Math 480: Experimental Mathematics

Fall 2020


Important Links

Instructor and Meeting Times

Instructor: Nathan McNew
Office hours: Monday and Wednesday 12:00--1:30 and by appointment
Office: 326 (2 × 163) 7800 York Road
Lecture: Monday and Wednesday: 5:00-6:15 YR 219 (or virtually)

Note that you do not need an appointment to attend regularly-scheduled office hours. If you have a conflict you may make an appointment to meet outside those times.

Course Description and Objectives

Course description:
A course based introduction to undergraduate research and mathematical exploration through computational experimentation. Programming, computational methods, algorithms, and software environments used by research mathematicians. Students will apply these tools to explore patterns and make conjectures and explore the role of computation in formal mathematical proofs.

Course objectives: Experimental mathematics is the use of numerical experimentation in research to discover and prove new phenomena. The idea has a rich history: Gauss, Euler, and Riemann were all experimental mathematicians. The goal of this course is to teach both the philosophy and practice of experimental mathematics. This will be demonstrated with examples from actual research resulting from computational experimentation. You will earn to program in SageMath and experiment with mathematical objects. Along the way, you will also learn about some beautiful ideas and interesting open problems in modern mathematics.

Prerequisites: COSC 236, MATH 267 MATH 273 or permission of instructor.


No required textbook. Selected resources will be posted here.


Problem sets will be posted on the homeworks tab of this page. Students will need to prepare written solutions for each of these problems, and these problems will be graded. These written solutions must be turned in before the corresponding class discussion of the solution for the solution to receive full credit. Students will be asked to participate in class, working out problems, and presenting material. Students will be required to complete a final project. Details on the final project will be given to the class in October. As part of the project, students will write a final paper, and will give a presentation.

Expect to spend a substantial amount of time studying, working on homework and preparing for the course. The general rule is two to three hours outside class for each hour inside; this translates to about 6-9 hours of homework and personal study per week.


There will be a single midterm exam covering the conceptual aspects of the course.

(Tentative) Wednesday, October 28

If you have a conflict with a scheduled exam contact your instructor as soon as possible.


Grades will be assigned based on homework, projects in class presentations and participation, and exams. They will be weighted in the students final grade as follows:

Problem Sets, Quizzes 15%
Class participation 10%
Project 1 15%
Project 2 15%
Midterm 15%
Final Presentation 10%
Final Paper 20%

Disabilities and Religious Observances

Any students with disabilities, including "invisible" disabilities such as chronic diseases and learning disabilities are encouraged to discuss appropriate accommodations with the instructor, either after class or during office hours.

Towson University is committed to providing equal access to its programs and services for students with disabilities, Students with disabilities should visit the Accessibility and Disabilities Services Web page, to learn about how to arrange for any appropriate accommodations. It is the student's responsibility to let the instructor know when he/she is a student with needs in this area. A memo from Disability Support Services (DSS) authorizing your accommodations will be needed.

If you have a religious observance that conflicts with your participation in the course, please meet with me before the end of the second week of the term to discuss appropriate accommodations.

Course Policies

Academic Integrity: This class is conducted in accordance with the Academic Integrity Policy. Cheating or plagiarism in any form is unacceptable. In particular:

On Exams: No assistance may be given or received except that you may ask the instructor for clarification of a problem.

On Homework: You are permitted and encouraged to collaborate with other students on the homework. However, after discussing the problems, you must write up the final solutions in your own words. You may use calculators and approved software. Additionally, you may consult your class notes and text. It is not permitted for someone to provide the answers for you. It is also not permitted to submit answers found on the internet as your own work.

See this page for more about plagiarism and how to avoid it.

Class attendance is expected. If you miss a class, it is your responsibility to get the material and the homework assignment from your fellow students.

Diversity Statement: Towson University values diversity and fosters a climate that is grounded in respect and inclusion, enriches the educational experience of students, supports positive classroom and workplace environments, promotes excellence, and cultivates the intellectual and personal growth of the entire university community.