![]() ![]() The course briefly touches on the subject of manifolds, i.e., smooth surfaces, which are important in fields such as topology, differential geometry, and Lie theory. In particular, linear algebra turns out to play a significant role, especially the space Rn and the determinant. Though some of the material at the beginning of MAT 218 might look familiar, fairly soon analysis in several variables takes on a flavor of its own. MAT 218 is in a sense a continuation of MAT 215: it generalizes the concepts of limits, differentiation, and integration from one to multiple dimensions. The majority of the course is spent studying linear transformations between vector spaces and their close relatives, matrices. One example of this is the set of n-tuples of real numbers. The most basic mathematical object this course deals with the vector spaces, a structure whose elements can be added and multiplied by scalars. ![]() MAT 217 is a course in linear algebra, a subject at the foundation of almost all branches of pure and applied math. ![]() See below for a first-hand description of MAT 215. The remainder of the course is spent on developing the theory of limits, differentiation, integration, sequences, and series. The course starts by addressing the question: what are real numbers? It then introduces its students to important topological preliminaries such as open and closed sets, compactness, and completeness. Go to the bottom of this page to download it.The goal of MAT 215 is to build the theory of analysis from the ground up, teaching students to think rigorously along the way.
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