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.

Learning Objectives

By the end of the course, students will be able to:

  1. 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;
  2. Prove theorems that use the above concepts;
  3. Independently study articles and books that use more abstract versions of the above concepts;
  4. Face courses in probability and stochastics having all the necessary prerequisites.

Measurable Outcomes

Successful students will be able to:

  1. Prove theorems related to functions in metric spaces.
  2. Solve common but non-trivial real analysis problems.
  3. Read and understand scientific papers that use real analysis concepts.

12 Credits
: Calculus, Linear algebra, Multivariate calculus.

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