Mathematical analysis 3, NMAI056, summer term 2023/24
I will roughly follow the lectures from the last year but I will update them.
Exam questions are the 12 questions given at the end of the last 13th lecture. Zápočet (credits for the tutorials)
I will give you credits the tutorials on Monday, May 13 (after the deadline for the last HW), provided that you sent
in at last 3/5 of the HWs.
Lecture 1, February 20, 2024 Metric spaces. Hemisphere is not flat. p-adic ultrametrics
Lecture 2, February 27, 2024 Ostrowski's theorem. Compact spaces
Lecture 3, March 5, 2024 The Heine-Borel theorem. Connectedness and the Fundamental
Theorem of Algebra
Lecture 4, March 12, 2024 Proof of the Fundamental Theorem of Algebra. Complete
spaces. The Baire Theorem
Lecture 5, March 19, 2024 C. Thomassen's proof of the Weak Jordan Theorem
Lecture 6, March 26, 2024 Applications of Baire's theorem: non-differentiable
continuous functions and transcendental growth rates of permutation classes
Lecture 7, April 2, 2024 The Basel problem and its solution by Fourier series
Lecture 8, April 9, 2024 Polya's theorem on random walkers
Lecture 9, April 16, 2024 Introduction to Complex Analysis I
Lecture 10, April 23, 2024 Introduction to Complex Analysis II
Lecture 11, April 30, 2024 Introduction to Complex Analysis III
Lecture 12, May 7, 2024 Differential equations I
Lecture 13, May 21, 2024 Differential equations II
May 2024