Suchergebnis: Katalogdaten im Herbstsemester 2020

Nummer	Titel	Typ	ECTS	Umfang	Dozierende
Statistik Master Die hier aufgelisteten Lehrveranstaltungen gehören zum Curriculum des Master-Studiengangs Statistik. Die entsprechenden KP gelten nicht als Mobilitäts-KP, auch wenn gewisse Lerneinheiten nicht an der ETH Zürich belegt werden können.
Auflagen-Lerneinheiten Das untenstehende Lehrangebot gilt nur für MSc Studierende mit Zulassungsauflagen.
406-0173-AAL	Linear Algebra I and II Belegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben. Alle anderen Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen.	E-	6 KP	13R	N. Hungerbühler
Kurzbeschreibung	Linear 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.
Lernziel	After 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.
Inhalt	Systems 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
Literatur	- 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
406-0243-AAL	Analysis I and II Belegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben. Alle anderen Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen.	E-	14 KP	30R	M. Akveld
Kurzbeschreibung	Mathematical tools for the engineer
Lernziel	Mathematics as a tool to solve engineering problems. Mathematical formulation of technical and scientific problems. Basic mathematical knowledge for engineers.
Inhalt	Complex numbers. Calculus for functions of one variable with applications. Simple Mathematical models in engineering. Multi variable calculus: gradient, directional derivative, chain rule, Taylor expansion, Lagrange multipliers. Multiple integrals: coordinate transformations, path integrals, integrals over surfaces, divergence theorem, applications in physics. Ordinary differential equations.
Literatur	Textbooks in English: - J. Stewart: Calculus, Cengage Learning, 2009, ISBN 978-0-538-73365-6. - J. Stewart: Multivariable Calculus, Thomson Brooks/Cole. - V. I. Smirnov: A course of higher mathematics. Vol. II. Advanced calculus. - W. L. Briggs, L. Cochran: Calculus: Early Transcendentals: International Edition, Pearson Education. ISBN 978-0-321-65193-8. 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-AAL	Stochastics (Probability and Statistics) Belegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben. Alle anderen Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen.	E-	4 KP	9R	M. Kalisch
Kurzbeschreibung	Introduction 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. Learning the statistical program R for applying the acquired concepts will be a central theme.
Lernziel	The 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".
Inhalt	From "Statistics for research" (online) 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 From "Introductory Statistics with R (online)" Ch 1: Basics Ch 2: The R Environment Ch 3: Probability and distributions Ch 4: Descriptive statistics and tables Ch 5: One- and two-sample tests Ch 6: Regression and correlation
Literatur	- "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-AAL	Probability and Statistics Belegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben. Alle anderen Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen.	E-	7 KP	15R	M. Schweizer
Kurzbeschreibung	Introduction to probability and statistics with many examples, based on chapters from the books "Probability and Random Processes" by G. Grimmett and D. Stirzaker and "Mathematical Statistics and Data Analysis" by J. Rice.
Lernziel	The goal of this course is to provide an introduction to the basic ideas and concepts from probability theory and mathematical statistics. In addition to a mathematically rigorous treatment, also an intuitive understanding and familiarity with the ideas behind the definitions are emphasized. Measure theory is not used systematically, but it should become clear why and where measure theory is needed.
Inhalt	Probability: Chapters 1-5 (Probabilities and events, Discrete and continuous random variables, Generating functions) and Sections 7.1-7.5 (Convergence of random variables) from the book "Probability and Random Processes". Most of this material is also covered in Chap. 1-5 of "Mathematical Statistics and Data Analysis", on a slightly easier level. Statistics: Sections 8.1 - 8.5 (Estimation of parameters), 9.1 - 9.4 (Testing Hypotheses), 11.1 - 11.3 (Comparing two samples) from "Mathematical Statistics and Data Analysis".
Literatur	Geoffrey Grimmett and David Stirzaker, Probability and Random Processes. 3rd Edition. Oxford University Press, 2001. John A. Rice, Mathematical Statistics and Data Analysis, 3rd edition. Duxbury Press, 2006.

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