Course syllabus
Course PM
This page contains the program of the course: lectures, exercise sessions and computer labs. 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 |
|---|---|---|
| 11/9 | Geometry. Euclid's elements. Eudoxus, Archimedes and the method of exhaustion. Non Euclidean geometry. | |
| 18/9 | Continuation of non Euclidean geometry. The geometry of Gauss and Riemann and its application in the theory of relativity. Beginning of analytic geometry. | |
| 25/9 | Continuation of analytic geometry, Hilbert spaces and quantum mechanics. | |
| 2/10 | Calculus. | |
| 9/10 | Calculus, continued. Solvability of algebraic equations. | |
| 16/10 | Complex analysis, Fourier analysis. | |
| 23/10 | No lecture this week! | |
| 30/10 | Rigour and metamathematics | |
| 6/11 | Google, Page rank and linear algebra | |
| 13/11 | Number theory and cryptography | |
| 20/11 | Data compression, compressed sensing and the geometry of Banach spaces | |
| 27/11 | No lecture this week! | |
| 4/12 | Beginning of presentations | |
| 7/1 | Presentations by Lina&Erik, Ajivit and Love in lecture room Euler | |
| 8/1 | Presentations in Pascal | |
| 10/1 | Presentations in Pascal |
Recommended exercises
| Day | Exercises |
|---|---|
| 2/10 | Try to do the exercise in the section on Fredholm determinants. Hint: Use the Taylor expansion of the logarithm! |
| 16/10 | 1. Lagrangian formalism for the pendulum. (At the end of the third set of slides.) 2. Solving a third degree equation using Tartaglia's method.(In the set of slides on algebraic equations.) |
| 30/10 | Complete d'Alembert's proof of the fundamental theorem of algebra. (In the fourth set of slides.) |
| 6/11 | Two exercises on the decimal expansion of rational numbers, see slides 5Persp |
| 13/11 | Proof of the general version of the Chinese remainder theorem, see slides 7Persp |
| 20/11 | The finite Fourier transform, see slides 10Persp |
Computer labs
Reference literature:
- Learning MATLAB, Tobin A. Driscoll. Provides a brief introduction to Matlab to the one who already knows computer programming. Available as e-book from Chalmers library.
-
Physical Modeling in MATLAB 3/E, Allen B. Downey
The book is free to download from the web. The book gives an introduction for those who have not programmed before. It covers basic MATLAB programming with a focus on modeling and simulation of physical systems.
Course summary:
| Date | Details | Due |
|---|---|---|