MVA200 Perspectives in Mathematics Autumn 20
Course PM
This page contains the program of the course: lectures, and suggested exercises. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.
Program
The schedule of the course is in TimeEdit.
Lectures
| Day | Sections | Content |
|---|---|---|
| 2/9 | Introduction, beginning of discussion of geometry. | |
| 9/9 | Continuation of discussion of geometry. Focus on Riemannian and non-Euclidean geometry | |
| 16/9 | Analytic geometry and linear algebra (that we started a little last week): Matrices, determinants and Hilbert space. | |
| 23/9 | Calculus. The early history plus some glimpses from the calculus of variations. | |
| 30/9 | Solvability of algebraic equations. | |
| 7/10 | Nobel prize in physics 2020. Complex analysis and Fourier analysis. | |
| 14/10 | Continuation of Complex Analysis and Fourier analysis | |
| 21/10 | An application: Compressed sensing. | |
| 28/10 | No lecture | |
| 4/11 | Rigour and Metamathematics. | |
| 11/11 | No lecture | |
| 18/11 |
Presentations start with Rahim Nkunzimana, who will talk about algebraic topology (history and some central concepts) and Rickard Cullman, who will talk about non-measurable sets and the Hausdorff paradox. |
|
| 25/11 |
Robert Antonio : History of number theory Jessica G: Machine learning Emelie L: Neural networks |
|
| 2/12 |
Albin N: Analytic number theory Victor L J: Psykometri |
|
| 9/12 |
Joakim Q: Black Jack William N: Regression
|
|
| 16/12 |
Natalia and Kawthar: Markov and his work. Rode G: History of probability theory. Emil Hietanen: Financial mathematics. |
|
| 13/1 |
Tanzeela A: Homology in group theory Kingsley AG: History of calculus Jens M: Topological matter in physics |
|
| 14/1 |
Jens Ifver, Jonatan Hellgren and Calvin Smith: Linear regression and mixed models. Kari K: Randomized control trials
|
Recommended exercises
| Day | Exercises |
|---|---|
| 16/9 | Do the suggested exercise on refraction of light on page 10 in the first set of slides. |
| 23/9 | Try to prove the formula for (Fredholm) determinants on page 26 in the second set of slides. |
| 30/9 | Try to do the exercise on the pendulum on page 19 in the third set of slides. |
| 7/10 | Try to solve the third degree equation on page 9 in the fourth set of slides. |
| 14/10 | |
Course summary:
| Date | Details | Due |
|---|---|---|