Lecturer, University of Surrey
2022/23:
Data science for dynamical systems
(4th Year/MSc level module, covering classification (learning) algorithms and applied Koopman theory; designed by
Stefan Klus);
2023/24:
Data science for dynamical systems
and
Manifolds and topology (3rd Year module designed by
Ian Roulstone);
2024/25:
-
Manifolds and topology (revised version). Course program (what do you need to know before the exam): (pdf)
Exercise sheets:
- Exercise Sheet 1: Deformations (pdf)
- Exercise Sheet 2: Topology and continuity (pdf)
- Exercise Sheet 3: Homeomorphisms (pdf)
- Exercise Sheet 4: Connectedness and path-connectedness (pdf)
- Exercise Sheet 5: Quotient spaces (pdf)
- Exercise Sheet 6: Projective space, Klein bottle, and first steps in manifolds (pdf)
- Exercise Sheet 7: Manifolds: parametrisation and basic constructions (pdf)
- Exercise Sheet 8: Smooth manifolds and tangent spaces (pdf)
- Exercise Sheet 9: Immersions, embeddings, and the Inverse Function Theorem (pdf)
- Exercise Sheet 10: Submersions. Preimage theorem. Manifolds with a boundary. (pdf)
- Data driven methods
2025/26:
Manifolds and topology (semester 1) and
Foundations of computing (semester 1).
Lecturer, University of Warwick
2021/22:
Hyperbolic Geometry (from week 6)
- Example Sheet 2: Classification of Isometries (pdf)
- Example Sheet 3: Isometries and Discrete Groups (pdf)
2018/19:
Metric Spaces
Course program (what do you need to know before the exam):
(pdf)
- Assignment 1: Getting to know metric spaces (pdf)
- Assignment 2: Convergence and continuity (pdf)
- Assignment 3: Getting to know topological spaces (pdf)
- Assignment 4: Continuity, metrizability, and Hausdorff property (pdf)
- Assignment 5: Normality and compactness of topological spaces (pdf)
- Assignment 6: Compactness and uniform continuity (pdf)
- Assignment 7: Connectedness in topological spaces (pdf)
- Assignment 8: Path-connected and complete spaces (pdf)
2017/18:
Complex Function Theory
Course program (what do you need to know before the exam):
(pdf)
- Assignment 1: Getting to know Hardy spaces (pdf)
- Assignment 2: Properties of Hardy space functions (pdf)
- Assignment 3: Functionals and operators on Hardy spaces (pdf)
Phase portraits of some important (for the course) functions
(pdf)
taken from Mathematics Calendar project.
Teaching Assistant, University of Warwick
Teaching Assistant, Independent University of Moscow
