The course covers:
* TeX and LaTeX. Presentations in Beamer and PowerPoint.
* Orientation and published in mathematical journals. Writing scientific papers in mathematics.
* Mathematical popular science. Writing a popular science article in mathematics.
* To hold lectures and presentations in mathematics.
- Teacher: Rikard Bögvad
This course consists of two parts. The first, on computability theory, introduces mathematical models of computation such as Turing machines and the lambda-calculus, and develops their theory, including the Halting Theorem, Rice’s Theorem, and as applications, undecidability results in other areas of mathematics. The second part, on formal languages and rewriting, develops the theory of regular languages and similar classes, their correspondence with finite state machines (automata), and their rewriting theory, as used in computer science, especially language processing and mathematical computation.
- Teacher: Peter LeFanu Lumsdaine
Kursen innehåller: Grundläggande beräkningseffektiva algoritmer för stora matriser; Principalkomponentanalys; Glesa och underbestämda system och deras relation till komprimering av data; Konstruktion av neurala nätverk och modeller för djup inlärning; Anpassning av hyperparametrar; Valda ämnen om särskilda matristyper.
Kurslitteratur: G. Strang, Linear algebra and learning from data
Observera att schema kommer att ändras till Tisdagar och fredagar 16:00 - 18:00
The main focus of the course is convex analysis and a rather modern treatment of optimization problems. It covers basic convex analysis and Lagrange duality theory with their applications in linear and nonlinear programming problems with and without constraints and a touch to modern convex optimization theory. It also provides links to other specific optimization problems such as matrix game, integer programming and dynamic programming.
The contents of the course may be applied in modelling and computation nearly everywhere when mathematical models or computations can not be made exact. In particular it provides a solid theoretic background and skill for understanding nature and mathematical structure of different problems so that practical problems can be tackled successfully. An apparent example of such is understanding (big) data to make optimization algorithms work for example in Machine learning.
Bazaraa, Sherali & Shetty: Nonlinear programming, Theory & Algorithms. John Wiley and Sons Ltd
- Teacher: Yishao Zhou
The course treats the foundations of general set topolog (topological spaces, continuity, compactness, connectedness, identification topologies) , the fundamental group, classification of closed surfaces.
John M. Lee: Introduction to Topological Manifolds. Springer
The course covers rings, ideals, prime ideals, nilpotents, zero-divisors, modules, Noetherian rings, Hilbert's basis theorem, finite extensions and Noetherian normalization, varieties, Nullstellensatz, prime ideal spectra, localization, primary decomposition. Algebraic geometry is the study of solutions to systems of polynomial equations. Commutative algebra is the underlying machinery. The course will give an introduction to these areas.
The course covers integration and measure theory and functional analysis, integration of measurable functions (Lebesgueintegraler), convergence theorems, product measure, Fubini's theorem, Banach spaces including LP-room and fundamental theorems on linear operators and functionals. Areas of application are in Fourier analysis, ergodic theory, probability theory, Sobolev spaces and partial differential equations.