Search result: Catalogue data in Autumn Semester 2024

High-Energy Physics (Joint Master with IP Paris) Information
Core Subjects
Core Courses in Theoretical Physics
NumberTitleTypeECTSHoursLecturers
402-0843-00LQuantum Field Theory I
Special Students UZH must book the module PHY551 directly at UZH.
W10 credits4V + 2UL. Senatore
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
Learning 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.
Lecture notesWill be provided as the course progresses
CompetenciesCompetencies
Subject-specific CompetenciesConcepts and Theoriesassessed
Techniques and Technologiesassessed
Method-specific CompetenciesAnalytical Competenciesassessed
Decision-makingfostered
Media and Digital Technologiesfostered
Problem-solvingassessed
Project Managementfostered
Social CompetenciesCommunicationfostered
Cooperation and Teamworkfostered
Customer Orientationfostered
Leadership and Responsibilityfostered
Self-presentation and Social Influence fostered
Sensitivity to Diversityfostered
Negotiationfostered
Personal CompetenciesAdaptability and Flexibilityfostered
Creative Thinkingassessed
Critical Thinkingassessed
Integrity and Work Ethicsfostered
Self-awareness and Self-reflection fostered
Self-direction and Self-management fostered
Core Courses in Experimental Physics
NumberTitleTypeECTSHoursLecturers
402-0891-00LPhenomenology of Particle Physics IW10 credits3V + 2UP. Crivelli, A. de Cosa
AbstractThe course focuses on the connection between particle physics theory and experimental results to provide a comprehensive modern view of the Standard Model. The covered topics are quantum electrodynamics (QED) and quantum chromodynamics (QCD).
Learning objectiveThe students will deepen the knowledge on particle physics acquired during their bachelor studies. They will be able to apply the basics of relativistic quantum field theory (QFT) to derive the Feynman rules and to apply those to compute QED and QCD processes. They will be able to explain and discuss the connection between theory and experiments.
ContentTopics to be covered in Phenomenology of Particle Physics I:
• Relativistic kinematics
• Decay rates and cross sections
• Quantisation of Klein-Gordon (boson) and Dirac (fermion)’s fields
• From the S-matrix to the Feynman rules of QED
• Scattering processes in QED/QCD and running of alpha and alpha_s
• Experimental tests of QED and QCD
LiteratureAs described in the entity: Lernmaterialien
CompetenciesCompetencies
Subject-specific CompetenciesConcepts and Theoriesassessed
Techniques and Technologiesfostered
Method-specific CompetenciesAnalytical Competenciesfostered
Problem-solvingfostered
Social CompetenciesCommunicationfostered
Personal CompetenciesCreative Thinkingfostered
Electives
Optional Subjects in Physics
NumberTitleTypeECTSHoursLecturers
402-0220-MSLExtended Research Project Restricted registration - show details
This course unit can only be booked together with a research project (402-0218-MS). This extension is not available for the options Proseminars, Particle Physics at PSI, Medical Physics and Experimental Foundations of Particle Physics. The extension is only possible with the agreement of the supervising professor. The extension must be booked at the same time as the research project.
W4 credits8ASupervisors
AbstractExtension of the Reseach Project
Learning objectiveStudents are enabled to:
• expand their knowledge in a specific area of physics,
• conduct a project (a) in a research laboratory or (b) on a specific topic of theoretical physics,
• discuss their project results and conclusions in a team,
• present their findings in written and oral form.

The extension allows for a more in-depth research experience.
CompetenciesCompetencies
Subject-specific CompetenciesConcepts and Theoriesassessed
Techniques and Technologiesassessed
Method-specific CompetenciesAnalytical Competenciesassessed
Decision-makingassessed
Media and Digital Technologiesfostered
Problem-solvingassessed
Project Managementfostered
Social CompetenciesCommunicationassessed
Cooperation and Teamworkfostered
Sensitivity to Diversityfostered
Negotiationfostered
Personal CompetenciesAdaptability and Flexibilityfostered
Creative Thinkingassessed
Critical Thinkingfostered
Integrity and Work Ethicsassessed
Self-awareness and Self-reflection fostered
Self-direction and Self-management fostered
402-0457-00LQuantum Technologies for Searches of New Physics
Does not take place this semester.
W6 credits2V + 1UP. Crivelli
AbstractRecent years have witnessed incredible progress in the development of new quantum technologies driven by their application in quantum information, metrology, high precision spectroscopy and quantum sensing. This course will present how these emerging technologies are powerful tools to address open questions of the Standard Model in a complementary way to what is done at the high energy frontier.
Learning objectiveThe aim of this course is to equip students of different backgrounds with a solid base to follow this rapidly developing and exciting multi-disciplinary field.
ContentThe first lectures will be dedicated to review the open questions of the Standard Model and the different Beyond Standard Model extensions which can be probed with quantum technologies. This will include searches for dark sector, dark matter, axion and axion-like particles, new gauge bosons (e.g Dark photons) and extra short-range forces.

The main part of the course will introduce the following (quantum) technologies and systems, and how they can be used for probing New Physics.
- Cold atoms
- Trapped ions
- Atoms interferometry
- Atomic clocks
- Cold molecules and molecular clocks
- Exotic Atoms
- Anti-matter
- Quantum Sensors
Prerequisites / NoticeThe preceding attendance of introductory particle physics, quantum mechanics and quantum electronics courses at the bachelor level is recommended.
402-0713-00LAstro-Particle Physics I Information W6 credits2V + 1UA. Biland
AbstractThis lecture gives an overview of the present research in the field of Astro-Particle Physics, including the different experimental techniques. In the first semester, main topics are the charged cosmic rays including the antimatter problem. The second semester focuses on the neutral components of the cosmic rays as well as on some aspects of Dark Matter.
Learning objectiveSuccessful students know:
- experimental methods to measure cosmic ray particles over full energy range
- current knowledge about the composition of cosmic ray
- possible cosmic acceleration mechanisms
- correlation between astronomical object classes and cosmic accelerators
- information about our galaxy and cosmology gained from observations of cosmic ray
ContentFirst semester (Astro-Particle Physics I):
- definition of 'Astro-Particle Physics'
- important historical experiments
- chemical composition of the cosmic rays
- direct observations of cosmic rays
- indirect observations of cosmic rays
- 'extended air showers' and 'cosmic muons'
- 'knee' and 'ankle' in the energy spectrum
- the 'anti-matter problem' and the Big Bang
- 'cosmic accelerators'
Lecture notesSee lecture home page: http://ihp-lx2.ethz.ch/AstroTeilchen/
LiteratureSee lecture home page: http://ihp-lx2.ethz.ch/AstroTeilchen/
CompetenciesCompetencies
Subject-specific CompetenciesConcepts and Theoriesassessed
Techniques and Technologiesassessed
Method-specific CompetenciesAnalytical Competenciesassessed
Media and Digital Technologiesfostered
Problem-solvingassessed
Social CompetenciesCommunicationfostered
Cooperation and Teamworkfostered
Personal CompetenciesAdaptability and Flexibilityfostered
Creative Thinkingfostered
Critical Thinkingassessed
Integrity and Work Ethicsfostered
Self-awareness and Self-reflection fostered
Self-direction and Self-management fostered
402-0715-00LLow Energy Particle PhysicsW6 credits2V + 1UA. S. Antognini, D. Ries
AbstractLow energy particle physics provides complementary information to high energy physics with colliders. In this lecture, we will concentrate on flagship experiments which have significantly improved our understanding of particle physics today, concentrating mainly on precision experiments with neutrons, muons and exotic atoms.
Learning objectiveYou will be able to present and discuss:
- the principle of the experiments
- the underlying technique and methods
- the context and the impact of these experiments on particle physics
ContentLow energy particle physics provides complementary information to high energy physics with colliders. At the Large Hadron Collider one directly searches for new particles at energies up to the TeV range. In a complementary way, low energy particle physics indirectly probes the existence of such particles and provides constraints for "new physics", making use of high precision and high intensities.

Besides the sensitivity to effects related with new physics (e.g. lepton flavor violation, symmetry violations, CPT tests, search for electric dipole moments, new low mass exchange bosons etc.), low energy physics provides the best test of QED (electron g-2), the best tests of bound-state QED (atomic physics and exotic atoms), precise determinations of fundamental constants, information about the CKM matrix, precise information on the weak and strong force even in the non-perturbative regime etc.

Starting from a general introduction on high intensity/high precision particle physics and the main characteristics of muons and neutrons and their production, we will then focus on the discussion of fundamental problems and ground-breaking experiments:

- search for rare decays and charged lepton flavor violation
- electric dipole moments and CP violation
- spectroscopy of exotic atoms and symmetries of the standard model
- what atomic physics can do for particle physics and vice versa
- neutron decay and primordial nucleosynthesis
- atomic clock
- Penning traps
- Ramsey spectroscopy
- Spin manipulation
- neutron-matter interaction
- ultra-cold neutron production
- various techniques: detectors, cryogenics, particle beams, laser cooling....
LiteratureGolub, Richardson & Lamoreaux: "Ultra-Cold Neutrons"
Rauch & Werner: "Neutron Interferometry"
Carlile & Willis: "Experimental Neutron Scattering"
Byrne: "Neutrons, Nuclei and Matter"
Klapdor-Kleingrothaus: "Non Accelerator Particle Physics"
Prerequisites / NoticeEinführung in die Kern- und Teilchenphysik / Introduction to Nuclear- and Particle-Physics
402-0725-00LExperimental Methods and Instruments of Particle PhysicsW6 credits3V + 1UM. Backhaus, D. Sgalaberna
AbstractIntroduction to particle sources and accelerators.
Theory of particle interaction with matter and signal formation.
Basics and concepts of particle detectors.
Momentum reconstruction, calorimetry and particle identification techniques.
Simulation methods, readout electronics, trigger and data acquisition.
Examples of key experiments.
Learning objectiveAcquire an in-depth understanding and overview of the essential elements of experimental methods in particle and astroparticle physics.
Content1. Examples of modern experiments
2. Introduction to particle sources and accelerators
3. Basics: Bethe-Bloch and physics of charged particle propagation in matter, interaction of photons with matter, hadronic interactions, signal formation
4. Detailed analysis of non-electronic, noble element, solid state, scintillator-based and Cherenkov particle detectors
5. Experimental techniques for particle tracking, calorimetry and identification
6. Monte Carlo simulations, trigger and data acquisition system readout
Lecture notesSlides are handed out regularly
LiteratureH.Kolanoski and N.Wermes, "Particle Detectors: Fundamentals and Applications".
C.Grupen and B.Schwartz, "Particle Detectors".
G.F.Knoll, "Radiation Detection and Measurements".
CompetenciesCompetencies
Subject-specific CompetenciesConcepts and Theoriesassessed
Techniques and Technologiesassessed
Personal CompetenciesCreative Thinkingfostered
Critical Thinkingfostered
402-0767-00LNeutrino PhysicsW6 credits2V + 1UA. Rubbia, D. Sgalaberna
AbstractTheoretical basis and selected experiments to determine the properties of neutrinos and their interactions (mass, spin, helicity, chirality, oscillations, charge-parity violation, interactions with leptons and quarks) and implications on physics beyond the Standard Model of elementary particles as well as on Cosmology.
Learning objectiveCritically analyze and elaborate the neutrino production and detection techniques.
Derive the theory of neutrino scattering and analyze its implications in neutrino experiments.
Analyze the phenomenology of neutrino oscillations and its implication on the physics Beyond the Standard Model of particles.
Derive the main concepts of the theory of neutrino masses within and beyond the Standard Model of particles and analyze the experimental techniques related to the measurement of the neutrino masses.
Describe the role of neutrinos in Cosmology and make connections with current and future neutrino experiments.
Review the experimental configurations and analyze the challenges in searches for leptonic Charge-Parity symmetry violation and the measurement of the neutrino mass hierarchy.
Content1. Introduction to Neutrinos and Neutrino Sources;
2. Neutrino Detectors
3. Neutrino Interactions
4. Neutrino Oscillations
5. Nature of Neutrino masses
6. Neutrinos in Cosmology
7. Search for leptonic Charge Parity violation and precision measurement of the neutrino oscillation probability
LiteratureA. Rubbia, “Phenomenology of Particle Physics”, Cambridge University Press

B. Kayser, F. Gibrat-Debu and F. Perrier, The Physics of Massive Neutrinos, World Scientific Lecture Notes in Physic, Vol. 25, 1989, and newer publications.

N. Schmitz, Neutrinophysik, Teubner-Studienbücher Physik, 1997.

D.O. Caldwell, Current Aspects of Neutrino Physics, Springer.

C. Giunti & C.W. Kim, Fundamentals of Neutrino Physics and Astrophysics, Oxford.

K.Zuber, “Neutrino Physics” CRC Press 2020
CompetenciesCompetencies
Subject-specific CompetenciesConcepts and Theoriesassessed
Techniques and Technologiesassessed
Method-specific CompetenciesAnalytical Competenciesassessed
Problem-solvingassessed
Personal CompetenciesCreative Thinkingfostered
Critical Thinkingassessed
402-0777-00LParticle Accelerator Physics and Modeling IW6 credits2V + 1UA. Adelmann
AbstractThis is the first of two courses, introducing particle accelerators from a theoretical point of view and covers state-of-the-art modelling techniques.
Learning objectiveYou obtain a theoretical understanding of the building blocks of particle accelerators. Modern numerical analysis tools allows you to model state-of-the-art particle accelerators. We will develop a Julia simulation tool (JuliAccel.jl) that reflects the theory from the lecture.
ContentHere is the rough plan of the topics, however the actual pace may vary relative to this plan.

- Recap of Relativistic Classical Mechanics and Electrodynamics
- Building Blocks of Particle Accelerators
- Lie Algebraic Structure of Classical Mechanics and Application to Particle Accelerators
- Symplectic Maps & Analysis of Maps
- Symplectic Particle Tracking
- Collective Effects
- Linear & Circular Accelerators
Lecture notesLecture notes
Prerequisites / NoticePhysics, Computational Science (RW) at MSc. Level
In exceptional cases students at BSc level can attend.
This lecture is also suited for PhD. students
CompetenciesCompetencies
Subject-specific CompetenciesConcepts and Theoriesassessed
402-0836-16LQuantum Simulations of Gauge Theories
Does not take place this semester.
W6 credits2V + 1UM. Krstic Marinkovic
AbstractDivided into three parts, the course introduces various aspects of lattice quantum field theory (QFT), gauge symmetries, quantum simulators, and implementation schemes. Other than highlighting the strengths and weaknesses of the lattice formulation of QFTs suitable for Monte Carlo simulations, the course discusses practical realization of quantum simulators for gauge theories.
Learning objectiveAfter acquiring the foundations on lattice formulation of gauge theories, and challenges of conventional Monte Carlo simulation approaches, the students will learn about different strategies for quantum simulation of gauge theories and their implementation on digital and analog quantum devices.
Content1. Background and Motivation
1.1 From Quantum Field Theories to Lattice field theories;
1.2 Lattice Gauge Theories - Lagrangian formulation, gauge symmetries, observables;
1.3 Monte Carlo simulations, sign problems, and complex actions.
2. Road-map for Quantum Simulation of Gauge Theories
2.1 Hamiltonian formulation, Wilson’s formulation, and the infinite Hilbert spaces;
2.2 Finite Hilbert spaces: Z(N) gauge theories. Dualizing the Ising model and relation with the toric code;
2.3 Finite Hilbert spaces: Quantum link models for Abelian gauge theories;
2.4 Finite Hilbert spaces: Quantum link models for non-Abelian gauge theories;
2.5 Exploring the physics of gauge theories - phases, dynamics, and thermalization;
2.6 Exploring methods for gauge theories - exact diagonalization, tensor networks, Monte Carlo.
3. Quantum Simulation Approaches and Platforms
3.1 Digital vs. analog quantum simulations;
3.2 Proposals for simulations of gauge theories, realization, and perspectives.
LiteratureQuantum chromodynamics on the lattice (Christof Gattringer, Christian B. Lang. Series Title: Lecture Notes in Physics.
DOI: https://doi.org/10.1007/978-3-642-01850-3)
From Quantum Link Models to D-Theory: A Resource Efficient Framework for the Quantum Simulation and Computation of Gauge Theories, U. J. Wiese
402-0830-00LGeneral Relativity Information 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.
Learning 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.
LiteratureParts of the lecture are based on the book "General Relativity" by R. Wald.

Other suggested textbooks:

“Gravitation" by C. Misner, K, Thorne and J. Wheeler
"Spacetime and Geometry: An Introduction to General Relativity” by S. Carroll
"Gravitation and Cosmology" by S. Weinberg
CompetenciesCompetencies
Concepts and Theoriesassessed
Techniques and Technologiesfostered
Method-specific CompetenciesAnalytical Competenciesassessed
402-0845-61LEffective Field Theories for Particle Physics
Special Students UZH must book the module PHY578 directly at UZH.
W6 credits2V + 1UA. Signer
AbstractThe focus of the course is on effective field theories (EFT) in the context of particle physics. EFTs provide a framework to systematically disentangle effects due to different scales. This will be discussed both in general terms and with specific phenomenological applications in mind.
Learning objectiveWe will start by introducing the core ideas of constructing EFTs and consider cases where the effect of heavy particles or large-scale modes are integrated out. Concepts like decoupling and matching as well as applications of the method of regions and the renormalisation group will be covered.

In the second part of the course several concrete examples of EFTs are presented. They allow for a consistent description of a wide variety of physical systems, from bound states with heavy quarks, jets in collider physics, non-perturbative strong interaction at low energies, to effects of heavy physics beyond the Standard Model.
Content- Introduction to EFTs
- Decoupling and matching
- Renormalisation group resummation
- Examples of EFTs:
- Heavy Quark Effective Theory (HQET)
- Non-Relativistic QCD and QED (NRQCD and NRQED)
- Soft-Collinear Effective Theory (SCET)
- Standard Model and Low Energy Effective Theory (SMEFT and LEFT)
- Chiral Perturbation Theory
Prerequisites / NoticeQFT-I (mandatory) and QFT-II (highly recommended)
CompetenciesCompetencies
Subject-specific CompetenciesConcepts and Theoriesfostered
402-0851-00LQCD: Theory and Experiment Information
Does not take place this semester.
Special Students UZH must book the module PHY561 directly at UZH.
W3 credits3GA. Gehrmann-De Ridder, R. Wallny
AbstractAn introduction to the theoretical aspects and experimental tests of QCD, with emphasis on perturbative QCD and related experiments at colliders.
Learning objectiveKnowledge acquired on basics of perturbative QCD, both of theoretical and experimental nature. Ability to perform simple calculations of perturbative QCD, as well as to understand modern publications on theoretical and experimental aspects of perturbative QCD.
ContentQCD Lagrangian and Feynman Rules
QCD running coupling
Parton model
DGLAP
Basic processes
Experimental tests at lepton and hadron colliders
Measurements of the strong coupling constant
Literature1) G. Dissertori, I. Knowles, M. Schmelling : "Quantum Chromodynamics: High Energy Experiments and Theory" (The International Series of Monographs on Physics, 115, Oxford University Press)
2) R. K. Ellis, W. J. Stirling, B. R. Webber : "QCD and Collider Physics" (Cambridge Monographs on Particle Physics, Nuclear Physics & Cosmology)"
Prerequisites / NoticeWill be given as block course, language: English.
For students of both ETH and University of Zurich.
402-0870-00LIntroduction to Quantum ElectrodynamicsW6 credits2V + 1UA. Lazopoulos
AbstractThis course provides a pedagogical introduction to Quantum Electrodynamics.
Learning objectiveStudents will be introduced to the theory of Quantum Electrodynamics, and the use of Feynman diagrams to arrive at theoretical predictions for phenomena related to the interaction of light and matter. The course is designed to complement Quantum Field Theory I for those students with a special interest in theoretical elementary particle physics.
ContentThe course will cover
- an introduction to QED as the quantum theory of interactions of light and matter.
- Feynman rules for QED
- Amplitudes and cross sections for simple processes in QED
- Gauge invariance and the Ward identity
- Ultraviolet singularities and Renormalization
- Infrared singularities and their cancelation
- The Ueling potential and the Lamb shift
- Anomalous magnetic moments
Lecture notesWill be provided at the Moodle site for the course.
LiteratureWill be provided at the Moodle site for the course.
CompetenciesCompetencies
Concepts and Theoriesassessed
Techniques and Technologiesassessed
Method-specific CompetenciesAnalytical Competenciesassessed
Problem-solvingassessed
402-0883-63LSymmetries in PhysicsW6 credits3GG. M. Graf
AbstractThe course gives an introduction to symmetry groups in physics. It
explains the relevant mathematical background (finite groups, Lie
groups and algebras as well as their representations), and illustrates
their important role across modern physics.
Learning objectiveThe aim of the course is to give a self-contained introduction into
finite group theory as well as Lie theory from a physicists point of
view. Abstract mathematical constructions will be illustrated with
examples from physics.
ContentFinite group theory, including representation theory and character
methods; applications to crystallography and solid state physics.
The symmetric group and the structure of its representations;
applications to identical particles. Clifford algebras; application to
relativistic wave equations equations. Simple Lie algebras and their
finite-dimensional representations. Description of representations of
SU(N) in terms of Young diagrams; applications in particle physics.
CompetenciesCompetencies
Subject-specific CompetenciesConcepts and Theoriesassessed
Techniques and Technologiesassessed
Method-specific CompetenciesAnalytical Competenciesassessed
Problem-solvingassessed
402-0886-00LQCD and Scattering Amplitudes Information
Special Students UZH must book the module PHY564 directly at UZH.
W6 credits2V + 1UA. Gehrmann-De Ridder
AbstractThe course presents the quantum field theory of the strong interaction (quantum chromodynamics, QCD) and discusses its applications to particle physics observables.
Learning objectiveThe course aims to familiarize the students with the concepts and applications of QCD and to introduce them to modern techniques for computations in QCD.
ContentContent:
* Review of non-Abelian gauge theories
* Renormalization of QCD and running coupling constant
* Jet observables in e^+e^- annihilation
* QCD at lepton-proton colliders
* Multiparticle production
* Spinor-helicity formalism
* Perturbation theory techniques: loops and phase space
Prerequisites / NoticeThe course assumes prior knowledge of the content of the quantum field theory 1+2 lectures.
CompetenciesCompetencies
Subject-specific CompetenciesConcepts and Theoriesfostered
Techniques and Technologiesfostered
Method-specific CompetenciesAnalytical Competenciesfostered
402-0897-00LIntroduction to String TheoryW6 credits2V + 1UJ. Brödel
AbstractString theory is an attempt to quantise gravity and unite it with the other fundamental forces of nature. It is related to numerous interesting topics and questions in quantum field theory. In this course, an introduction to the basics of string theory is provided.
Learning objectiveWithin this course, a basic understanding and overview of the concepts and notions employed in string theory shall be given. More advanced topics will be touched upon towards the end of the course briefly in order to foster further research.
Content- mechanics of point particles and extended objects
- string modes and their quantisation; higher dimensions, supersymmetry
- critical dimension and no-ghost theorem
- D-branes, T-duality
- two-dimensional conformal field theories
LiteratureB. Zwiebach, A First Course in String Theory, CUP (2004).
D. Lust, S. Theisen, Lectures on String Theory, Lecture Notes in Physics, Springer (1989).
M.B. Green, J.H. Schwarz, E. Witten, Superstring Theory I, CUP (1987).
J. Polchinski, String Theory I & II, CUP (1998).
Prerequisites / NoticeRecommended: Quantum Field Theory I (in parallel)
CompetenciesCompetencies
Subject-specific CompetenciesConcepts and Theoriesassessed
Method-specific CompetenciesAnalytical Competenciesassessed
Problem-solvingassessed
Optional Subjects in Mathematics
NumberTitleTypeECTSHoursLecturers
401-3531-00LDifferential Geometry I Information
At most one of the three course units (Bachelor Core Courses)
401-3461-00L Functional Analysis I
401-3531-00L Differential Geometry I
401-3601-00L Probability Theory
can be recognised for the Master's degree in Mathematics or Applied Mathematics. In this case, you cannot change the category assignment by yourself in myStudies but must take contact with the Study Administration Office (www.math.ethz.ch/studiensekretariat) after having received the credits.
W9 credits4V + 1UU. Lang
AbstractIntroduction to differential geometry and differential topology. Contents: Curves, (hyper-)surfaces in R^n, geodesics, curvature, Theorema Egregium, Theorem of Gauss-Bonnet. Hyperbolic space. Differentiable manifolds, immersions and embeddings, Sard's Theorem, mapping degree and intersection number, vector bundles, vector fields and flows, differential forms, Stokes' Theorem.
Learning objectiveLearn the basic concepts and results in differential geometry and differential topology. Learn to describe, compute, and solve problems in the language of differential geometry.
ContentCurves, (hyper-)surfaces in R^n, first and second fundamental forms, geodesics, curvature, Theorema Egregium, Theorem of Gauss-Bonnet, minimal surfaces. Hyperbolic space. Differentiable manifolds, immersions and embeddings, Sard's Theorem, mapping degree and intersection number, vector bundles, vector fields and flows, differential forms, Stokes' Theorem.
Lecture notesPartial lecture notes are available from https://people.math.ethz.ch/~lang/
LiteratureDifferential geometry in R^n:
- Manfredo P. do Carmo: Differential Geometry of Curves and Surfaces
- S. Montiel, A. Ros: Curves and Surfaces
- Wolfgang Kühnel: Differentialgeometrie. Kurven-Flächen-Mannigfaltigkeiten
- Christian Bär: Elementare Differentialgeometrie
Differential topology:
- Dennis Barden & Charles Thomas: An Introduction to Differential Manifolds
- Victor Guillemin & Alan Pollack: Differential Topology
- Morris W. Hirsch: Differential Topology
- John M. Lee: Introduction to Smooth Manifolds
CompetenciesCompetencies
Subject-specific CompetenciesConcepts and Theoriesassessed
Techniques and Technologiesassessed
Method-specific CompetenciesAnalytical Competenciesassessed
Problem-solvingassessed
Social CompetenciesSensitivity to Diversityassessed
Personal CompetenciesCreative Thinkingassessed
Critical Thinkingassessed
401-3461-00LFunctional Analysis I Information
At most one of the three course units (Bachelor Core Courses)
401-3461-00L Functional Analysis I
401-3531-00L Differential Geometry I
401-3601-00L Probability Theory
can be recognised for the Master's degree in Mathematics or Applied Mathematics. In this case, you cannot change the category assignment by yourself in myStudies but must take contact with the Study Administration Office (www.math.ethz.ch/studiensekretariat) after having received the credits.
W9 credits4V + 1UM. Burger
AbstractBaire category; Banach and Hilbert spaces, bounded linear operators; basic principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed graph theorem; spectral theory of self-adjoint operators in Hilbert spaces. Basics of
Sobolev spaces.
Learning objectiveAcquire a good degree of fluency with the fundamental concepts and tools belonging to the realm of linear Functional Analysis, with special emphasis on the geometric structure of Banach and Hilbert spaces, and on the basic properties of linear maps.
LiteratureRecommended references include the following:

Michael Struwe: "Funktionalanalysis I" (Skript available at https://people.math.ethz.ch/~struwe/Skripten/FA-I-2019.pdf)

Haim Brezis: "Functional analysis, Sobolev spaces and partial differential equations". Springer, 2011.

Peter D. Lax: "Functional analysis". Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002.

Elias M. Stein and Rami Shakarchi: "Functional analysis" (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011.

Manfred Einsiedler and Thomas Ward: "Functional Analysis, Spectral Theory, and Applications", Graduate Text in Mathematics 276. Springer, 2017.

Walter Rudin: "Functional analysis". International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991.
Prerequisites / NoticeSolid background on the content of all Mathematics courses of the first two years of the undergraduate curriculum at ETH.Most importantly: fluency with point set topology and measure theory, in part. Lebesgue integration and L^p spaces.
CompetenciesCompetencies
Subject-specific CompetenciesConcepts and Theoriesassessed
Method-specific CompetenciesAnalytical Competenciesassessed
Problem-solvingassessed
Personal CompetenciesCreative Thinkingassessed
Critical Thinkingassessed
Proseminars and Semester Papers
NumberTitleTypeECTSHoursLecturers
402-0218-MSLResearch Project Restricted registration - show details W8 credits15ASupervisors
AbstractStudents conduct a small research project within a research group or carry out a guided self-study of original papers on a given theoretical topic. The results are submitted in a written report and an oral presentation.
Learning objectiveStudents are enabled to:
• expand their knowledge in a specific area of physics,
• conduct a project (a) in a research laboratory or (b) on a specific topic of theoretical physics,
• discuss their project results and conclusions in a team,
• present their findings in written and oral form.
CompetenciesCompetencies
Subject-specific CompetenciesConcepts and Theoriesassessed
Techniques and Technologiesassessed
Method-specific CompetenciesAnalytical Competenciesassessed
Decision-makingassessed
Media and Digital Technologiesfostered
Problem-solvingassessed
Project Managementfostered
Social CompetenciesCommunicationassessed
Cooperation and Teamworkfostered
Sensitivity to Diversityfostered
Negotiationfostered
Personal CompetenciesAdaptability and Flexibilityfostered
Creative Thinkingassessed
Critical Thinkingfostered
Integrity and Work Ethicsassessed
Self-awareness and Self-reflection fostered
Self-direction and Self-management fostered
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