This course will provide the fundamental concepts of real analysis.
In particular we will deal with the following topics:
- Metric spaces,
- Normed spaces,
- Riemann-Stieltjes integral,
- Lebesgue measure and integral.
By the end of the course, students will be able to:
- Read and understand applied and theoretical articles in scientific journals that use concepts like distances, norms, convergence of functions, polynomial approximation, Fourier series, Lebesgue measure and integration;
- Prove theorems that use the above concepts;
- Independently study articles and books that use more abstract versions of the above concepts;
- Face courses in probability and stochastics having all the necessary prerequisites.
Successful students will be able to:
- Prove theorems related to functions in metric spaces.
- Solve common but non-trivial real analysis problems.
- Read and understand scientific papers that use real analysis concepts.
Prerequisites: Calculus, Linear algebra, Multivariate calculus.