Search result: Catalogue data in Autumn Semester 2019
Mathematics Master | ||||||
Electives For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields. | ||||||
Electives: Applied Mathematics and Further Application-Oriented Fields ¬ | ||||||
Selection: Further Realms | ||||||
Number | Title | Type | ECTS | Hours | Lecturers | |
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227-0423-00L | Neural Network Theory | W | 4 credits | 2V + 1U | H. Bölcskei, E. Riegler | |
Abstract | The class focuses on fundamental mathematical aspects of neural networks with an emphasis on deep networks: Universal approximation theorems, capacity of separating surfaces, generalization, reproducing Kernel Hilbert spaces, support vector machines, fundamental limits of deep neural network learning, dimension measures, feature extraction with scattering networks | |||||
Objective | After attending this lecture, participating in the exercise sessions, and working on the homework problem sets, students will have acquired a working knowledge of the mathematical foundations of neural networks. | |||||
Content | 1. Universal approximation with single- and multi-layer networks 2. Geometry of decision surfaces 3. Separating capacity of nonlinear decision surfaces 4. Generalization 5. Reproducing Kernel Hilbert Spaces, support vector machines 6. Deep neural network approximation theory: Fundamental limits on compressibility of signal classes, Kolmogorov epsilon-entropy of signal classes, covering numbers, fundamental limits of deep neural network learning 7. Learning of real-valued functions: Pseudo-dimension, fat-shattering dimension, Vapnik-Chervonenkis dimension 8. Scattering networks | |||||
Lecture notes | Detailed lecture notes will be provided as we go along. | |||||
Prerequisites / Notice | This course is aimed at students with a strong mathematical background in general, and in linear algebra, analysis, and probability theory in particular. | |||||
401-3502-69L | Reading Course To start an individual reading course, contact an authorised supervisor Link and register your reading course in myStudies. | W | 2 credits | 4A | Supervisors | |
Abstract | For this Reading Course proactive students make an individual agreement with a lecturer to acquire knowledge through independent literature study. | |||||
Objective | ||||||
401-3503-69L | Reading Course To start an individual reading course, contact an authorised supervisor Link and register your reading course in myStudies. | W | 3 credits | 6A | Supervisors | |
Abstract | For this Reading Course proactive students make an individual agreement with a lecturer to acquire knowledge through independent literature study. | |||||
Objective | ||||||
401-3504-69L | Reading Course To start an individual reading course, contact an authorised supervisor Link and register your reading course in myStudies. | W | 4 credits | 9A | Supervisors | |
Abstract | For this Reading Course proactive students make an individual agreement with a lecturer to acquire knowledge through independent literature study. | |||||
Objective | ||||||
401-0000-00L | Communication in Mathematics | W | 2 credits | 1V | W. Merry | |
Abstract | Don't hide your Next Great Theorem behind bad writing. This course teaches fundamental communication skills in mathematics: how to write clearly and how to structure mathematical content for different audiences, from theses, to preprints, to personal statements in applications. In addition, the course will help you establish a working knowledge of LaTeX. | |||||
Objective | Knowing how to present written mathematics in a structured and clear manner. | |||||
Content | Topics covered include: - Language conventions and common errors. - How to write a thesis (more generally, a mathematics paper). - How to use LaTeX. - How to write a personal statement for Masters and PhD applications. | |||||
Lecture notes | Full lecture notes will be made available on my website: Link | |||||
Prerequisites / Notice | There are no formal mathematical prerequisites. | |||||
401-0000-99L | Communication in Mathematics (Upgrade 2018 → 2019) This course unit is only for students who got 1 ECTS credit from last year's course unit 401-0000-00L CiM. (Registration now closed.) | W | 1 credit | 1V | W. Merry | |
Abstract | Don't hide your Next Great Theorem behind bad writing. This course teaches fundamental communication skills in mathematics: how to write clearly and how to structure mathematical content for different audiences, from theses, to preprints, to personal statements in applications. In addition, the course will help you establish a working knowledge of LaTeX. | |||||
Objective | Knowing how to present written mathematics in a structured and clear manner. | |||||
Content | Topics covered include: - Language conventions and common errors. - How to write a thesis (more generally, a mathematics paper). - How to use LaTeX. - How to write a personal statement for Masters and PhD applications. | |||||
Lecture notes | Full lecture notes will be made available on my website: Link | |||||
Prerequisites / Notice | There are no formal mathematical prerequisites. |
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