This course will introduce students to important concepts in effective academic writing by thinking about and thinking through popular music. Our complex relationships to popular music confront us with a host of challenging social, cultural, political, and ethical issues. How do we use music to construct, maintain, or challenge private and public identities? How are race, gender, class, sexuality, and the nation constructed through popular music? What is the role of music in our everyday lives?

(Offered as EUST 101 and MUSI 101) This course teaches the close reading of music through guided listening in a variety of traditions and historical periods. The topic may change from year to year. In 2015-16, we focus on aural analysis of musical texture and form through an historical survey of works stretching from medieval Europe (twelfth-century Gregorian chant) to twentieth- and twenty-first-century America (blues, swing, Broadway, bebop, and minimalism). Composers whose works we will study include: Hildegard von Bingen, G. Palestrina, C. Monteverdi, J.S. Bach, W.A. Mozart, L.

Fall and spring semesters. The Department.

An introduction to Lebesgue measure and integration; topology of the real numbers, inner and outer measures and measurable set; the approximation of continuous and measurable functions; the Lebesgue integral and associated convergence theorems; the Fundamental Theorem of Calculus.  Four class hours per week.

Requisite:  MATH 355.  Spring semester.  Professor TBA.

The quadratic formula shows us that the roots of a quadratic polynomial possess a certain symmetry. Galois Theory is the study of the corresponding symmetry for higher degree polynomials. We will develop this theory starting from a basic knowledge of groups, rings and fields. One of our main goals will be to prove that there is no general version of the quadratic formula for a polynomial of degree five or more. Along the way, we will also show that a circular cake can be divided into 17 (but not 7) equal slices using only a straight-edged knife. 

Fall and spring semesters. The Department.

(Offered as STAT 370 and MATH 370.) This course examines the theory behind common statistical inference procedures including estimation and hypothesis testing. Beginning with exposure to Bayesian inference, the course will cover Maximum Likelihood Estimators, sufficient statistics, sampling distributions, joint distributions, confidence intervals, hypothesis testing and test selection, non-parametric procedures, and linear models. Four class hours per week.

Requisite: STAT 111 or STAT 135 and STAT 360, or consent of the instructor. Spring semester.  Professor Horton.

A stochastic process is a collection of random variables used to model the evolution of a system over time.  Unlike deterministic systems, stochastic processes involve an element of randomness or uncertainty. Examples include stock market fluctuations, audio signals, EEG recordings, and random movement such as Brownian motion and random walks. Topics will include Markov chains, martingales, Brownian motion, and stochastic integration, including Ito’s formula. Four class hours per week, with weekly in-class computer labs.

Completeness of the real numbers; topology of n-space including the Bolzano-Weierstrass and Heine-Borel theorems; sequences, properties of functions continuous on sets; infinite series, uniform convergence. The course may also study the Gamma function, Stirling’s formula, or Fourier series. Four class hours per week. 

A brief consideration of properties of sets, mappings, and the system of integers, followed by an introduction to the theory of groups and rings including the principal theorems on homomorphisms and the related quotient structures; integral domains, fields, polynomial rings. Four class hours per week.