Applied Mathematics - Math 345

Professor Marcus Pendergrass

Applied Mathematics focuses on solving real-world problems using mathematical tools and techniques, in conjunction with computer modeling and simulation. This semester, the theme for the course is "The Mathematics of Music, and vice versa." We will begin by focusing on the mathematics of sound, then move onto the application of mathematical techniques for generating musical compositions. By the end of the semester, each student will have created their own software synthesizer, and will have used it to create an original musical composition.

Here is a quick presentation introducing the main themes of the course: Keynote, PDF.


Linear Algebra (Math 231), Calculus III (Math 242), or permission of instructor. (No prior musical knowledge is assumed.)

Determination of Course Grade

  • Homework/Projects: 40%
  • Two Tests: 40%
  • Final Exam: 20%

Final Exam Date

Friday, December 14, from 2 pm until 5 pm.

Attendance and Excused Absences

You are expected to attend every class.  If you are late for class, you are counted as absent. You assume full responsibility for all material covered during any absence. A grade of "0" will be assigned for all work missed due to unexcused absences. If you have four or more unexcused absences, you may be withdrawn from the class with a grade of WF.

Make-up Policy

  • Late homeworks or projects are not accepted. If you are going to miss class on the day that a homework or project is due, you must turn it in early.
  • If you are going to miss class on the day of a test, then you must get in contact with me before the test or quiz is given to arrange a make-up. Make-up tests will only be allowed for reasonable absences.
  • If you have a legitimate College-sponsored event in which you must participate (such as a sporting event) scheduled on the same day as a test, then you must arrange with me to take the test or quiz early.

Laptops, Tablets, Phones, Texting, etc.

  • All cell phones should be turned off during class, or put in silent mode.
  • No texting or other use of the internet during class.

Course Topics

  • Sound mathematics
  • Pure tones
  • Amplitude envelopes
  • Fourier series
  • Instantaneous frequency
  • Frequency modulation
  • Effects
  • Pitch and rhythm
  • Scales
  • Generating melodies and accompaniments
  • Organizing a musical composition
  • Others as time permits