Search result: Catalogue data in Autumn Semester 2020
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. | ||||||
Seminar or Semester Paper | ||||||
Number | Title | Type | ECTS | Hours | Lecturers | |
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363-1100-00L | Risk Case Study Challenge Does not take place this semester. | W | 3 credits | 2S | A. Bommier, S. Feuerriegel, J. Teichmann | |
Abstract | This seminar provides master students at ETH with the challenging opportunity of working on a real risk case in close collaboration with a company. For Fall 2019 the Partner will be Credit Suisse and the topic of cases will focus on machine learning applications in finance. | |||||
Objective | Students work in groups on a real risk-related case of a business relevant topic provided by experts from Risk Center partners. While gaining substantial insights into the risk modeling and management of the industry, students explore the case or problem on their own, working in teams, and develop possible solutions. The cases allow students to use logical problem solving skills with emphasis on evidence and application and involve the integration of scientific knowledge. Typically, the cases can be complex, cover ambiguities, and may be addressed in more than one way. During the seminar, students visit the partners’ headquarters, interact and conduct interviews with risk professionals. The final results will be presented at the partners' headquarters. | |||||
Content | Get a basic understanding of o Risk management and risk modelling o Machine learning tools and applications o How to communicate your results to risk professionals For that you work in a group of 4 students together with a Case Manager from the company. In addition you are coached by the Lecturers on specific aspects of machine learning as well as communication and presentation skills. | |||||
Prerequisites / Notice | Please apply for this course via the official website (Link). Apply no later than September 13, 2019. The number of participants is limited to 16. | |||||
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 GESS Science in Perspective: Language Courses ETH/UZH | ||||||
» see GESS Science in Perspective: Type A: Enhancement of Reflection Capability | ||||||
» Recommended GESS Science in Perspective (Type B) for D-MATH. | ||||||
Master's Thesis | ||||||
Number | Title | Type | ECTS | Hours | Lecturers | |
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, E. Kowalski | ||
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 | |||||
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 MathBib training course | |||||
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 | Thesis work should prove the students' ability to independent, structured and scientific working. | |||||
Content | Five-month project to solve a research question. The content can be more theoretical (e.g. proving a new result) or applied (developing new methods or making a very sophisticated application and adapting existing methods). | |||||
Prerequisites / Notice | Supervisors are chosen on a first-come-first-served basis. Collaborations with industry are possible. | |||||
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 | |||||
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 | 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. | |||||
Literature | 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) 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. Learning the statistical program R for applying the acquired concepts will be a central theme. | |||||
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". | |||||
Content | 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 | |||||
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 | M. Schweizer | |
Abstract | 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. | |||||
Objective | 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. | |||||
Content | 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". | |||||
Literature | 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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