Mathematical analysis 3, NMAI056, summer term 2024/25
I will closely follow the lectures I gave a year ago but sometimes will update them.
Exam questions to be updated Zápočet (credits for the tutorials)
Five HWs are assigned at the end of each lecture, except the last one. Please, send me by e-mail their solutions by the end
of the coming Sunday. Solutions will be discussed on the tutorial on Tuesday. You get credit for solving (in the sense
I explained in the tutorial) at least 3/5 of the HWs.
Lecture 1, February 19, 2025 Metric spaces. Hemisphere is not flat. p-adic ultrametrics
Lecture 2, February 26, 2025 Ostrowski's theorem. Compact metric spaces
Lecture 3, March 5, 2025 Continuity and compactness. The Heine - Borel theorem
Connectedness. The fundamental theorem of algebra
Lecture 4, March 12, 2025 A proof of the fundamental theorem of algebra. Complete spaces
Baire's theorem
Lecture 5, March 19, 2025 The weak Jordan theorem, Thomassen's proof
Lecture 6, March 26, 2025 Applications of Baire's theorem: non-differentiable
continuous functions, transcendental growths of permutations
Lecture 7, April 2, 2025 Solving the Basel problem by Fourier series
Lecture 8, April 9, 2025 A theorem on (random) walks in Z^d of G. Polya
April 2025