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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.
Self-reflexive narratives, improvisation, non-linearity, slow cinema, alternative representations of time and space, experimental film grammars, poetic scripts, collective direction, Brechtian techniques. All of these processes and more will be explored in this hands-on production based course. Working collaboratively and on your peers’ work in various roles is required for this course. This course is appropriate to students doing advanced work in film and video as we will be taking a project from research, writing and structuring to post-production in the span of a term.
Students will work towards completing one moving image piece or body or work of their own devising during the course of the semester. This course is primarily intended for seventh- and eighth-term students with a Plan concentration in Film/Video who have already taken Advanced Projects I in the prior fall, but exceptions may be made by permission of the instructor.