Math 415: History of Mathematics, Spring 2018

Instructor: Dr. Brant Jones
Email: jones3bc at jmu dot edu
Office: 325 Roop Hall
Section 0001 class meetings: TuTh 2:00 pm - 3:15 pm in Burruss Hall Room 034
Class webpage:
Office hours: Tuesday 3:30 - 4:30 and Wednesday 1:00 - 4:00 pm in Roop 325, or by appointment.

Section 0001 final exam: Tuesday, May 1 from 1:00 - 3:00 pm in our usual room.


This is the webpage for the course, where I will post assignments, problems and announcements. Please bookmark it, and reload it before each class.

Here are two sample book reviews: from New York Times and American Mathematical Monthly (don't choose either of these books, please).

The median grade on the midterm problems was a B. As a reminder, I grade your work on a 4-point scale and average the results together. So, if you received mostly B's and a few A's on the exam, this would contribute a B+ to your course grade. (Canvas has its own percentage scale which you may feel free to either ignore or convert to the 4-point scale.)


The required text Journey Through Genius by William Dunham is available at the University Bookstore (and elsewhere) for about $15. We plan to cover most of the chapters this semester.


Date Lecture/preparationTo do...
Tuesday, January 9Welcome! Obtain a copy of the textbook.
Thursday, January 11Read Chapter 1. Problem set 1
Tuesday, January 16Read Chapter 2. Supplemental materials:
  Geometric rearrangement can be misleading...
  (Highly recommended!) Byrne's (color) edition of Euclid's Elements
  Joyce's (hyperlinked) edition of Euclid's Elements
  Heath's edition of Euclid's Elements (with extensive commentary)
Thursday, January 18 Problem set 2
Tuesday, January 23Read Chapter 3.
Thursday, January 25 Truncated icosahedron = shape of a soccer ball Problem set 3
Tuesday, January 30Read Chapter 4.
Thursday, February 1 Problem set 4
Tuesday, February 6Assessment day! (No class.)
Thursday, February 8Read Chapter 5. Finish problem set...
Tuesday, February 13Discuss Diophantus' Arithmetica (~250), and the Islamic Golden Age (~800-1258):
  works of al-Khwarizmi and
  Omar Khayyam
Thursday, February 15 Problem set 5
Tuesday, February 20Finish problem set 5.
Thursday, February 22Read Chapter 6.
Tuesday, February 27Review for midterm, bring questions. Midterm practice problems
Thursday, March 1Midterm exam. Book selection due (via email, subject: 415 book review)!
March 5 - 9Spring break! (No class.)
Tuesday, March 13Read Chapter 7. See also:
  Briggs' first logarithm table
  Napier rods for division
  Pascaline machine for arithmetic
  A more elaborate calculator from The Arithmeum in Bonn
Thursday, March 15 Problem set
Tuesday, March 20Read Chapter 8.
Thursday, March 23 Problem set
Tuesday, March 27Read Chapters 9 and 10 (Euler).
Thursday, March 29 Problem set
Tuesday, April 3Read Chapters 11 and 12 (Cantor).
Thursday, April 5 Problem set
Tuesday, April 10Presentations.
Thursday, April 13Presentations.
Tuesday, April 17Presentations.
Thursday, April 20Presentations.
Tuesday, April 24Presentations.
Thursday, April 26Presentations.


This class covers selected topics from the history of mathematics. We will focus on specific mathematical ideas and theorems, with a view towards developing a common set of themes in the types of mathematical questions and techniques that have been employed throughout history. MATH 245 is a formal prerequisite for this course.

There are several activities that will contribute to your learning in this class:


You will be able to see scores for your assignments as the semester progresses on your JMU Canvas account under the gradebook for this course.

I do not have a set grade distribution for the course, so there is no competition for grades, and it is entirely possible that everyone in the class could receive an A. I do not usually assign WP or WF grades. I want all of my students to succeed and am happy to work with you if you are not satisfied with your current work.

Honor Code

In this course, you are encouraged to discuss problems and study with other students in order to enhance your own learning and understanding of the material. However, assessments must reflect your own work. You are expected to abide by the JMU Honor Code.


I do not accept late assignments nor allow makeups for missed coursework.

If you need to miss an exam, you should make arrangements with me at least one week ahead of time. I will assign a zero score for missed work if you do not communicate the reason for your absence in advance or if I do not approve the absence.


Being a student is a full-time job, and this is a challenging class. Make sure you are budgeting enough time to think about the course outside of lecture. Generally speaking, I expect you to spend at least one hour outside of class for each hour of lecture, reading and thinking about the textbook. You don't need to spend all of this time working by yourself; consider starting a study group to share ideas about the reading.

Please take advantage of office hours, and feel free to drop by my office at other times. You do not need an appointment. If I'm in my office, I'll be happy to discuss the course with you. If you cannot make the regular office hours, email me so that we can schedule an appointment.

JMU abides by Section 504 of the Rehabilitation Act of 1973 and the Americans with Disabilities Act, which mandate reasonable accommodations be provided for students with documented disabilities. If you have a disability and may require some type of instructional and/or examination accommodations, please contact me early in the semester so that I can provide or facilitate provision of accommodations you may need. If you have not already done so, you will need to register with the Office of Disability Services, the designated office on campus to provide services for students with disabilities. The office is located in Wilson Hall, Room 107 and you may call 540-568-6705 for more information.

Please see for common JMU academic policies regarding: Attendance, Academic Honesty, Adding/Dropping Courses, Disability Accommodations, Inclement Weather, and Religious Accommodations.