Instructor: Dr. Bence BORDA;

Reference book: Walter Rudin: Principles of Mathematical Analysis (any edition)

Prerequisite: Calculus

Course description: The most important concepts, methods and applications of real analysis and the theory of metric spaces are covered, with an emphasis on examples and problem solving. The course is self-contained, the only prerequisite is calculus. We do not follow any textbook, but for those who wish to consult one Rudin's Principles of Mathematical Analysis is recommended.


  1. Review: sets, functions, real numbers, Euclidean spaces
  2. Metric spaces: topology, convergence, continuity, compactness, connectedness, completeness, separability
  3. Differentiation: derivatives of functions of one or several variables, mean value theorems, minimum and maximum of functions
  4. Integrals: indefinite and Riemann integrals, inequalities, estimating sums with integrals
  5. Infinite series: numerical series, sequences and series of functions, the metric space C([a,b]), power series and analytic functions