Suchergebnis: Katalogdaten im Herbstsemester 2024
Doktorat Informationstechnologie und Elektrotechnik  A minimum of 12 ECTS credit points must be obtained during doctoral studies (also see sub-categories for details) More Information at https://ee.ethz.ch/doctoral-studies.html | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
 Vertiefung FachwissenThe courses on offer below are only a small selection out of a much larger available number of courses. Please discuss your course selection with your PhD supervisor. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| 151-0371-00L | Advanced Model Predictive Control Number of participants limited to 60. | W | 4 KP | 2V + 1U | M. Zeilinger, A. Carron, L. Hewing, J. Köhler | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | Model predictive control (MPC) has established itself as a powerful control technique for complex systems under state and input constraints. This course discusses the theory and application of recent advanced MPC concepts, focusing on system uncertainties and safety, as well as data-driven formulations and learning-based control. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | Design, implement and analyze advanced MPC formulations for robust and stochastic uncertainty descriptions, in particular with data-driven formulations. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Inhalt | Topics include - Nominal MPC for uncertain systems (nominal robustness) - Robust MPC - Stochastic MPC - Review of regression methods - Set-membership Identification and robust data-driven MPC - Bayesian regression and stochastic data-driven MPC - MPC as safety filter for reinforcement learning | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Skript | Lecture notes will be provided. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | Basic courses in control, advanced course in optimal control, basic MPC course (e.g. 151-0660-00L Model Predictive Control in Spring Semester) strongly recommended. Background in linear algebra and stochastic systems recommended. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 227-0105-00L | Introduction to Estimation and Machine Learning  | W | 6 KP | 4G | H.‑A. Loeliger | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | Mathematical basics of estimation and machine learning, with a view towards applications in signal processing. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | Students master the basic mathematical concepts and algorithms of estimation and machine learning. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Inhalt | Review of probability theory; basics of statistical estimation; least squares and linear learning; Hilbert spaces; singular-value decomposition; kernel methods, neural networks, and more | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Skript | Lecture notes will be handed out as the course progresses. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | solid basics in linear algebra and probability theory | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 227-0146-00L | Data Conversion System Design Up until HS23 named Analog-to-Digital Converters | W | 6 KP | 2V + 2U | T. Burger, G. Cervelli, R. Reutemann | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | This course provides a thorough treatment of integrated data conversion systems from system level specifications and trade-offs, over architecture choice down to circuit implementation. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | Data conversion systems are substantial sub-parts of many electronic systems, e.g. the audio conversion system of a home-cinema systems or the base-band front-end of a wireless modem. Data conversion systems usually determine the performance of the overall system in terms of dynamic range and linearity. Students will learn the underlying principles of data conversion and be introduced to the different methods and circuit architectures to implement such a conversion. The conversion methods such as successive approximation or algorithmic conversion are explained based on their operation principle accompanied with the appropriate mathematical calculations, including effects of non-idealties in some cases. After successful completion of the course students should understand the concept of an ideal ADC, know all major converter architectures, their principle of operation and what governs their performance. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Inhalt | - Introduction: examples of data conversion architectures; information representation; abstraction, categorization and symbolic representation; basic conversion algorithms; data converter application; tradeoffs among key parameters; ADC taxonomy. - Dual-slope & successive approximation register (SAR) converters: dual slope principle & converter; SAR ADC operating principle; SAR implementation with a capacitive array; range extension with segmented array. - Algorithmic & pipelined A/D converters: algorithmic conversion principle; sample & hold stage; pipe-lined converter; multiplying DAC; flash sub-ADC and n-bit MDAC; redundancy for correction of non-idealties, error correction. - Performance metrics and non-linearity: ideal ADC; offset, gain error, differential and integral non-linearities; capacitor mismatch; impact of capacitor mismatch on SAR ADC's performance. - Flash, folding an interpolating analog-to-digital converters: flash ADC principle, thermometer to binary coding, sparkle correction; limitations of flash converters; the folding principle, residue extraction; folding amplifiers; cascaded folding; interpolation for folding converters; cascaded folding and interpolation. - Noise in analog-to-digital converters: types of noise; noise calculation in electronic circuit, kT/C-noise, sampled noise; noise analysis in switched-capacitor circuits; aperture time uncertainty and sampling jitter. - Delta-sigma A/D-converters: linearity and resolution; from delta-modulation to delta-sigma modulation; first-oder delta-sigma modulation, circuit level implementation; clock-jitter & SNR in delta-sigma modulators; second-order delta-sigma modulation, higher-order modulation, design procedure for a single-loop modulator. - Digital-to-analog converters: introduction; current scaling D/A converter, current steering DAC, calibration for improved performance, delta-sigma D/A-converters. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Skript | Slides are available online under https://iis-students.ee.ethz.ch/lectures/analog-to-digital-converters/ | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literatur | - B. Razavi, Principles of Data Conversion System Design, IEEE Press, 1994 - M. Gustavsson et. al., CMOS Data Converters for Communications, Springer, 2010 - R.J. van de Plassche, CMOS Integrated Analog-to-Digital and Digital-to-Analog Converters, Springer, 2010 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | It is highly recommended to attend the course "Analog Integrated Circuits" of Prof. T. Jang as a preparation for this course. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kompetenzen |
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| 227-0225-00L | Linear System Theory | W | 6 KP | 5G | J. Lygeros, A. Tsiamis | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | The class is intended to provide a comprehensive overview of the theory of linear dynamical systems, stability analysis, and their use in control and estimation. The focus is on the mathematics behind the physical properties of these systems and on understanding and constructing proofs of properties of linear control systems. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | Students should be able to apply the fundamental results in linear system theory to analyze and control linear dynamical systems. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Inhalt | - Proof techniques and practices. - Linear spaces, normed linear spaces and Hilbert spaces. - Ordinary differential equations, existence and uniqueness of solutions. - Continuous and discrete-time, time-varying linear systems. Time domain solutions. Time invariant systems treated as a special case. - Controllability and observability, duality. Time invariant systems treated as a special case. - Stability and stabilization, observers, state and output feedback, separation principle. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Skript | Available on the course Moodle platform. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | Sufficient mathematical maturity, in particular in linear algebra, analysis. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kompetenzen |
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| 227-0377-10L | Physics of Failure and Reliability of Electronic Devices and Systems | W | 3 KP | 2V | I. Shorubalko, M. Held | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | Understanding the physics of failures and failure mechanisms enables reliability analysis and serves as a practical guide for electronic devices design, integration, systems development and manufacturing. The field gains additional importance in the context of managing safety, sustainability and environmental impact for continuously increasing complexity and scaling-down trends in electronics. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | Provide an understanding of the physics of failure and reliability. Introduce the degradation and failure mechanisms, basics of failure analysis, methods and tools of reliability testing. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Inhalt | Summary of reliability and failure analysis terminology; physics of failure: materials properties, physical processes and failure mechanisms; failure analysis; basics and properties of instruments; quality assurance of technical systems (introduction); introduction to stochastic processes; reliability analysis; component selection and qualification; maintainability analysis (introduction); design rules for reliability, maintainability, reliability tests (introduction). | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Skript | Comprehensive copy of transparencies | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literatur | Reliability Engineering: Theory and Practice, 8th Edition, Springer 2017, DOI 10.1007/978-3-662-54209-5 Reliability Engineering: Theory and Practice, 8th Edition (2017), DOI 10.1007/978-3-662-54209-5 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 227-0417-00L | Information Theory I | W | 6 KP | 4G | A. Lapidoth | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | This course covers the basic concepts of information theory and of communication theory. Topics covered include the entropy rate of a source, mutual information, typical sequences, the asymptotic equi-partition property, Huffman coding, channel capacity, the channel coding theorem, the source-channel separation theorem, and feedback capacity. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | The fundamentals of Information Theory including Shannon's source coding and channel coding theorems | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Inhalt | The entropy rate of a source, Typical sequences, the asymptotic equi-partition property, the source coding theorem, Huffman coding, Arithmetic coding, channel capacity, the channel coding theorem, the source-channel separation theorem, feedback capacity | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literatur | T.M. Cover and J. Thomas, Elements of Information Theory (second edition) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 227-0492-00L | Statistical Learning Theory: on the sample complexity problem | W | 1 KP | 2S | S. Mendelson | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | The course will be devoted to the solution of a classical question in Statistical Learning Theory: identifying the optimal sample complexity (with respect to the squared loss) under minimal assumptions. The main ngredients are elements of the small-ball method and the notion of median-of-means tournaments - with one additional application: an optimal mean estimation procedure for random vectors. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| 227-0579-00L | Hardware Security | W | 8 KP | 2V + 2U + 2A | K. Razavi | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | This course covers the security of commodity computer hardware (e.g., CPU, DRAM, etc.) with a special focus on cutting-edge hands-on research. The aim of the course is familiarizing the students with hardware security and more specifically microarchitectural and circuit-level attacks and defenses through lectures and implementing some of these advanced attacks. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | By the end of the course, the students will be familiar with the state of the art in commodity computer hardware attacks and defenses. More specifically, the students will learn about: - security problems of commodity hardware that we use everyday and how you can defend against them. - relevant computer architecture and operating system aspects of these issues. - hands-on techniques for performing hardware attacks. This is the course where you get credit points by building some of the most advanced exploits on the planet! The luckiest team will collect a Best Demo Award at the end of the course. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literatur | Slides, relevant literature and manuals will be made available during the course. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | Experience with Linux, low-level systems programming and computer architecture. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kompetenzen |
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| 227-0654-00L | Carbon-based Nanoelectronics | W | 6 KP | 2V + 1U + 1A | M. Perrin, G. Borin Barin | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | This course explores the exciting realm of carbon-based nanoelectronics, where the remarkable quantum properties of materials like graphene, carbon nanotubes, graphene nanoribbons, and single molecules are used for building electronic devices. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | The objective of this course is to understand how the electronic properties of carbon-based materials can be exploited for fabricating quantum devices. We will delve into both the theoretical and experimental aspects, discussing how these materials' unique properties can be translated into device functionality. On the theoretical side, we'll cover how the chemical structure of the material and its dimensionality, ranging from 0D to 2D, affects the electronic properties. We'll also discuss how charge carriers flow through the devices and what charge transport mechanisms are at play. On the experimental side, we'll cover how such devices are fabricated, including how the materials are synthesized. We'll also discuss how to characterize the devices and assess their performance. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Inhalt | The course will cover the following carbon-based materials: - Single-molecule - Graphene (single layer, bilayer, twisted bilayer) - Graphene nanoribbons - Carbon nanotubes For each material, we will discuss: - Electronic structure and charge transport properties - Material synthesis and characterization - Device integration and characterization The course also includes a presentation by each student in which a related scientific publication is discussed. This presentation is compulsory and accounts for 30% of the grade. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Skript | Lecture slides are distributed every week. In addition, relevant scientific articles and book chapters will be provided for self-study. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literatur | In addition to the slides, the following supplementary books can be recommended: 1. "Electronic Transport in Mesoscopic Systems", S. Datta, Cambridge University Press (1997) 2. "Semiconductor Nanostructures, Quantum States and Electronic Transport", T. Ihn, Oxford University Press (2010) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | A basic knowledge of solid-state physics and quantum mechanics is required. The course is taught in English. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kompetenzen |
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| 227-0671-00L | Nanodevices and Circuits for the Beyond-Moore Era | W | 3 KP | 2V | M. Csontos, I. Shorubalko | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | Big Data, AI and the Internet of Things demand new hardware which overcomes the limitations of von Neumann architectures. The lecture gives an insight how the fundamental physics and the resulting complex functionalities of nanodevices and circuits offer viable alternatives. Their increased computational power and energy efficiency are demonstrated through neuromorphic computing applications. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | The students will gain a firm understanding in the theory and pioneering experiments of electronic and heat transport at atomic- to nanometer length-scales. Advanced device functionalities enabled by recently discovered material systems will be covered. The students will learn how to exploit such phenomena for designing nanodevices and circuits to energy-efficiently implement neuromorphic algorithms for a sustainable future of information technologies. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Skript | The presentation slides and further material will be provided every week. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | Basic knowledge of solid state physics and semiconductors. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kompetenzen |
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| 227-0689-00L | System Identification | W | 4 KP | 2V + 1U | R. Smith | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | Theory and techniques for the identification of dynamic models from experimentally obtained system input-output data. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | To provide a series of practical techniques for the development of dynamical models from experimental data, with the emphasis being on the development of models suitable for feedback control design purposes. To provide sufficient theory to enable the practitioner to understand the trade-offs between model accuracy, data quality and data quantity. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Inhalt | Introduction to modeling: Black-box and grey-box models; Parametric and non-parametric models; ARX, ARMAX (etc.) models. Predictive, open-loop, black-box identification methods. Time and frequency domain methods. Subspace identification methods. Optimal experimental design, Cramer-Rao bounds, input signal design. Parametric identification methods. On-line and batch approaches. Closed-loop identification strategies. Trade-off between controller performance and information available for identification. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literatur | "System Identification; Theory for the User" Lennart Ljung, Prentice Hall (2nd Ed), 1999. Additional papers will be available via the course Moodle. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | Control systems (227-0216-00L) or equivalent. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 227-0955-00L | Seminar in Electromagnetics, Photonics and Terahertz | W | 3 KP | 2S | J. Leuthold | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | Selected topics of the current research activities at the IEF and closely related institutions are discussed. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | Have an overview on the research activities of the IEF institute. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 252-0535-00L | Advanced Machine Learning | W | 10 KP | 3V + 2U + 4A | J. M. Buhmann, C. Cotrini Jimenez | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | Machine learning algorithms provide analytical methods to search data sets for characteristic patterns. Typical tasks include the classification of data, function fitting and clustering, with applications in image and speech analysis, bioinformatics and exploratory data analysis. This course is accompanied by practical machine learning projects. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | Students will be familiarized with advanced concepts and algorithms for supervised and unsupervised learning; reinforce the statistics knowledge which is indispensible to solve modeling problems under uncertainty. Key concepts are the generalization ability of algorithms and systematic approaches to modeling and regularization. Machine learning projects will provide an opportunity to test the machine learning algorithms on real world data. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Inhalt | The theory of fundamental machine learning concepts is presented in the lecture, and illustrated with relevant applications. Students can deepen their understanding by solving both pen-and-paper and programming exercises, where they implement and apply famous algorithms to real-world data. Topics covered in the lecture include: Fundamentals: What is data? Bayesian Learning Computational learning theory Supervised learning: Ensembles: Bagging and Boosting Max Margin methods Neural networks Unsupservised learning: Dimensionality reduction techniques Clustering Mixture Models Non-parametric density estimation Learning Dynamical Systems | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Skript | No lecture notes, but slides will be made available on the course webpage. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literatur | C. Bishop. Pattern Recognition and Machine Learning. Springer 2007. R. Duda, P. Hart, and D. Stork. Pattern Classification. John Wiley & Sons, second edition, 2001. T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical Learning: Data Mining, Inference and Prediction. Springer, 2001. L. Wasserman. All of Statistics: A Concise Course in Statistical Inference. Springer, 2004. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | The course requires solid basic knowledge in analysis, statistics and numerical methods for CSE as well as practical programming experience for solving assignments. Students should have followed at least "Introduction to Machine Learning" or an equivalent course offered by another institution. PhD students are required to obtain a passing grade in the course (4.0 or higher based on project and exam) to gain credit points. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 327-2210-00L | Thin Films Technology - From Fundamentals to Oxide Electronics Students who already took "327-2104-00L Inorganic Thin Films: Processing, Properties and Applications" AND "327-2132-00 Multifunctional Ferroic Materials: Growth and Characterisation" are not allowed to attend this course. | W | 5 KP | 4G | M. Trassin, C. Schneider | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | Oxide films with a thickness of just a few atoms can now be grown with a precision matching that of semiconductors. This opens up a whole world of functional device concepts and fascinating phenomena that would not occur in the expanded bulk crystal. We will give an introduction to thin films deposition techniques and applications with a focus on the growth of multifunctional oxide thin films. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | In this course students will obtain an overarching view on thin film deposition techniques with a focus on epitaxial deposition processes. The main learning objectives are: - Identification of most relevant deposition technique for a given application. - Understanding of growth mechanism and growth modes. - Understanding strategies for engineering the functionalities of the films using the deposition process. - Selection of the most appropriate characterization technique. - Understanding device concepts and fundamental limits in the technology relevant ultra-thin limit. - Assessing the relevance of scientific literature dealing with complex oxide thin films. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Inhalt | A lab visit visit will be organized and students will participate to the design of thin films with atomic precision. General description of the leading deposition routes including physical and chemical vapor deposition techniques (PVD and CVD) as well as so called "wet techniques" (e.g. spin coating and spray pyrolysis). Growth modes and processes. Part of the course discusses vacuum technologies. Fundamental characterization techniques for application-relevant thin films as well as state of the art approaches for in situ and ex-situ determination of the structural, chemical and ferroic (ferromagnetic and ferroelectric) properties of films: (XRD for thin films, RHEED, EDX, scanning probe microscopy techniques, laser-optical characterization and many more) Epitaxy for the advanced design and characterization of high quality thin films for energy efficient oxide electronics. Types of ferroic order, multiferroics, mulitfiunctional oxide materials, epitaxial strain related effects, oxide thin film based devices and examples. Regular discussions on preselected scientific literature and mini-seminars will be organized. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kompetenzen |
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| 401-3055-64L | Algebraic Methods in Combinatorics Findet dieses Semester nicht statt. | W | 5 KP | 2V + 1U | keine Angaben | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. This course provides a gentle introduction to Algebraic methods, illustrated by examples and focusing on basic ideas and connections to other areas. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | The students will get an overview of various algebraic methods for solving combinatorial problems. We expect them to understand the proof techniques and to use them autonomously on related problems. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Inhalt | Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. While in the past many of the basic combinatorial results were obtained mainly by ingenuity and detailed reasoning, the modern theory has grown out of this early stage and often relies on deep, well-developed tools. One of the main general techniques that played a crucial role in the development of Combinatorics was the application of algebraic methods. The most fruitful such tool is the dimension argument. Roughly speaking, the method can be described as follows. In order to bound the cardinality of of a discrete structure A one maps its elements to vectors in a linear space, and shows that the set A is mapped to linearly independent vectors. It then follows that the cardinality of A is bounded by the dimension of the corresponding linear space. This simple idea is surprisingly powerful and has many famous applications. This course provides a gentle introduction to Algebraic methods, illustrated by examples and focusing on basic ideas and connections to other areas. The topics covered in the class will include (but are not limited to): Basic dimension arguments, Spaces of polynomials and tensor product methods, Eigenvalues of graphs and their application, the Combinatorial Nullstellensatz and the Chevalley-Warning theorem. Applications such as: Solution of Kakeya problem in finite fields, counterexample to Borsuk's conjecture, chromatic number of the unit distance graph of Euclidean space, explicit constructions of Ramsey graphs and many others. The course website can be found at https://moodle-app2.let.ethz.ch/course/view.php?id=15757 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Skript | Lectures will be on the blackboard only, but there will be a set of typeset lecture notes which follow the class closely. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | Students are expected to have a mathematical background and should be able to write rigorous proofs. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 401-5680-00L | Foundations of Data Science Seminar | Z | 0 KP | H. Bölcskei, A. Bandeira, Y. Chen, J. Peters, F. Yang | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | Research colloquium | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| 402-0475-00L | Terahertz Science and Applications | W | 6 KP | 2V + 1U | E. Abreu | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | The Terahertz (THz) range (0.1 – 10 THz), lies between the infrared and microwave spectral regions and has become accessible in the past few years. This new capability has had great impact in scientific research, and has led to technological advances and to the development of a variety of applications and devices. This course provides an introduction to THz science, technology and applications. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | The goal of this course is to enable students to determine whether a THz solution can be applied to a particular scientific or technological problem. Armed with the fundamentals of THz science and of current THz technologies, covered in this introductory course, students will be able to weigh the capabilities, advantages and limitations of THz tools to address topics ranging from phonons in solid state systems and molecular vibrations in solutions to medical imaging and wireless communications. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Skript | Will be distributed via moodle. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literatur | Yun-Shik Lee, Principles of Terahertz Science and Technology, Springer 2009 Additional references distributed via moodle. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | Basic knowledge in physics, especially in electromagnetism, is required. No formal prerequisites. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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