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This course covers the breadth of university calculus: differentiation, integration, infinite series, and ordinary differential equations. It focuses on concepts and interconnections. In order to cover this much material, computational techniques are de-emphasized. The approach is historically based and classical, following original texts where possible.
Multivariable calculus is one of the core parts of an undergraduate mathematics curriculum. Introductory calculus mostly concentrates on situations where there is one input and one output variable; multivariable extends differentiation, integration, and differential equations to cases where there are multiple input and output variables. In this way, multivariable calculus combines calculus and linear algebra; the subject can also be called vector and matrix calculus.
Everything is geometry! This class is about two things: first, about how mathematicians have extended the concept of "geometry" beyond triangles and circles, into higher-dimensional spaces, curved spaces, spaces of functions, discrete spaces, and more. Second, about how this extension of "geometry" can allow us to apply our powerful geometric intuition to a wide range of problems that might not initially seem geometric, both within mathematics, and in physics, computer science, and elsewhere.
Discrete mathematics studies problems that can be broken up into distinct pieces. Some examples of these sorts of systems are letters or numbers in a password, pixels on a computer screen, the connections between friends on Facebook, and driving directions (along established roads) between two cities. In this course we will develop the tools needed to solve relevant, real-world problems. Topics will include: combinatorics (clever ways of counting things), number theory and graph theory. Possible applications include probability, social networks, optimization, and cryptography.
The seventeenth-century Flemish painter-diplomat Peter Paul Rubens is at the heart of a course that proposes the intrinsic baroqueness of diverse strains of high modernism. Our transdisciplinary project crosses entrenched nationalistic and chronological borders between modern and early modern art and artists including Bacon, Guston, Manet, Newman, Picasso, Bearden, and Titian in addition to Robert Rauschenberg (1925-2008), himself a more conceptually various and possibly more prolific artist even than Rubens (1577-1640) to whom some 3,000 paintings and drawings have been attributed.
In this course, we will explore various projects that aim to connect people with their surroundings and communities.
We will also explore the strategies that various artists have implemented to increase their audiences and interest in the arts.
We will analyze and design projects that seek sustainability, diversification, and access to the experience of art and culture.
By evaluating environments we could design artistic projects that promote art, artistic education, and the promotion of cultural products as actions to build community, identity, and a creative economy.