Search result: Catalogue data in Spring Semester 2021
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. | ||||||
GESS Science in Perspective Two credits are needed from the "Science in Perspective" programme with language courses excluded if three credits from language courses have already been recognised for the Bachelor's degree. see Link (Eight credits must be acquired in this category: normally six during the Bachelor’s degree programme, and two during the Master’s degree programme. A maximum of three credits from language courses from the range of the Language Center of the University of Zurich and ETH Zurich may be recognised. In addition, only advanced courses (level B2 upwards) in the European languages English, French, Italian and Spanish are recognised. German language courses are recognised from level C2 upwards.) | ||||||
» see Science in Perspective: Type A: Enhancement of Reflection Capability | ||||||
» Recommended Science in Perspective (Type B) for D-MATH | ||||||
» see Science in Perspective: Language Courses ETH/UZH | ||||||
Master's Thesis | ||||||
Number | Title | Type | ECTS | Hours | Lecturers | |
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401-2000-00L | Scientific Works in Mathematics Target audience: Third year Bachelor students; Master students who cannot document to have received an adequate training in working scientifically. | O | 0 credits | M. Burger | ||
Abstract | Introduction to scientific writing for students with focus on publication standards and ethical issues, especially in the case of citations (references to works of others.) | |||||
Objective | Learn the basic standards of scientific works in mathematics. | |||||
Content | - Types of mathematical works - Publication standards in pure and applied mathematics - Data handling - Ethical issues - Citation guidelines | |||||
Lecture notes | Moodle of the Mathematics Library: Link | |||||
Prerequisites / Notice | Directive Link | |||||
401-2000-01L | Lunch Sessions – Thesis Basics for Mathematics Students Details and registration for the optional MathBib training course: Link | Z | 0 credits | Speakers | ||
Abstract | Optional course "Recherchieren in der Mathematik" (held in German) by the Mathematics Library. | |||||
Objective | ||||||
401-4990-02L | Master's Thesis Only students who fulfil the following criteria are allowed to begin with their Master's thesis: a. successful completion of the Bachelor's programme; b. fulfilling of any additional requirements necessary to gain admission to the Master's programme; c. They have acquired at least 16 credits in the category “Core courses” for Programme Regulations 2014 and 40 credits in the category “Main Areas” for Programme Regulations 2020. Successful participation in the course unit 401-2000-00L Scientific Works in Mathematics is required. For more information, see Link | O | 30 credits | 57D | Supervisors | |
Abstract | The master's thesis concludes the study programme. Thesis work should prove the students' ability to independent, structured and scientific working. | |||||
Objective | Die Studierenden sollen mit der Master-Arbeit, die den Abschluss des Studiengangs bildet, ihre Fähigkeit zu selbständiger, strukturierter und wissenschaftlicher Tätigkeit unter Beweis stellen. | |||||
Course Units for Additional Admission Requirements The courses below are only available for MSc students with additional admission requirements. | ||||||
Number | Title | Type | ECTS | Hours | Lecturers | |
406-0173-AAL | Linear 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 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, 8.6 A Practical Introduction to MATLAB: Link Matlab Primer: Link | |||||
Literature | - Gilbert Strang: Introduction to linear algebra. Wellesley-Cambridge Press - A Practical Introduction to MATLAB: Link - Matlab Primer: Link - 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 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-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 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. | |||||
Objective | 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". 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 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: Link "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: Link | |||||
406-2604-AAL | 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- | 7 credits | 15R | J. Teichmann | |
Abstract | - Statistical models - Methods of moments - Maximum likelihood estimation - Hypothesis testing - Confidence intervals - Introductory Bayesian statistics - Linear regression model - Rudiments of high-dimensional statistics | |||||
Objective | The goal of this part of the course is to provide a solid introduction into statistics. It offers of a wide overview of the main tools used in statistical inference. The course will start with an introduction to statistical models and end with some notions of high-dimensional statistics. Some time will be spent on proving certain important results. Tools from probability and measure theory will be assumed to be known and hence will be only and occasionally recalled. | |||||
Lecture notes | Script of Prof. Dr. S. van de Geer | |||||
Literature | These references could be use complementary sources: R. Berger and G. Casella, Statistical Inference J. A. Rice, Mathematical Statistics and Data Analysis L. Wasserman, All of Statistics |
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