History of Mathematics
MA484 Winter 2024: Northern Michigan University

This is the syllabus for History of Mathematics


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

  • Math 541 | 1:00 - 2:00 pm | MWF | TSB 2906 | zoom
  • 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.


    You need to be able to read, think and have some mathematical curiosity.:


    We will read the book Journey through Genius, roughly one chapter per week. The Burton text will only be used as a starting point for papers and projects.

  • Journey through Genius by William Dunham (required, find at the University Bookstore)
  • The History of Mathematics by David M. Burton (optional)
  • Office Hours

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

  • Assignments - 50%
  • Exams - 25%
  • Final Project - 25%
  • Assignments

    There will be weekly problem sets. In many of the problems you 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.

  • Some assignments may require that you write biographical sketches or construct timelines.
  • You are welcome to work with your classmates on your assignments but your final writeup must be your own.
  • You are encouraged to ask me questions about the problem sets.
  • Exams

  • March 13
  • April 17

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

    Final Project

    In lieu of a final exam, you will complete a final project. Here are details of the project.

  • Part I: 6-10 page paper
  • Part II: 10-15 minute presentation on your topic (poster or slideshow is recommended)
  • You can work alone or in pairs.
  • You may talk to anyone about the paper but the writing must be your own.
  • The writing center may be helpful.
  • Deadline to submit topic: March 22
  • Deadline to submit annotated bibliography: April 1
    (A list of sources (at least two), with descriptions of why you're using them)
  • Deadline to submit final paper: May 2
  • The final paper will be worth 100 points. Grading will be based as follows:
  • Laptops & Phones

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

    Learning Outcomes

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

  • Describe the development of various areas of mathematics within and across various civilizations
  • Describe the changing character of mathematics over time
  • Give examples of significant theorems and applications of mathematics
  • Solve some famous mathematical 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.

  • Week 1 :: Hippocrates' Quadrature of the Lune (440 BC) :: Chapter 1
  • Week 2 :: Euclid's Proof of the Pythagorean Theorem (300 BC) :: Chapter 2
  • Week 3 :: Euclid's Proof of the Pythagorean Theorem (300 BC) :: Chapter 2
  • Week 4 :: Euclid & the Infinitude of Primes (300 BC) :: Chapter 3
  • Week 5 :: Euclid & the Infinitude of Primes (300 BC) :: Chapter 3
  • Week 6 :: Archimdes' Determination of Circular Area (225 BC) :: Chapter 4
  • Week 7 :: Cardano & the Solution of the Cubic (1545) :: Chapter 6
  • Week 8 :: A Gem from Isaac Newton (Late 1660s):: Chapter 7
  • Week 9 :: Bernoullis & the Harmonic Series (1689) :: Chapter 8
  • Week 10:: The Extraordinary Sums of Leonhard Euler (1734) :: Chapter 9
  • Week 11:: A Sampler of Euler's Number Theory (1736) :: Chapter 10
  • Week 12:: The Non-Denumerability of the Continuum (1874) :: Chapters 11 & 12
  • Week 13 & 14 :: Review & Student Presentations
  • 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.