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Math Camp 1: Functional analysis

math Camp 1: Functional analysisAbout the primerGoalTo briefly review concepts in Functional analysis thatwill be used throughout the course. The followingconcepts will be described1. Function spaces2. Metric spaces3. Dense subsets4. Linear spaces5. Linear functionals The definitions and concepts come primarily from Introductory RealAnalysis by Kolmogorov and Fomin (highly recommended).6. Norms and semi-norms of linear spaces7. Euclidean spaces8. Orthogonality and bases9. Separable spaces10. Complete metric spaces11. Hilbert spaces12.

6. Norms and semi-norms of linear spaces 7. Euclidean spaces 8. Orthogonality and bases 9. Separable spaces 10. Complete metric spaces 11. Hilbert spaces 12. Riesz representation theorem 13. Convex functions 14. Lagrange multipliers

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