Music and language are intimately connected as forms of communication, meaning, and interaction, but this intimacy has been characterized in many ways in different times and places. In this course, we will explore a variety of the ways in which music and language have been related and made distinct by examining how music and language are understood in different social, historical, and cultural contexts.
Music is sometimes portrayed as an abstract art, standing apart from the mundane everyday. However, music has also functioned as a tool for a large range of social and individual purposes throughout human history. Rather than tendentiously opposing these claims--music is an art or it is a tool--this survey course explores the vast diversity of ways that humans have put music to use in their social worlds.
Fall semester: Through composition, analysis, and performance, we will build a solid working understanding of basic principles of melody and harmony common in Western musical traditions. Assignments include harmonizing melodies, writing short melodies and accompaniments, and composing in several forms such as 12-bar blues, classical minuets, and "Broadway"-style 32-bar AABA form. On several occasions we will use our instruments and voices to bring musical examples to life in the classroom. Two class meetings and one lab session per week.
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 into 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.
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 Culiuc.
Independent reading course.
Fall and spring semesters. The Department.
This course builds upon the material in MATH 355 (Introduction to Analysis) in order to rigorously develop basic tools for studying functions of more than one real variable. While the setting in MATH 355 is the real number line, the context for this course will be the n-dimensional Euclidean space. Many facets of analysis on this n-dimensional space will be explored including its topological properties as well as differentiation and Riemann integration in n-variables. The course will cover fundamental results such as the celebrated implicit and inverse function theorems.
(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.
Requisite: STAT 111 or STAT 135 and STAT 360, or consent of the instructor. Limited to 25 students. Spring semester. Professor Horton.
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.
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 355.
