S311 | 3588 | Judge

9:05-9:55A Daily BH240 The study of calculus in many dimensions developed hand in hand with theoretical physics during the 18th, 19th and early 20th century. Indeed, today it serves as the language for much of modern theoretical physics. Yet, multidimensional calculus has many applications outside of physics such as computer imaging and economics. It serves as the foundation upon which modern geometry is built, and it finds use in many unexpected parts of mathematics, for example number theory. It pervades modern mathematics. S311 is the first part of a full year honors course in multidimensional calculus. As in the usual course, the goal is to master the techniques of differentiation and integration in many dimensions. But in S311 we take the 'high roads' of local differential forms. A theorem and proof approach to the material will solidify these roads, and along the way I will point out applications to theoretical physics. It should prove to be an interesting journey.