Courses

Detailed analysis of selected examples of music literature from various stylistic eras, moving from the simpler to the more complex types of composition, the second semester being devoted principally to the larger genres such as sonata and fugue.

Real numbers, infima and suprema; sequences and series of real numbers, convergence and limits, Cauchy sequences and completeness; topology of the real line, Bolzano-Weierstrass and Heine-Borel theorems; real-valued functions of a real variable, continuity and uniform continuity. Emphasis on proofs.

Real numbers, infima and suprema; sequences and series of real numbers, convergence and limits, Cauchy sequences and completeness; topology of the real line, Bolzano-Weierstrass and Heine-Borel theorems; real-valued functions of a real variable, continuity and uniform continuity; intermediate#value and extreme-value theorems. Emphasis on proofs.

A continuation of MATH 4210. Limits, derivatives, theory of the Riemann integral, sequences of functions, uniform convergence and power series. Emphasis on the development of proofs by students.

A continuation of MATH 5210 Analysis I. Limits; theory of the Riemann integral; sequences of functions; uniform convergence; power series. Emphasis on the development of proofs by students.

A continuation of MATH 3380, this course’s topics include differentiation, integration, series, and sequences of functions, and associated topics.

This course covers the theory of integration with special emphasis on Lebesgue integrals. Topics include: Lebesgue integral, Bounded Convergence theorem, differentiation and integration, absolute continuity, and Lp spaces.

Sequences and series of functions, modes of convergence, power series, elementary functions; derivatives and antiderivatives, the mean-value theorem; Riemann integration and the Fundamental Theorem of Calculus; R^n and abstract spaces, functions of several variables. Emphasis on proofs.

Sequences and series of functions, modes of convergence, power series, elementary functions; derivatives and power series, elementary functions; derivatives and antiderivatives, the mean-value theorem; Riemann integration and the Fundamental Theorem of Calculus; R^n and abstract spaces, functions of several variables. Emphasis on proofs.

Survey of a variety of technical approaches to composition in the 20th century and such organizing techniques as harmony, voice leading, textural design, form, and orchestration.