Real analysis: metric spaces, differentiation, integration, measure theory, functional analysis, and Fourier analysis.
- Sequences and series of numbers
- Metric spaces, compactness and completeness
- Continuity
- Differentiation
- Riemann–Stieltjes integration
- Sequences and series of functions
- Measure and measurable functions
- The Lebesgue integral
- \(L^p\) spaces and convolution
- Hilbert spaces and duality
- Fourier analysis
- Problems from the joint analysis exams