MATH-555-001 — Spring 2018, TR 11:00am–12:15pm, VC 1027
There are many reasonable descriptions of functional analysis, but the way I like to think of it is: infinite dimensional linear algebra. It is linear algebra because it is concerned with various vector spaces, and it is infinite dimensional because, well, they are infinite dimensional vector spaces. This allows for the study of a much wider array of spaces than finite dimensional linear algebra because, for instance, even polynomials or spaces of continuous functions are infinite dimensional vector spaces. Moreover, since functional analysis at its core shares so much with linear algebra, you can imagine the vast applications it can have. So, you might be asking yourself: “where is the analysis?” This is a valid question, and the answer lies in the word “infinite.” On our vector spaces, it will be important to discuss distances between vectors, or the length (norm) of vectors. We will prove during the course that all finite dimensional normed vector spaces of a given dimension are equivalent in a precise sense. This is far from true in the infinite dimensional case, and the richness this entails is part of what makes functional analysis so interesting.
We will use Introductory Functional Analysis with Applications, by Erwin Kreyszig. Prerequisites include the content of MATH-421 and MATH-450, especially topics related to abstract vector spaces, the dual of a vector space, inner product spaces, convergence, completeness, continuity and open and closed sets.
|Monday, 15 January||Martin Luther King Day, no class|
|Friday, 19 January||Last day to add/drop with full refund|
|4–11 March||Spring break, no class|
|Friday, 23 March||Last day to withdraw for
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