# Search result: Catalogue data in Spring Semester 2020

Number Title Type ECTS Hours Lecturers Statistics Master 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 RequirementsThe courses below are only available for MSc students with additional admission requirements. 406-0173-AAL Linear Algebra I and IIEnrolment 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 credits 13R N. Hungerbühler Abstract 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. Objective 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. Content 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, 8.6A Practical Introduction to MATLAB: http://www.math.ethz.ch/~grsam/Numerik_MAVT_WS0203/docs/intro.pdfMatlab 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-AAL Analysis 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- 14 credits 30R M. Akveld Abstract Mathematical tools for the engineer Objective Mathematics as a tool to solve engineering problems. Mathematical formulation of technical and scientific problems. Basic mathematical knowledge for engineers. Content Short 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. Literature Textbooks 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 EducationTextbooks 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)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 credits 9R M. Kalisch Abstract Introduction to basic methods and fundamental concepts of statistics andprobability theory for non-mathematicians. The concepts are presented onthe basis of some descriptive examples. The course will be based on thebook "Statistics for research" by S. Dowdy et.al. and on thebook "Introductory Statistics with R" by P. Dalgaard. Objective The objective of this course is to build a solid fundament in probabilityand statistics. The student should understand some fundamental concepts andbe able to apply these concepts to applications in the realworld. Furthermore, the student should have a basic knowledge of thestatistical programming language "R". The main topics of the course are:- Introduction to probability- Common distributions- Binomialtest- z-Test, t-Test- Regression Content From "Statistics for research":Ch 1: The Role of StatisticsCh 2: Populations, Samples, and Probability DistributionsCh 3: Binomial DistributionsCh 6: Sampling Distribution of AveragesCh 7: Normal DistributionsCh 8: Student's t DistributionCh 9: Distributions of Two Variables [Regression]From "Introductory Statistics with R":Ch 1: BasicsCh 2: Probability and distributionsCh 3: Descriptive statistics and tablesCh 4: One- and two-sample testsCh 5: Regression and correlation Literature "Statistics for research" by S. Dowdy et. al. (3rdedition); 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; ISBN978-0-387-79053-4; DOI: 10.1007/978-0-387-79054-1From within the ETH, this book is freely available online under:http://www.springerlink.com/content/m17578/ 406-2604-AAL Probability and StatisticsEnrolment 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 credits 15R M. Schweizer Abstract - Discrete probability spaces- Continuous models- Limit theorems- Introduction to statistics Objective The goal of this course is to provide an introduction to the basic ideas and concepts from probability theory and mathematical statistics. This includes a mathematically rigorous treatment as well as intuition and getting acquainted with the ideas behind the definitions. The course does not use measure theory systematically, but does point out where this is required and what the connections are. Content - Probability: Chapters 1-12 from the book by DasGupta - Statistics: Chapters 8-11 from the book by Rice Lecture notes There will be lecture notes (in German) that are continuously updated during the semester. Literature A. DasGupta, Fundamentals of Probability: A First Course, Springer (2010)J. A. Rice, Mathematical Statistics and Data Analysis, Duxbury Press, second edition (1995) Prerequisites / Notice Some of the exercise classes associated to the original course (which is in German) will be offered in English.