Mathematics and its Applications

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**Population Dynamics**" Mario Natiello (lp2: 2009-10-26--12-11)

The course will display mathematical methods and techniques in Population Dynamics, focusing on epidemiology. One goal of the course is to illustrate both the mathematical methods used in population dynamics and the epistemological approach necessary to achieve realistic and usable models. Deterministic (time-discrete and time-continuous) and Stochastic approaches will be considered. The course rests on elementary notions of Linear Algebra, Dynamical Systems and Probability and Statistics. However, most of the necessary ideas will be freshened up along the course.

First meeting:**Wednesday, October 28, 13:15 in MH:332A**, Web-page: http://www.maths.lth.se/matematiklth/personal/mario/popdyn/intro.html - "
**Complex Analysis I**" Frank Wikström (lp3: 2010-01-18--03-05)

Repetition of background theory for functions in one complex variable. Complex vector spaces, complex structures and the operator d-bar. Holomorphic functions in several variables and their main properties. Comparison with the theory of functions in one variable will be emphasized. Integral formulas in one and several variables: Cauchy integral formula, Bochner-Martinelli formula. Hartog's extension theorem. Approximation of holomorphic functions by polynomials. Runge's theorem, polynomial Convexity. Existence domains for holomorphic functions in one and several variables. Introduction to pseudoconvexity. Holomorphic and biholomorphic mappings, Riemann mapping theorem and it cannot be generalized to several variables. Introduction to automorphic groups and invariant distance.

First meeting:**Wednesday, January 20, 13:15 in MH:333**, Web-page: http://www.maths.lth.se/matematiklth/personal/frankw/doktorandkurs - "
**Quantum Computing**" Sergei Silvestrov (lp4: 2010-03-15--05-21)

This course deals with the new and quickly expanding field of quantum computation. Quantum computations and algorithms use quantum mechanical principles and allow to solve tasks far beyond capabilities of conventional computing. Mathematically this is achieved through combination of methods from matrix theory, geometry and discrete mathematics. The aim of the course is to explain the main notions, methods, algorithms and applications of quantum computations. The course is intended for PhD students and advanced undergraduate students in Natural Sciences and Engineering. Especially students with interests in mathematics and computations, physics, computer sciences, information technology, nanoengineering and related subjects will benefit from this course.

First meeting:**Tuesday, March 23, 13:15 i MH:309A**(extra meeting**Thursday, March 25, 11:00**), Web-page: http://www.maths.lth.se/matematiklth/personal/ssilvest/QuantumComputing/