Graduate level courses at KTH and Stockholm University 2008-2009
Spring 2009
Bayesian networks
KTH, Timo Koski
Room 3721 (KTH), Tuesdays at 10-12. Course start: January 13
Ergodteori och stokastisk kalkyl
KTH, Michael Björklund, Boualem Djehiche
Room 3733 (KTH), Mondays at 10-12. Course start: January 12
Graduate reading course in algebraic statistics
KTH, Alexander Engström, Timo Koski, Lars Svensson
Room 3733 (KTH), Fridays at 15-17. Course start: November 28
Introduction to the theory of spectral sequences
SU, Sergei Merkulov
Room 306 (SU), Fridays at 13-15. Course start: January 23
Numerical nonlinear programming
KTH, SF3840, Anders Forsgren
Room 3721 (KTH), Thurdays at 13-15. Course start: January 15
Course page
The course deals with algorithms and fundamental theory for nonlinear
finite-dimensional optimization problems. Fundamental optimization concepts,
such as convexity and duality are also introduced. The main focus is nonlinear
programming, unconstrained and constrained. Areas considered are unconstrained
minimization, linearly constrained minimization and nonlinearly constrained
minimization. The focus is on methods which are considered modern and efficient
today.
Unconstrained nonlinear programming: optimality conditions, Newton methods,
quasi-Newton methods, conjugate gradients, least-squares problems.
Constrained nonlinear programming: optimality conditions, quadratic
programming, SQP methods, penalty methods, barrier methods, dual methods.
Linear programming is treated as a special case of nonlinear programming.
Semidefinite programming and linear matrix inequalities are also covered.
Operator theory: an easy introduction
KTH, Håkan Hedenmalm
Room 3733 (KTH), Tuesdays at 15-17. Course start: January 27
Spectral theory and its applications
KTH, Ari Laptev
Room 3733 (KTH), Fridays at 9-12. Course start: January 16
Topics in mathematics V:
Clifford algebras, geometric algebra, and applications
KTH, SF 2725, Lars Svensson and Douglas Lundholm
Room 3721 (KTH), Thurdays at 15-17. Course start: January 29
Course page (in Swedish)
It is well known that the complex numbers form a powerful tool in
the description of plane geometry. The geometry of 3-dimensional space
is traditionally described with the help of the scalar product and the
cross product. However, already before these concepts were
established, Hamilton had discovered the quaternions, an algebraic
system with three imaginary units which makes it possible to deal
effectively with geometric transformations in three dimensions.
Clifford originally introduced the notion nowadays known as
Clifford algebra (but which he himself called geometric algebra) as a
generalization of the complex numbers to arbitrarily many imaginary
units. The conceptual framework for this was laid by Grassmann already
in 1844, but it is only now that one has fully begun to appreciate the
algebraisation of geometry in general that the constructions of
Clifford and Grassmann result in. Among other things, one obtains an
algebraic description of geometric operations in vector spaces such as
orthogonal complements, intersections, and sums of subspaces, which
gives a way of proving geometric theorems that lies closer to the
classical synthetic method of proof than for example Descartes's
coordinate geometry. This formalism gives in addition a natural
language for the formulation of classical physics and mechanics.
The best known application of Clifford algebras is probably the
"classical" theory of orthogonal maps and spinors which is used
intensively in modern theoretical physics and differential
geometry.
This course will run as a graduate course, but it will also be
possible to take it as an advanced level course.
Read more here:
Youngtablåer
SU, Rikard Bøgvad
Room 306 (KTH), Wednesdays at 10-12 (might change). Course start: February 4
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Higher
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