This course is intended for students with little or no background in music who would like to develop a theoretical and practical understanding of how music works. Students will be introduced to the technical details of music such as musical notation, intervals, basic harmony, meter and rhythm. Familiarity with basic music theory will enable students to read and perform at sight as well as provide an introduction to the composition of melodies with chordal accompaniment.
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?
This course aims to instill an appreciation of various types of music mainly from the so-called classical tradition of Western music from eleventh-century Gregorian chant through twentieth-century genres such as the American musical, minimalism, and jazz (the blues, swing, bebop, and cool jazz). Additionally, our chronological survey will include genres such as the symphony, the concerto, program music, piano music (Romantic character pieces and ragtime), and opera. In addition to works by long-canonized composers (e.g.
Fall and spring semesters. The Department.
An introduction to general topology: the topology of Euclidean, metric and abstract spaces, with emphasis on such notions as continuous mappings, compactness, connectedness, completeness, separable spaces, separation axioms, and metrizable spaces. Additional topics may be selected to illustrate applications of topology in analysis or to introduce the student briefly to algebraic topology. Four class hours per week. Offered in alternate years.
An elliptic curve is the set of zeros of a cubic polynomial in two variables. If the polynomial has rational coefficients, it is natural to ask for a description of those zeros whose coordinates are either integers or rational numbers. Our study of elliptic curves will focus on this fundamental problem and reveal a fascinating interplay between algebra, geometry, analysis and number theory. Topics discussed will include the geometry and group structure of elliptic curves, the Nagell-Lutz Theorem describing points of finite order, and the Mordell-Weil theorem on the finite
Independent reading course.
Fall and spring semesters. The Department.
(Offered as STAT 370 and MATH 370) This course examines the theory underlying common statistical procedures including visualization, exploratory analysis, estimation, hypothesis testing, modeling, and Bayesian inference. Topics include maximum likelihood estimators, sufficient statistics, confidence intervals, hypothesis testing and test selection, non-parametric procedures, and linear models.
Completeness of the real numbers; topology of n-space including the Bolzano-Weierstrass and Heine-Borel theorems; sequences, properties of continuous functions 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.
Fall 2020 sections of MATH 355 will be online-only, in which case the course’s full syllabus will be covered through a combination of synchronous meetings for each section and asynchronous lectures supported by an ample number of Zoom office hours.
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.
Requisite: MATH 211 and either MATH 271 or 272, or consent of the instructor. Students with a grade of B+ or lower in linear algebra are encouraged to take another 200-level course with proofs before taking MATH 350.
