Topics in Geometry
MA541 Winter 2024: Northern Michigan University

This is the syllabus for Topics in Geometry.


  • Dr. Josh Thompson | Office - JAMR 2226 | email
  • Classroom

  • Math 541 | 2:00 - 3:40 pm | MW | WSTN 3202 | zoom
  • Text

  • Geometry & Topology, by Miles Reid & Balazs Szendroi (Main)
  • Other references

  • Modern Geometry, by James Smart
  • Introduction to Geometry by H.S.M. Coxeter
  • Notes on Geometry Elmer Rees
  • Office Hours

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

  • Written Homework: 30%
  • Presentations: 15%
  • Midterm: 25%
  • Final Exam: 30%
  • Homework

    In most of the homework you will be writing proofs. As always in mathematics, 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.


    You will be asked to present examples, problems and theorems at the board. Many will also be assigned as written homeowork, some will be theorems from the text. Grades will be given using the homework rubric above.


    The examinations will be a combination of in-class and take-home projects.

  • Midterm: March 13
  • Final: May 1, 2-3:50 pm
  • Course Description

    We will develop Euclidean, projective and hyperbolic geometry using tools of elementary algebra and analysis.

    Learning Outcomes

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

  • Prove theoroms from Euclidean geometry.
  • Prove theorems from projective geometry.
  • Prove theorems from hyperbolic geometry.
  • 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.

    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 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.