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The most important calculus is calculus on manifolds. It explains how to make sense of computations, and to make the computations themselves easy. The main concepts and ideas in this theory are intrinsic, i.e., they are independent of the choice of coordinates. That is why modern math speaks the language of manifolds. The course leads directly to de Rham cohomology and the Stokes formula, which is one of the cornerstones of the theory. Prerequisites: Multivariable calculus, one-variable calculus (differentiability, derivative, and integration) and linear algebra (vectors and linear forms, linear transformations and determinant). Curriculum:
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