Suchergebnis: Katalogdaten im Frühjahrssemester 2020

Mathematik Bachelor Information
Wahlfächer
Auswahl: Finanz- und Versicherungsmathematik
NummerTitelTypECTSUmfangDozierende
401-3956-00LEconomic Theory of Financial Markets
Findet dieses Semester nicht statt.
W4 KP2VM. V. Wüthrich
KurzbeschreibungThis lecture provides an introduction to the economic theory of financial markets. It presents the basic financial and economic concepts to insurance mathematicians and actuaries.
LernzielThis lecture aims at providing the fundamental financial and economic concepts to insurance mathematicians and actuaries. It focuses on portfolio theory, cash flow valuation and deflator techniques.
InhaltWe treat the following topics:
- Fundamental concepts in economics
- Portfolio theory
- Mean variance analysis, capital asset pricing model
- Arbitrage pricing theory
- Cash flow theory
- Valuation principles
- Stochastic discounting, deflator techniques
- Interest rate modeling
- Utility theory
Voraussetzungen / BesonderesThe exams ONLY take place during the official ETH examination period.

This course will be held in English and counts towards the diploma of "Aktuar SAV". For the latter, see details under Link.

Knowledge in probability theory, stochastic processes and statistics is assumed.
401-3936-00LData Analytics for Non-Life Insurance PricingW4 KP2VC. M. Buser, M. V. Wüthrich
KurzbeschreibungWe study statistical methods in supervised learning for non-life insurance pricing such as generalized linear models, generalized additive models, Bayesian models, neural networks, classification and regression trees, random forests and gradient boosting machines.
LernzielThe student is familiar with classical actuarial pricing methods as well as with modern machine learning methods for insurance pricing and prediction.
InhaltWe present the following chapters:
- generalized linear models (GLMs)
- generalized additive models (GAMs)
- neural networks
- credibility theory
- classification and regression trees (CARTs)
- bagging, random forests and boosting
SkriptThe lecture notes are available from:
Link
Voraussetzungen / BesonderesThis course will be held in English and counts towards the diploma of "Aktuar SAV".
For the latter, see details under Link

Good knowledge in probability theory, stochastic processes and statistics is assumed.
401-4920-00LMarket-Consistent Actuarial ValuationW4 KP2VM. V. Wüthrich, H. Furrer
KurzbeschreibungIntroduction to market-consistent actuarial valuation.
Topics: Stochastic discounting, full balance sheet approach, valuation portfolio in life and non-life insurance, technical and financial risks, risk management for insurance companies.
LernzielGoal is to give the basic mathematical tools for describing insurance products within a financial market and economic environment and provide the basics of solvency considerations.
InhaltIn this lecture we give a full balance sheet approach to the task of actuarial valuation of an insurance company. Therefore we introduce a multidimensional valuation portfolio (VaPo) on the liability side of the balance sheet. The basis of this multidimensional VaPo is a set of financial instruments. This approach makes the liability side of the balance sheet directly comparable to its asset side.

The lecture is based on four sections:
1) Stochastic discounting
2) Construction of a multidimensional Valuation Portfolio for life insurance products (with guarantees)
3) Construction of a multidimensional Valuation Portfolio for a run-off portfolio of a non-life insurance company
4) Measuring financial risks in a full balance sheet approach (ALM risks)
LiteraturMarket-Consistent Actuarial Valuation, 3rd edition.
Wüthrich, M.V.
EAA Series, Springer 2016.
ISBN: 978-3-319-46635-4

Wüthrich, M.V., Merz, M.
Claims run-off uncertainty: the full picture.
SSRN Manuscript ID 2524352 (2015).

England, P.D, Verrall, R.J., Wüthrich, M.V.
On the lifetime and one-year views of reserve risk, with application to IFRS 17 and Solvency II risk margins.
Insurance: Mathematics and Economics 85 (2019), 74-88.

Wüthrich, M.V., Embrechts, P., Tsanakas, A.
Risk margin for a non-life insurance run-off.
Statistics & Risk Modeling 28 (2011), no. 4, 299--317.

Financial Modeling, Actuarial Valuation and Solvency in Insurance.
Wüthrich, M.V., Merz, M.
Springer Finance 2013.
ISBN: 978-3-642-31391-2

Cheridito, P., Ery, J., Wüthrich, M.V.
Assessing asset-liability risk with neural networks.
Risks 8/1 (2020), article 16.
Voraussetzungen / BesonderesThe exams ONLY take place during the official ETH examination period.

This course will be held in English and counts towards the diploma of "Aktuar SAV".
For the latter, see details under Link.

Knowledge in probability theory, stochastic processes and statistics is assumed.
Auswahl: Mathematische Physik, Theoretische Physik
Im Bachelor-Studiengang Mathematik ist auch 402-0204-00L Elektrodynamik als Wahlfach anrechenbar, aber nur unter der Bedingung, dass 402-0224-00L Theoretische Physik nicht angerechnet wird (weder im Bachelor- noch im Master-Studiengang). Wenden Sie sich für die Kategoriezuordnung nach dem Verfügen des Prüfungsresultates an das Studiensekretariat (Link).
NummerTitelTypECTSUmfangDozierende
401-3814-00LQuantum Mechanics for Mathematicians
NOTICE: The class scheduled for 5 March 2020 has been cancelled.
W4 KP2VJ. Wisniewska
KurzbeschreibungIntroduction to quantum mechanics aimed at mathematics students
LernzielThe course begins with the fundamentals of classical mechanics and its mathematical description i.e. Hamiltonian dynamics. We will introduce the notion of states and observables in the classical setting and further on its counter parts in the quantum setting. We then will discuss quantisation and the mathematical formulation of quantum mechanics. Further on we will study the Heisenberg’s uncertainty relations and quantum entanglement. The course then goes on to study the dynamics of quantum systems described by the Schrödinger’s equation.
Inhalt1. Hamiltonian mechanics and fundamentals of symplectic geometry
2. Classical observables and Poisson bracket
3. Basic principles of quantum mechanics and quantisation
4. Heisenberg’s uncertainty relations
5. Quantum entanglement and EPR paradox
6. Schrödinger’s equation
LiteraturTakhtajan, Leon A.
Quantum mechanics for mathematicians.
Graduate Studies in Mathematics, 95. American Mathematical Society, Providence, RI, 2008. xvi+387 pp. ISBN: 978-0-8218-4630-8
Voraussetzungen / BesonderesPrerequisites:
Essential: Differential Geometry 1
Recommended: basic Functional Analysis and Algebraic Topology
401-2334-00LMethoden der mathematischen Physik II Information Belegung eingeschränkt - Details anzeigen W6 KP3V + 2UG. Felder
KurzbeschreibungGruppentheorie: Gruppen, Darstellungen von Gruppen, unitäre und orthogonale Gruppen, Lorentzgruppe. Lie Theorie: Lie Algebren und Lie Gruppen. Darstellungstheorie:
Darstellungstheorie endlicher Gruppen, Darstellungen von Lie Algebren und Lie Gruppen, physikalische Anwendungen (Eigenwertprobleme mit Symmetrie)
Lernziel
402-0206-00LQuantum Mechanics IIW10 KP3V + 2UG. Blatter
KurzbeschreibungMany-body quantum physics rests on symmetry considerations that lead to two kinds of particles, fermions and bosons. Formal techniques include Hartree-Fock theory and second-quantization techniques, as well as quantum statistics with ensembles. Few- and many-body systems include atoms, molecules, the Fermi sea, elastic chains, radiation and its interaction with matter, and ideal quantum gases.
LernzielBasic command of few- and many-particle physics for fermions and bosons, including second quantisation and quantum statistical techniques. Understanding of elementary many-body systems such as atoms, molecules, the Fermi sea, electromagnetic radiation and its interaction with matter, ideal quantum gases and relativistic theories.
InhaltThe description of indistinguishable particles leads us to (exchange-) symmetrized wave functions for fermions and bosons. We discuss simple few-body problems (Helium atoms, hydrogen molecule) und proceed with a systematic description of fermionic many body problems (Hartree-Fock approximation, screening, correlations with applications on atomes and the Fermi sea). The second quantisation formalism allows for the compact description of the Fermi gas, of elastic strings (phonons), and the radiation field (photons). We study the interaction of radiation and matter and the associated phenomena of radiative decay, light scattering, and the Lamb shift. Quantum statistical description of ideal Bose and Fermi gases at finite temperatures concludes the program. If time permits, we will touch upon of relativistic one particle physics, the Klein-Gordon equation for spin-0 bosons and the Dirac equation describing spin-1/2 fermions.
SkriptQuanten Mechanik I und II in German.
LiteraturG. Baym, Lectures on Quantum Mechanics (Benjamin, Menlo Park, California, 1969)
L.I. Schiff, Quantum Mechanics (Mc-Graw-Hill, New York, 1955)
A. Messiah, Quantum Mechanics I & II (North-Holland, Amsterdam, 1976)
E. Merzbacher, Quantum Mechanics (John Wiley, New York, 1998)
C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum Mechanics I & II (John Wiley, New York, 1977)
P.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals (Mc Graw-Hill, New York, 1965)
A.L. Fetter and J.D. Walecka, Theoretical Mechanics of Particles and Continua (Mc Graw-Hill, New York, 1980)
J.J. Sakurai, Modern Quantum Mechanics (Addison Wesley, Reading, 1994)
J.J. Sakurai, Advanced Quantum mechanics (Addison Wesley)
F. Gross, Relativistic Quantum Mechanics and Field Theory (John Wiley, New York, 1993)
Voraussetzungen / BesonderesBasic knowledge of single-particle Quantum Mechanics
Auswahl: Mathematische Optimierung, Diskrete Mathematik
(noch) kein Angebot in diesem Semester
Auswahl: Theoretische Informatik
Im Bachelor-Studiengang Mathematik ist auch 401-3052-05L Graph Theory als Wahlfach anrechenbar, aber nur unter der Bedingung, dass 401-3052-10L Graph Theory nicht angerechnet wird (weder im Bachelor- noch im Master-Studiengang). Wenden Sie sich für die Kategoriezuordnung nach dem Verfügen des Prüfungsresultates an das Studiensekretariat (Link).
NummerTitelTypECTSUmfangDozierende
252-0408-00LCryptographic Protocols Information W6 KP2V + 2U + 1AM. Hirt, U. Maurer
KurzbeschreibungThe course presents a selection of hot research topics in cryptography. The choice of topics varies and may include provable security, interactive proofs, zero-knowledge protocols, secret sharing, secure multi-party computation, e-voting, etc.
LernzielIndroduction to a very active research area with many gems and paradoxical
results. Spark interest in fundamental problems.
InhaltThe course presents a selection of hot research topics in cryptography. The choice of topics varies and may include provable security, interactive proofs, zero-knowledge protocols, secret sharing, secure multi-party computation, e-voting, etc.
Skriptthe lecture notes are in German, but they are not required as the entire
course material is documented also in other course material (in english).
Voraussetzungen / BesonderesA basic understanding of fundamental cryptographic concepts
(as taught for example in the course Information Security or
in the course Cryptography Foundations) is useful, but not required.
263-4660-00LApplied Cryptography Information Belegung eingeschränkt - Details anzeigen
Number of participants limited to 150.
W8 KP3V + 2U + 2PK. Paterson
KurzbeschreibungThis course will introduce the basic primitives of cryptography, using rigorous syntax and game-based security definitions. The course will show how these primitives can be combined to build cryptographic protocols and systems.
LernzielThe goal of the course is to put students' understanding of cryptography on sound foundations, to enable them to start to build well-designed cryptographic systems, and to expose them to some of the pitfalls that arise when doing so.
InhaltBasic symmetric primitives (block ciphers, modes, hash functions); generic composition; AEAD; basic secure channels; basic public key primitives (encryption,signature, DH key exchange); ECC; randomness; applications.
LiteraturTextbook: Boneh and Shoup, “A Graduate Course in Applied Cryptography”, Link.
Voraussetzungen / BesonderesIdeally, students will have taken the D-INFK Bachelors course “Information Security" or an equivalent course at Bachelors level.
Auswahl: Weitere Gebiete
NummerTitelTypECTSUmfangDozierende
401-4944-20LMathematics of Data ScienceW8 KP4GA. Bandeira
KurzbeschreibungMostly self-contained, but fast-paced, introductory masters level course on various theoretical aspects of algorithms that aim to extract information from data.
LernzielIntroduction to various mathematical aspects of Data Science.
InhaltThese topics lie in overlaps of (Applied) Mathematics with: Computer Science, Electrical Engineering, Statistics, and/or Operations Research. Each lecture will feature a couple of Mathematical Open Problem(s) related to Data Science. The main mathematical tools used will be Probability and Linear Algebra, and a basic familiarity with these subjects is required. There will also be some (although knowledge of these tools is not assumed) Graph Theory, Representation Theory, Applied Harmonic Analysis, among others. The topics treated will include Dimension reduction, Manifold learning, Sparse recovery, Random Matrices, Approximation Algorithms, Community detection in graphs, and several others.
SkriptLink
Voraussetzungen / BesonderesThe main mathematical tools used will be Probability, Linear Algebra (and real analysis), and a working knowledge of these subjects is required. In addition
to these prerequisites, this class requires a certain degree of mathematical maturity--including abstract thinking and the ability to understand and write proofs.


We encourage students who are interested in mathematical data science to take both this course and ``227-0434-10L Mathematics of Information'' taught by Prof. H. Bölcskei. The two courses are designed to be
complementary.
A. Bandeira and H. Bölcskei
252-0220-00LIntroduction to Machine Learning Information Belegung eingeschränkt - Details anzeigen
Limited number of participants. Preference is given to students in programmes in which the course is being offered. All other students will be waitlisted. Please do not contact Prof. Krause for any questions in this regard. If necessary, please contact Link
W8 KP4V + 2U + 1AA. Krause
KurzbeschreibungThe course introduces the foundations of learning and making predictions based on data.
LernzielThe course will introduce the foundations of learning and making predictions from data. We will study basic concepts such as trading goodness of fit and model complexitiy. We will discuss important machine learning algorithms used in practice, and provide hands-on experience in a course project.
Inhalt- Linear regression (overfitting, cross-validation/bootstrap, model selection, regularization, [stochastic] gradient descent)
- Linear classification: Logistic regression (feature selection, sparsity, multi-class)
- Kernels and the kernel trick (Properties of kernels; applications to linear and logistic regression); k-nearest neighbor
- Neural networks (backpropagation, regularization, convolutional neural networks)
- Unsupervised learning (k-means, PCA, neural network autoencoders)
- The statistical perspective (regularization as prior; loss as likelihood; learning as MAP inference)
- Statistical decision theory (decision making based on statistical models and utility functions)
- Discriminative vs. generative modeling (benefits and challenges in modeling joint vy. conditional distributions)
- Bayes' classifiers (Naive Bayes, Gaussian Bayes; MLE)
- Bayesian approaches to unsupervised learning (Gaussian mixtures, EM)
LiteraturTextbook: Kevin Murphy, Machine Learning: A Probabilistic Perspective, MIT Press
Voraussetzungen / BesonderesDesigned to provide a basis for following courses:
- Advanced Machine Learning
- Deep Learning
- Probabilistic Artificial Intelligence
- Seminar "Advanced Topics in Machine Learning"
263-5300-00LGuarantees for Machine Learning Information Belegung eingeschränkt - Details anzeigen W5 KP2V + 2AF. Yang
KurzbeschreibungThis course teaches classical and recent methods in statistics and optimization commonly used to prove theoretical guarantees for machine learning algorithms. The knowledge is then applied in project work that focuses on understanding phenomena in modern machine learning.
LernzielThis course is aimed at advanced master and doctorate students who want to understand and/or conduct independent research on theory for modern machine learning. For this purpose, students will learn common mathematical techniques from statistical learning theory. In independent project work, they then apply their knowledge and go through the process of critically questioning recently published work, finding relevant research questions and learning how to effectively present research ideas to a professional audience.
InhaltThis course teaches some classical and recent methods in statistical learning theory aimed at proving theoretical guarantees for machine learning algorithms, including topics in

- concentration bounds, uniform convergence
- high-dimensional statistics (e.g. Lasso)
- prediction error bounds for non-parametric statistics (e.g. in kernel spaces)
- minimax lower bounds
- regularization via optimization

The project work focuses on active theoretical ML research that aims to understand modern phenomena in machine learning, including but not limited to

- how overparameterization could help generalization ( interpolating models, linearized NN )
- how overparameterization could help optimization ( non-convex optimization, loss landscape )
- complexity measures and approximation theoretic properties of randomly initialized and
trained NN
- generalization of robust learning ( adversarial robustness, standard and robust error tradeoff )
- prediction with calibrated confidence ( conformal prediction, calibration )
Voraussetzungen / BesonderesIt’s absolutely necessary for students to have a strong mathematical background (basic real analysis, probability theory, linear algebra) and good knowledge of core concepts in machine learning taught in courses such as “Introduction to Machine Learning”, “Regression”/ “Statistical Modelling”. It's also helpful to have heard an optimization course or approximation theoretic course. In addition to these prerequisites, this class requires a certain degree of mathematical maturity—including abstract thinking and the ability to understand and write proofs.
401-3502-20LReading Course Belegung eingeschränkt - Details anzeigen
To start an individual reading course, contact an authorised supervisor
Link
and register your reading course in myStudies.
W2 KP4ABetreuer/innen
KurzbeschreibungIn diesem Reading Course wird auf Eigeninitiative und auf individuelle Vereinbarung mit einem Dozenten/einer Dozentin hin ein Stoff durch eigenständiges Literaturstudium erarbeitet.
Lernziel
401-3503-20LReading Course Belegung eingeschränkt - Details anzeigen
To start an individual reading course, contact an authorised supervisor
Link
and register your reading course in myStudies.
W3 KP6ABetreuer/innen
KurzbeschreibungIn diesem Reading Course wird auf Eigeninitiative und auf individuelle Vereinbarung mit einem Dozenten/einer Dozentin hin ein Stoff durch eigenständiges Literaturstudium erarbeitet.
Lernziel
401-3504-20LReading Course Belegung eingeschränkt - Details anzeigen
To start an individual reading course, contact an authorised supervisor
Link
and register your reading course in myStudies.
W4 KP9ABetreuer/innen
KurzbeschreibungIn diesem Reading Course wird auf Eigeninitiative und auf individuelle Vereinbarung mit einem Dozenten/einer Dozentin hin ein Stoff durch eigenständiges Literaturstudium erarbeitet.
Lernziel
Kern- und Wahlfächer (Mathematik Master)
» Wahlfächer (Mathematik Master)
» Kernfächer (Mathematik Master)
Weitere geeignete Fächer im zweiten Studienjahr
NummerTitelTypECTSUmfangDozierende
401-2334-00LMethoden der mathematischen Physik II Information Belegung eingeschränkt - Details anzeigen W6 KP3V + 2UG. Felder
KurzbeschreibungGruppentheorie: Gruppen, Darstellungen von Gruppen, unitäre und orthogonale Gruppen, Lorentzgruppe. Lie Theorie: Lie Algebren und Lie Gruppen. Darstellungstheorie:
Darstellungstheorie endlicher Gruppen, Darstellungen von Lie Algebren und Lie Gruppen, physikalische Anwendungen (Eigenwertprobleme mit Symmetrie)
Lernziel
401-2200-13LDarstellungstheorie endlicher Gruppen Belegung eingeschränkt - Details anzeigen
Hauptzielgruppe: Studierende Mathematik Bachelor 4. Semester (und 6. Semester, falls es noch freie Plätze gibt).
Maximale Teilnehmerzahl: 12
W4 KP2SR. Pink
Kurzbeschreibung-Grundlegende Begriffe aus der Darstellungstheorie
-Zerlegung in irreduzible Darstellungen
-Charaktertheorie
-Berechnung von Charaktertabellen
-Anwendungen zur Gruppentheorie, insbesondere Satz von Burnside
LernzielMethoden und Resultate der Darstellungstheorie.
Vortragstechnik.
LiteraturRepresentations and Characters of Groups, Gordon James & Martin Liebeck, Cambridge Verlag.
Voraussetzungen / BesonderesDas Seminar richtet sich primär an Studierende im 4. Semester, die die Vorlesung Algebra I bei mir besucht haben.
Am Donnerstag den 6. Januar um 15:00 im Raum HG G43 findet eine Vorbesprechung statt, an der Sie unbedingt teilnehmen sollten.
Seminare
Dieses Semester haben viele Seminare eine Warteliste mit speziellem Auswahlverfahren. Falls keine anderen Auswahlkriterien vorliegen, werden bei der definitiven Belegung zuerst jene Studierenden berücksichtigt, welche noch keine andere Seminarbelegung haben. Wenn Sie sich in zwei Wartelisten eintragen, so tun Sie dies am besten so: wählen Sie zuerst das Seminar aus, das Sie bevorzugen, und wählen Sie anschliessend eine Ausweichmöglichkeit aus.
NummerTitelTypECTSUmfangDozierende
401-2200-13LDarstellungstheorie endlicher Gruppen Belegung eingeschränkt - Details anzeigen
Hauptzielgruppe: Studierende Mathematik Bachelor 4. Semester (und 6. Semester, falls es noch freie Plätze gibt).
Maximale Teilnehmerzahl: 12
W4 KP2SR. Pink
Kurzbeschreibung-Grundlegende Begriffe aus der Darstellungstheorie
-Zerlegung in irreduzible Darstellungen
-Charaktertheorie
-Berechnung von Charaktertabellen
-Anwendungen zur Gruppentheorie, insbesondere Satz von Burnside
LernzielMethoden und Resultate der Darstellungstheorie.
Vortragstechnik.
LiteraturRepresentations and Characters of Groups, Gordon James & Martin Liebeck, Cambridge Verlag.
Voraussetzungen / BesonderesDas Seminar richtet sich primär an Studierende im 4. Semester, die die Vorlesung Algebra I bei mir besucht haben.
Am Donnerstag den 6. Januar um 15:00 im Raum HG G43 findet eine Vorbesprechung statt, an der Sie unbedingt teilnehmen sollten.
401-3110-20LQuadratic Forms, Markov Numbers and Diophantine Approximation Information Belegung eingeschränkt - Details anzeigen
Number of participants limited to 22.
W4 KP2SP. Bengoechea Duro
KurzbeschreibungIn 1880 Andrei A. Markov discovered beautiful connections between minima of binary real quadratic forms, badly approximable numbers by rationals, and a certain Diophantine equation which describes an affine cubic surface, now and days called Markov surface. We will use Markov's theory as a unifying thread to talk about quadratic forms, Diophantine approximation and hyperbolic geometry.
Lernziel
InhaltContinued fractions; representation of real numbers by rationals; Hurwitz's theorem; Lagrange spectrum; badly approximable numbers; binary quadratic forms; Markov numbers; Markov tree; geometric interpretation of Markov numbers; the still open Unicity Conjecture
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