial status, handicap/disability, sexual orientation or veteran status. If you have a civil rights inquiry, contact the Affirmative Action Office at 906-227-2420.

    Americans with Disabilities Act Statement: If you have a need for disability-related accommodations or services, please inform the Coordinator of Disability Services in the Dean of Students Office at 2001 C. B. Hedgcock Building (227-1737 or disserv@nmu.edu). Reasonable and effective accommodations and services will be provided to students if requests are made in a timely manner, with appropriate documentation, in accordance with federal, state, and University guidelines.

    The Registrar: Withdrawing from any course or any matters relating to registration are the responsibility of the student. For more information regarding this topic, check out the Registrars Website.