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

 

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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

 

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Computer labs

 

Reference literature:

  1. 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.
  2. 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.

 

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Course summary:

Date Details Due