Lehrinhalte
stochastic models of financial markets in discrete time, (model of periodn), derivatives (options and futures), trading strategies and arbitrage, equivalent risk-neutral probability measures, securing and valuation of options, the Black-Scholes formula
Literatur
Bingham, Kiesel: Risk-Neutral Valuation;
Elliott, Kopp: Mathematics of Financial Markets;
Irle: Finanzmathematik;
Musiela, Rutkowski: Martingale Methods in Financial Modelling;
Pliska: Introduction to Mathematical Finance;
Shreve: Stochastic Calculus for Finance I (Discrete Time Models)
Voraussetzungen
recommended: Introduction to Stochastics, Probability Theory
stochastic models of financial markets in discrete time, (model of periodn), derivatives (options and futures), trading strategies and arbitrage, equivalent risk-neutral probability measures, securing and valuation of options, the Black-Scholes formula
Literatur
Bingham, Kiesel: Risk-Neutral Valuation;
Elliott, Kopp: Mathematics of Financial Markets;
Irle: Finanzmathematik;
Musiela, Rutkowski: Martingale Methods in Financial Modelling;
Pliska: Introduction to Mathematical Finance;
Shreve: Stochastic Calculus for Finance I (Discrete Time Models)
Voraussetzungen
recommended: Introduction to Stochastics, Probability Theory
- Lehrende: Frank Aurzada
Semester: Verão 2019
- Lehrende: Leon Berghoff-Flüel
- Lehrende: Daniel Derr
- Lehrende: Leonie Füg
- Lehrende: Robert Haller
- Lehrende: Gelöschter User (TU-ID gelöscht)
- Lehrende: Cedric Wenz
Semester: Verão 2019
Lehrinhalte
We will study models for spatially extended systems of many interacting particles that are subject to noise. The most prominent example is the Ising model, but we will also consider other models like the Potts model. For these models, we will consider the question of infinite volume limits, phase transitions, correlation inequalities, thermodynamic variables, and alternative (e.g. Random walk) representations.
Literatur
1) Sacha Friedli and Yvan Velenik: Statistical Mechanics of Lattice Systems, Cambridge University Press 2017. 2) Hugo Duminil-Copin: Graphical Representations of Lattice Spin Models, availabe from his home page.
Voraussetzungen
Probability Theory or Wahrscheinlichkeitstheorie
We will study models for spatially extended systems of many interacting particles that are subject to noise. The most prominent example is the Ising model, but we will also consider other models like the Potts model. For these models, we will consider the question of infinite volume limits, phase transitions, correlation inequalities, thermodynamic variables, and alternative (e.g. Random walk) representations.
Literatur
1) Sacha Friedli and Yvan Velenik: Statistical Mechanics of Lattice Systems, Cambridge University Press 2017. 2) Hugo Duminil-Copin: Graphical Representations of Lattice Spin Models, availabe from his home page.
Voraussetzungen
Probability Theory or Wahrscheinlichkeitstheorie
- Lehrende: Volker Martin Betz
Semester: Verão 2019
Lehrinhalte
Selected chapters from mathematics in their historical context. In particular
- Outline of the history of mathematics;
- Numbers from antiquity to modern times;
- Irrational numbers, Fibonacci numbers, continued fractions;
- Infinity from Zenon to Cantor;
- Infinitely small quantities, measure theory, and non-standard analysis;
- School mathematics versus university mathematics.
Voraussetzungen
Analysis 1 and Linear Algebra 1
Selected chapters from mathematics in their historical context. In particular
- Outline of the history of mathematics;
- Numbers from antiquity to modern times;
- Irrational numbers, Fibonacci numbers, continued fractions;
- Infinity from Zenon to Cantor;
- Infinitely small quantities, measure theory, and non-standard analysis;
- School mathematics versus university mathematics.
Voraussetzungen
Analysis 1 and Linear Algebra 1
- Lehrende: Burkhard Kümmerer
- Lehrende: Malte Ott
Semester: Verão 2019
Lehrinhalte
model constructions (e.g. ultra-products, elementary chains); classical preservation theorems (expressive completeness results); model theoretic games, back&forth, partial isomomorphy; types and saturation properties; countable models and categoricity; Fraïssé limits and 0-1-laws
Literatur
Cori/Lascar: Mathematical Logik
Chang/Keisler: Model Theory
Hodges: Model Theory
Hodges: A Shorter Model Theory
Marker: Model Theory, an Introduction
Rothmaler: Modelltheorie
Poizat: A Course in Model Theory
Voraussetzungen
recommended: Introduction to Mathematical Logic
Online-Angebote
moodle
model constructions (e.g. ultra-products, elementary chains); classical preservation theorems (expressive completeness results); model theoretic games, back&forth, partial isomomorphy; types and saturation properties; countable models and categoricity; Fraïssé limits and 0-1-laws
Literatur
Cori/Lascar: Mathematical Logik
Chang/Keisler: Model Theory
Hodges: Model Theory
Hodges: A Shorter Model Theory
Marker: Model Theory, an Introduction
Rothmaler: Modelltheorie
Poizat: A Course in Model Theory
Voraussetzungen
recommended: Introduction to Mathematical Logic
Online-Angebote
moodle
- Lehrende: Martin Otto
Semester: Verão 2019
Lehrinhalte
Investigation of existence, uniqueness and regularity of linear and nonlinear partial differential equations with methods of functional analysis. The emphasis lies on consideration of partial differential equations with applications, for example in hydrodynamics or material science. The contents of the lecture depends partially on the field of research of the lecturer.
Investigation of existence, uniqueness and regularity of linear and nonlinear partial differential equations with methods of functional analysis. The emphasis lies on consideration of partial differential equations with applications, for example in hydrodynamics or material science. The contents of the lecture depends partially on the field of research of the lecturer.
- Lehrende: Matthias Hieber
Semester: Verão 2019
Lehrinhalte
- Reduced basis methods via Galerkin projection: construction, analysis and application
- proper orthogonal decomposition
- greedy algorithm
- estimation of the error in the solution and in functional outputs
Literatur
- Haasdonk: Reduced Basis Methods for Parametrized PDEs -- A Tutorial Introduction for Stationary and Instationary Problems, IANS, University of Stuttgart, Germany, 2014
- Quarteroni, Manzoni, Negri: Reduced Basis Methods for Partial Differential Equations: An Introduction, Springer, 2016
- Hesthaven, Rozza, Stamm: Certified Reduced Basis Methods for Parametrized Partial Differential Equations, Springer, 2016
Voraussetzungen
recommended: Numerical Methods for Partial Differential Equations
- Reduced basis methods via Galerkin projection: construction, analysis and application
- proper orthogonal decomposition
- greedy algorithm
- estimation of the error in the solution and in functional outputs
Literatur
- Haasdonk: Reduced Basis Methods for Parametrized PDEs -- A Tutorial Introduction for Stationary and Instationary Problems, IANS, University of Stuttgart, Germany, 2014
- Quarteroni, Manzoni, Negri: Reduced Basis Methods for Partial Differential Equations: An Introduction, Springer, 2016
- Hesthaven, Rozza, Stamm: Certified Reduced Basis Methods for Parametrized Partial Differential Equations, Springer, 2016
Voraussetzungen
recommended: Numerical Methods for Partial Differential Equations
- Lehrende: Pia Domschke
Semester: Verão 2019