Topology
MA516 Fall 2019: Northern Michigan University

This is the syllabus for Topology Math 516. Here you'll find information on prerequisites, grading policy, homework, study resources, exam dates and a tentative course schedule.

Classroom

Math 516 :: JAMR 3309 :: 1:00 - 1:50 pm :: MWTF

Course Webpage

  • http://euclid.nmu.edu/~joshthom/Teaching/MA516

    • Textbook

    Topology, 2nd Ed. by James R. Munkres.

    Office Hours

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

    • Grading

    There are 280 possible points which constitute your grade. You may earn them as follows.

  • Problem Sets - 140 points (50%)
  • Midterm - 70 points (25%)
  • Final- 70 points (25%)

    • Problem Sets

    There will be fourteen problem sets, one each week. 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. Problems 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. Solutions that are suspected of being opied will not be graded.

    You are encouraged to ask me questions about the problem sets.

    Midterm

  • October 23

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

    Other Resources

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

    • 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.
  • Compute the Fundamental Group of various manifolds.

    • 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 work through chapters 1,2,3,9,11,12

  • Chapter 1 :: Set Theory & Logic :: Week 1
  • Chapter 2 :: Topological Spaces & Continuous Functions :: Weeks 2-7
  • Chapter 3 :: Connectedness & Compactness :: Weeks 8-9
  • Chapter 9 :: The Fundamental Group :: Weeks 10-11
  • Chapter 11 :: The Seifert-van Kampen Theorem :: Week 12
  • Chapter 12 :: Classification of Surfaces :: Weeks 13-14

    • 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.