New or Modified Courses

New or Modified Courses

Link to new or modified Graduate Courses

Math 5: The Math of Music and Sound

Instructor: Prof. A. Barnett
Time: 08F: MWF 10:00AM

Sound and music are integral parts of all cultures and are critical to human and animal communications. The production, transmission, and perception of sound is woven through with mathematics. With the goal of expanding both scientific and artistic horizons (and teaching you some ear-opening practical skills) we explore vibration, resonance, waves, musical instruments, the human ear, speech, architectural acoustics, harmony and dissonance, tuning systems, and composition.

Prerequisites: high-school algebra, trigonometry, and physics. Familiarity with musical notation or some instrument will help.

Other notes: Satisfies the QDS distrib. No prior knowledge of calculus needed (but we will teach you a tiny bit). We will also do a bunch of recording and analysis using laptops, and complete class projects. Whether an arts or science major, this course will be interesting to you.

Math 76: Topics in Applied Mathematics

Instructor: Prof. D. Rockmore
Time: 08W: 10A, 09W: Arrange

The numerical nature of twenty-first century society means that applied mathematics is everywhere: animation studios, search engines, hedge funds and derivatives markets, and drug design. Students will gain an in-depth introduction to an advanced topic in applied mathematics. Possible subjects include digital signal and image processing, quantum chaos, computational biology, cryptography, coding theory, waves in nature, inverse problems, information theory, stochastic processes, machine learning, and mathematical finance. Prerequisite: Mathematics 22, 23, or permission of the instructor.

Math 86: Mathematical Finance I

Instructor: Prof. C. Sutton
Time: 08S: MWF 1:45--2:50, 08F: Arrange

Financial derivatives can be thought of as insurance against uncertain future financial events. This course will take a mathematically rigorous approach to understanding the Black-Scholes-Merton model and its applications to pricing financial derivatives and risk management. Topics may include: arbitrage-free pricing, binomial tree models, Ito calculus, the Black-Scholes analysis, Monte Carlo simulation, pricing of equities options, and hedging. Prerequisites: Mathematics 20/60 and Mathematics 23, as well as some programming experience (e.g., Computer Science 5).

Math 116: Numerical methods for PDEs and waves

Instructor: Prof. A. Barnett
Time: 08F: TTh 10:00--11:50

The Laplace equation (describing steady-state diffusion, heat flow, electrostatics) and Helmholtz equation (describing linear waves, acoustics, electromagnetics, optics, quantum) are linear PDE boundary value problems and are ubiquitous in modeling the real world. They may be solved numerically by recasting the problem onto the boundary; this is more efficient at short wavelengths (and easier to code) than standard discretization methods. You will build codes, analyse their errors, explore phenomena in wave scattering and quantum chaos (short-wavelength asymptotics), connect with current research. Along the way you'll pick up some general applied math and numerical analysis.

Prerequisites: Math 22 (lin alg), Math 23 (diff eq). Very helpful: Math 43 (complex), Math 46 (applied math), Math 35/63 (real analysis). Some computer programming highly recommended. Undergraduates welcome by permission of instructor.