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 to be updated
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
April 2024