Search result: Catalogue data in Spring Semester 2022

Statistics Master Information
The following courses belong to the curriculum of the Master's Programme in Statistics. The corresponding credits do not count as external credits even for course units where an enrolment at ETH Zurich is not possible.
Course Units for Additional Admission Requirements
The courses below are only available for MSc students with additional admission requirements.
NumberTitleTypeECTSHoursLecturers
406-0173-AALLinear Algebra I and II
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-6 credits13RN. Hungerbühler
AbstractLinear algebra is an indispensable tool of engineering mathematics. The course is an introduction to basic methods and fundamental concepts of linear algebra and its applications to engineering sciences.
Learning objectiveAfter completion of this course, students are able to recognize linear structures and to apply adequate tools from linear algebra in order to solve corresponding problems from theory and applications. In addition, students have a basic knowledge of the software package Matlab.
ContentSystems of linear equations, Gaussian elimination, solution space, matrices, LR decomposition, determinants, structure of linear spaces, normed vector spaces, inner products, method of least squares, QR decomposition, introduction to MATLAB, applications.
Linear maps, kernel and image, coordinates and matrices, coordinate transformations, norm of a matrix, orthogonal matrices, eigenvalues and eigenvectors, algebraic and geometric multiplicity, eigenbasis, diagonalizable matrices, symmetric matrices, orthonormal basis, condition number, linear differential equations, Jordan decomposition, singular value decomposition, examples in MATLAB, applications.

Reading:

Gilbert Strang "Introduction to linear algebra", Wellesley-Cambridge Press: Chapters 1-6, 7.1-7.3, 8.1, 8.2, 8.6

A Practical Introduction to MATLAB: http://www.math.ethz.ch/~grsam/Numerik_MAVT_WS0203/docs/intro.pdf

Matlab Primer: http://www.math.ethz.ch/~grsam/Numerik_MAVT_WS0203/docs/primer.pdf
Literature- Gilbert Strang: Introduction to linear algebra. Wellesley-Cambridge Press

- A Practical Introduction to MATLAB: http://www.math.ethz.ch/~grsam/Numerik_MAVT_WS0203/docs/intro.pdf

- Matlab Primer: http://www.math.ethz.ch/~grsam/Numerik_MAVT_WS0203/docs/primer.pdf

- K. Nipp / D. Stoffer, Lineare Algebra, vdf Hochschulverlag, 5. Auflage 2002

- K. Meyberg / P. Vachenauer, Höhere Mathematik 1, Springer 2003
406-0243-AALAnalysis I and II Information
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-14 credits30RM. Akveld
AbstractMathematical tools for the engineer
Learning objectiveMathematics as a tool to solve engineering problems. Mathematical formulation of technical and scientific problems. Basic mathematical knowledge for engineers.
ContentShort introduction to mathematical logic.
Complex numbers.
Calculus for functions of one variable with applications.
Simple types of ordinary differential equations.
Simple Mathematical models in engineering.

Multi variable calculus: gradient, directional derivative, chain rule, Taylor expansion. Multiple integrals: coordinate transformations, path integrals, integrals over surfaces, divergence theorem, applications in physics.
LiteratureTextbooks in English:
- J. Stewart: Calculus, Cengage Learning, 2009, ISBN 978-0-538-73365-6
- J. Stewart: Multivariable Calculus, Thomson Brooks/Cole (e.g. Appendix G on complex numbers)
- V. I. Smirnov: A course of higher mathematics. Vol. II. Advanced calculus
- W. L. Briggs, L. Cochran: Calculus: Early Transcendentals: International Edition, Pearson Education
Textbooks in German:
- M. Akveld, R. Sperb: Analysis I, vdf
- M. Akveld, R. Sperb: Analysis II, vdf
- L. Papula: Mathematik für Ingenieure und Naturwissenschaftler, Vieweg Verlag
- L. Papula: Mathematik für Ingenieure 2, Vieweg Verlag
406-0603-AALStochastics (Probability and Statistics)
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-4 credits9RM. Kalisch
AbstractIntroduction to basic methods and fundamental concepts of statistics and
probability theory for non-mathematicians. The concepts are presented on
the basis of some descriptive examples. The course will be based on the
book "Statistics for research" by S. Dowdy et.al. and on the
book "Introductory Statistics with R" by P. Dalgaard.
Learning objectiveThe objective of this course is to build a solid fundament in probability
and statistics. The student should understand some fundamental concepts and
be able to apply these concepts to applications in the real
world. Furthermore, the student should have a basic knowledge of the
statistical programming language "R". The main topics of the course are:
- Introduction to probability
- Common distributions
- Binomialtest
- z-Test, t-Test
- Regression
ContentFrom "Statistics for research":
Ch 1: The Role of Statistics
Ch 2: Populations, Samples, and Probability Distributions
Ch 3: Binomial Distributions
Ch 6: Sampling Distribution of Averages
Ch 7: Normal Distributions
Ch 8: Student's t Distribution
Ch 9: Distributions of Two Variables [Regression]

From "Introductory Statistics with R":
Ch 1: Basics
Ch 2: Probability and distributions
Ch 3: Descriptive statistics and tables
Ch 4: One- and two-sample tests
Ch 5: Regression and correlation
Literature"Statistics for research" by S. Dowdy et. al. (3rd
edition); Print ISBN: 9780471267355; Online ISBN: 9780471477433; DOI:
10.1002/0471477435;
From within the ETH, this book is freely available online under:
http://onlinelibrary.wiley.com/book/10.1002/0471477435

"Introductory Statistics with R" by Peter Dalgaard; ISBN
978-0-387-79053-4; DOI: 10.1007/978-0-387-79054-1
From within the ETH, this book is freely available online under:
http://www.springerlink.com/content/m17578/
406-2604-AALProbability and Statistics
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-7 credits15RF. Balabdaoui
Abstract- Probability spaces
- Discrete models, Randiom walk
- Conditional probabilities, independence
- Continuous models
- Limit theorems
==============================
- Methods of moments
- Maximum likelihood estimation
- Hypothesis testing
- Confidence intervals
- Introductory Bayesian statistics
- Linear regression model
Learning objectiveThe first part of the course gives an overview of the main concepts needed to understand probability theory (sample spaces, discrete models, random walk, contiuous models and limit theorems such as the Laws of Large Numbers and the Central limit theorem. Note that this part of the lectures will be given in German. The second part covers some fundamental results of mathematical statistics including estimation methods, hypothesis testing as well as the linear regression model. This part of the lectures will be offered in Englisch.
Lecture notesWahrscheinlichkeitstheorie: basiert auf dem Skript "Wahrscheinlichkeitsrechnung und Statistik" von Prof. H. Foellmer und Prof. H. Kuensch (mit Ergaenzungen von Prof. J. Teichmann)


Statistics: based on the script "Statistics for Mathematics" by Prof. S. van de Geer
LiteratureA. DasGupta, Fundamentals of Probability: A First Course, Springer (2010)

R. Berger and G. Casella, Statistical Inference, Duxbury Press (1990)

J. A. Rice, Mathematical Statistics and Data Analysis, Wadsworth, second edition (1995)
Prerequisites / NoticeThe exam will be in German. The questions about the Statistics part will be also written in English.

The questions in the exercise sheets will be given in the same language of the lecture.
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