Search result: Catalogue data in Autumn Semester 2020

Mathematics Master Information
Application Area
Only necessary and eligible for the Master degree in Applied Mathematics.
One of the application areas specified must be selected for the category Application Area for the Master degree in Applied Mathematics. At least 8 credits are required in the chosen application area.
Simulation of Semiconductor Devices
227-0158-00LSemiconductor Devices: Transport Theory and Monte Carlo Simulation Information
Does not take place this semester.
The course was offered for the last time in HS19.
W4 credits2G
AbstractThe lecture combines quasi-ballistic transport theory with application to realistic devices
of current and future CMOS technology.
All aspects such as quantum mechanics, phonon scattering or Monte Carlo techniques to
solve the Boltzmann equation are introduced. In the exercises advanced devices such
as FinFETs and nanosheets are simulated.
ObjectiveThe aim of the course is a fundamental understanding of the derivation of the Boltzmann
equation and its solution by Monte Carlo methods. The practical aspect is to become
familiar with technology computer-aided design (TCAD) and perform simulations of
advanced CMOS devices.
ContentThe covered topics include:
- quantum mechanics and second quantization,
- band structure calculation including the pseudopotential method
- phonons
- derivation of the Boltzmann equation including scattering in the Markov limit
- stochastic Monte Carlo techniques to solve the Boltzmann equation
- TCAD environment and geometry generation
- Stationary bulk Monte Carlo simulation of velocity-field curves
- Transient Monte Carlo simulation for quasi-ballistic velocity overshoot
- Monte Carlo device simulation of FinFETs and nanosheets
Lecture notesLecture notes (in German)
LiteratureFurther reading will be recommended in the lecture.
Prerequisites / NoticeKnowledge of quantum mechanics is not required. Basic knowledge of semiconductor
physics is useful, but not necessary.
Systems Design
363-0541-00LSystems Dynamics and ComplexityW3 credits3GF. Schweitzer
AbstractFinding solutions: what is complexity, problem solving cycle.

Implementing solutions: project management, critical path method, quality control feedback loop.

Controlling solutions: Vensim software, feedback cycles, control parameters, instabilities, chaos, oscillations and cycles, supply and demand, production functions, investment and consumption
ObjectiveA successful participant of the course is able to:
- understand why most real problems are not simple, but require solution methods that go beyond algorithmic and mathematical approaches
- apply the problem solving cycle as a systematic approach to identify problems and their solutions
- calculate project schedules according to the critical path method
- setup and run systems dynamics models by means of the Vensim software
- identify feedback cycles and reasons for unintended systems behavior
- analyse the stability of nonlinear dynamical systems and apply this to macroeconomic dynamics
ContentWhy are problems not simple? Why do some systems behave in an unintended way? How can we model and control their dynamics? The course provides answers to these questions by using a broad range of methods encompassing systems oriented management, classical systems dynamics, nonlinear dynamics and macroeconomic modeling.
The course is structured along three main tasks:
1. Finding solutions
2. Implementing solutions
3. Controlling solutions

PART 1 introduces complexity as a system immanent property that cannot be simplified. It introduces the problem solving cycle, used in systems oriented management, as an approach to structure problems and to find solutions.

PART 2 discusses selected problems of project management when implementing solutions. Methods for identifying the critical path of subtasks in a project and for calculating the allocation of resources are provided. The role of quality control as an additional feedback loop and the consequences of small changes are discussed.

PART 3, by far the largest part of the course, provides more insight into the dynamics of existing systems. Examples come from biology (population dynamics), management (inventory modeling, technology adoption, production systems) and economics (supply and demand, investment and consumption). For systems dynamics models, the software program VENSIM is used to evaluate the dynamics. For economic models analytical approaches, also used in nonlinear dynamics and control theory, are applied. These together provide a systematic understanding of the role of feedback loops and instabilities in the dynamics of systems. Emphasis is on oscillating phenomena, such as business cycles and other life cycles.

Weekly self-study tasks are used to apply the concepts introduced in the lectures and to come to grips with the software program VENSIM.
Another objective of the self-study tasks is to practice efficient communication of such concepts.
These are provided as home work and two of these will be graded (see "Prerequisites").
Lecture notesThe lecture slides are provided as handouts - including notes and literature sources - to registered students only. All material is to be found on the Moodle platform. More details during the first lecture
Theoretical Physics
In the Master's programme in Applied Mathematics 402-0205-00L Quantum Mechanics I is eligible as a course unit in the application area Theoretical Physics, but only if 402-0224-00L Theoretical Physics wasn't or isn't recognised for credits (neither in the Bachelor's nor in the Master's programme). For the category assignment take contact with the Study Administration Office (Link) after having received the credits.
402-0809-00LIntroduction to Computational PhysicsW8 credits2V + 2UA. Adelmann
AbstractThis course offers an introduction to computer simulation methods for physics problems and their implementation on PCs and super computers. The covered topics include classical equations of motion, partial differential equations (wave equation, diffusion equation, Maxwell's equations), Monte Carlo simulations, percolation, phase transitions, and complex networks.
ObjectiveStudents learn to apply the following methods: Random number generators, Determination of percolation critical exponents, numerical solution of problems from classical mechanics and electrodynamics, canonical Monte-Carlo simulations to numerically analyze magnetic systems. Students also learn how to implement their own numerical frameworks and how to use existing libraries to solve physical problems. In addition, students learn to distinguish between different numerical methods to apply them to solve a given physical problem.
ContentIntroduction to computer simulation methods for physics problems. Models from classical mechanics, electrodynamics and statistical mechanics as well as some interdisciplinary applications are used to introduce the most important object-oriented programming methods for numerical simulations (typically in C++). Furthermore, an overview of existing software libraries for numerical simulations is presented.
Lecture notesLecture notes and slides are available online and will be distributed if desired.
LiteratureLiterature recommendations and references are included in the lecture notes.
Prerequisites / NoticeLecture and exercise lessons in english, exams in German or in English
402-2203-01LClassical Mechanics Information Restricted registration - show details W7 credits4V + 2UN. Beisert
AbstractA conceptual introduction to theoretical physics: Newtonian mechanics, central force problem, oscillations, Lagrangian mechanics, symmetries and conservation laws, spinning top, relativistic space-time structure, particles in an electromagnetic field, Hamiltonian mechanics, canonical transformations, integrable systems, Hamilton-Jacobi equation.
ObjectiveFundamental understanding of the description of Mechanics in the Lagrangian and Hamiltonian formulation. Detailed understanding of important applications, in particular, the Kepler problem, the physics of rigid bodies (spinning top) and of oscillatory systems.
402-0861-00LStatistical PhysicsW10 credits4V + 2UG. Blatter
AbstractThe lecture focuses on classical and quantum statistical physics. Various techniques, cumulant expansion, path integrals, and specific systems are discussed: Fermions, photons/phonons, Bosons, magnetism, van der Waals gas. Phase transitions are studied in mean field theory (Weiss, Landau). Including fluctuations leads to critical phenomena, scaling, and the renormalization group.
ObjectiveThis lecture gives an introduction into the basic concepts and applications of statistical physics for the general use in physics and, in particular, as a preparation for the theoretical solid state physics education.
ContentThermodynamics, three laws of thermodynamics, thermodynamic potentials, phenomenology of phase transitions.
Classical statistical physics: micro-canonical-, canonical-, and grandcanonical ensembles, applications to simple systems.
Quantum statistical physics: single particle, ideal quantum gases, fermions and bosons, statistical interaction.
Techniques: variational approach, cumulant expansion, path integral formulation.
Degenerate fermions: Fermi gas, electrons in magnetic field.
Bosons: photons and phonons, Bose-Einstein condensation.
Magnetism: Ising-, XY-, Heisenberg models, Weiss mean-field theory.
Van der Waals gas-liquid transition in mean field theory.
General mean-field (Landau) theory of phase transitions, first- and second order, tricritical point.
Fluctuations: field theory approach, Gauss theory, self-consistent field, Ginzburg criterion.
Critical phenomena: scaling theory, universality.
Renormalization group: general theory and applications to spin models (real space RG), phi^4 theory (k-space RG), Kosterlitz-Thouless theory.
Lecture notesLecture notes available in English.
LiteratureNo specific book is used for the course. Relevant literature will be given in the course.
402-0843-00LQuantum Field Theory I
Special Students UZH must book the module PHY551 directly at UZH.
W10 credits4V + 2UC. Anastasiou
AbstractThis course discusses the quantisation of fields in order to introduce a coherent formalism for the combination of quantum mechanics and special relativity.
Topics include:
- Relativistic quantum mechanics
- Quantisation of bosonic and fermionic fields
- Interactions in perturbation theory
- Scattering processes and decays
- Elementary processes in QED
- Radiative corrections
ObjectiveThe goal of this course is to provide a solid introduction to the formalism, the techniques, and important physical applications of quantum field theory. Furthermore it prepares students for the advanced course in quantum field theory (Quantum Field Theory II), and for work on research projects in theoretical physics, particle physics, and condensed-matter physics.
402-0830-00LGeneral Relativity Information
Special Students UZH must book the module PHY511 directly at UZH.
W10 credits4V + 2UR. Renner
AbstractIntroduction to the theory of general relativity. The course puts a strong focus on the mathematical foundations of the theory as well as the underlying physical principles and concepts. It covers selected applications, such as the Schwarzschild solution and gravitational waves.
ObjectiveBasic understanding of general relativity, its mathematical foundations (in particular the relevant aspects of differential geometry), and some of the phenomena it predicts (with a focus on black holes).
ContentIntroduction to the theory of general relativity. The course puts a strong focus on the mathematical foundations, such as differentiable manifolds, the Riemannian and Lorentzian metric, connections, and curvature. It discusses the underlying physical principles, e.g., the equivalence principle, and concepts, such as curved spacetime and the energy-momentum tensor. The course covers some basic applications and special cases, including the Newtonian limit, post-Newtonian expansions, the Schwarzschild solution, light deflection, and gravitational waves.
LiteratureSuggested textbooks:

C. Misner, K, Thorne and J. Wheeler: Gravitation
S. Carroll - Spacetime and Geometry: An Introduction to General Relativity
R. Wald - General Relativity
S. Weinberg - Gravitation and Cosmology
» Electives Theoretical Physics
Transportation Science
101-0417-00LTransport Planning MethodsW6 credits4GA. Erath Rusterholtz, M. van Eggermond
AbstractThe course provides the necessary knowledge to develop models supporting and also evaluating the solution of given planning problems.
The course is composed of a lecture part, providing the theoretical knowledge, and an applied part in which students develop their own models in order to evaluate a transport project/ policy by means of cost-benefit analysis.
Objective- Knowledge and understanding of statistical methods and algorithms commonly used in transport planning
- Comprehend the reasoning and capabilities of transport models
- Ability to independently develop a transport model able to solve / answer planning problem
- Getting familiar with cost-benefit analysis as a decision-making supporting tool
ContentThe course provides the necessary knowledge to develop models supporting the solution of given planning problems and also introduces cost-benefit analysis as a decision-making tool. Examples of such planning problems are the estimation of traffic volumes, prediction of estimated utilization of new public transport lines, and evaluation of effects (e.g. change in emissions of a city) triggered by building new infrastructure and changes to operational regulations.

To cope with that, the problem is divided into sub-problems, which are solved using various statistical models (e.g. regression, discrete choice analysis) and algorithms (e.g. iterative proportional fitting, shortest path algorithms, method of successive averages).

The course is composed of a lecture part, providing the theoretical knowledge, and an applied part in which students develop their own models in order to evaluate a transport project/ policy by means of cost-benefit analysis. Interim lab session take place regularly to guide and support students with the applied part of the course.
Lecture notesMoodle platform (enrollment needed)
LiteratureWillumsen, P. and J. de D. Ortuzar (2003) Modelling Transport, Wiley, Chichester.

Cascetta, E. (2001) Transportation Systems Engineering: Theory and Methods, Kluwer Academic Publishers, Dordrecht.

Sheffi, Y. (1985) Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods, Prentice Hall, Englewood Cliffs.

Schnabel, W. and D. Lohse (1997) Verkehrsplanung, 2. edn., vol. 2 of Grundlagen der Strassenverkehrstechnik und der Verkehrsplanung, Verlag für Bauwesen, Berlin.

McCarthy, P.S. (2001) Transportation Economics: A case study approach, Blackwell, Oxford.
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