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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.
In the United States, recent years have witnessed an upsurge in right-wing organizing and violence, culminating in the 2021 insurrection at the United States Capitol that sought to overturn the legitimate results of a democratic election. This is not a uniquely American problem. Across much of the globe, political parties organized around hyper-nationalism have gained steam, in some cases mobilized through charismatic leaders wrapping their hateful politics in faux-populist rhetoric.
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.