MA2223 2016-2017 Solutions - Homework 6-10 - Metric Spaces.
Real Analysis 8601-8602. Prerequisites for 8601: strong understanding of a year of undergrad real analysis, such as our 5615H-5616H or equivalent, with substantial experience writing proofs .Courses named Advanced Calculus are insufficient preparation. The necessary mathematical background includes careful treatment of limits (of course!), continuity, Riemann integration on Euclidean spaces.
Organization of this Page. The links contain basic information for the courses I an teaching, or have taught. For courses offered in the current semester, the policies link contains the exam schedule, grading policy, etc. If present, the homework link contains, in addition to the homework assignments, a discussion of what is covered in the course.. Although brief, this discussion is far more.
Linear spaces, metric spaces, normed spaces: 2: Linear maps between normed spaces: 3: Banach spaces: 4: Lebesgue integrability: 5: Lebesgue integrable functions form a linear space: 6: Null functions: 7: Monotonicity, Fatou's Lemma and Lebesgue dominated convergence: 8: Hilbert spaces: 9: Baire's theorem and an application: 10.
K. Hoffman, Analysis in Euclidean space. Prentice-Hall. M.P. do Carmo, Differential Forms and Applications. Springer Verlag. Books relevant for the second term: M.P. do Carmo, Differential Forms and Applications. Springer Verlag. J.R. Munkres, Analysis on manifolds. Westview Press. M. Spivak, Calculus on manifolds. Benjamin. A roadmap on the 4H extra reading material is here. The references.