# Search result: Catalogue data in Autumn Semester 2017

Mathematics Bachelor | ||||||

First Year | ||||||

» First Year Compulsory Courses | ||||||

» Minor Courses | ||||||

» GESS Science in Perspective | ||||||

First Year Compulsory Courses | ||||||

First Year Examination Block 1 | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|---|

401-1151-00L | Linear Algebra I | O | 7 credits | 4V + 2U | M. Akveld | |

Abstract | Introduction to the theory of vector spaces for mathematicians and physicists: Basics, vector spaces, linear transformations, solutions of systems of equations and matrices, determinants, endomorphisms, eigenvalues and eigenvectors. | |||||

Objective | - Mastering basic concepts of Linear Algebra - Introduction to mathematical methods | |||||

Content | - Basics - Vectorspaces and linear maps - Systems of linear equations and matrices - Determinants - Endomorphisms and eigenvalues | |||||

Literature | - H. Schichl and R. Steinbauer: Einführung in das mathematische Arbeiten. Springer-Verlag 2012. Link: http://link.springer.com/book/10.1007%2F978-3-642-28646-9 - G. Fischer: Lineare Algebra. Springer-Verlag 2014. Link: http://link.springer.com/book/10.1007/978-3-658-03945-5 - K. Jänich: Lineare Algebra. Springer-Verlag 2004. Link: http://link.springer.com/book/10.1007/978-3-662-08375-8 - S. H. Friedberg, A. J. Insel and L. E. Spence: Linear Algebra. Pearson 2003. Link - R. Pink: Lineare Algebra I und II. Lecture notes. Link: https://people.math.ethz.ch/%7epink/ftp/LA-Zusammenfassung-20150901.pdf | |||||

402-1701-00L | Physics I | O | 7 credits | 4V + 2U | A. Wallraff | |

Abstract | This course gives a first introduction to Physics with an emphasis on classical mechanics. | |||||

Objective | Acquire knowledge of the basic principles regarding the physics of classical mechanics. Skills in solving physics problems. | |||||

252-0847-00L | Computer Science | O | 5 credits | 2V + 2U | B. Gärtner | |

Abstract | This lecture is an introduction to programming based on the language C++. We cover fundamental types, control statements, functions, arrays, and classes. The concepts will be motivated and illustrated through algorithms and applications. | |||||

Objective | The goal of this lecture is an algorithmically oriented introduction to programming. | |||||

Content | This lecture is an introduction to programming based on the language C++. We cover fundamental types, control statements, functions, arrays, and classes. The concepts will be motivated and illustrated through algorithms and applications. | |||||

Lecture notes | Lecture notes in English and Handouts in German will be distributed electronically along with the course. | |||||

Literature | Andrew Koenig and Barbara E. Moo: Accelerated C++, Addison-Wesley, 2000. Stanley B. Lippman: C++ Primer, 3. Auflage, Addison-Wesley, 1998. Bjarne Stroustrup: The C++ Programming Language, 3. Auflage, Addison-Wesley, 1997. Doina Logofatu: Algorithmen und Problemlösungen mit C++, Vieweg, 2006. Walter Savitch: Problem Solving with C++, Eighth Edition, Pearson, 2012 | |||||

First Year Examination Block 2 | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-1261-07L | Analysis I | O | 10 credits | 6V + 3U | M. Einsiedler | |

Abstract | Introduction to the differential and integral calculus in one real variable: fundaments of mathematical thinking, numbers, sequences, basic point set topology, continuity, differentiable functions, ordinary differential equations, Riemann integration. | |||||

Objective | The ability to work with the basics of calculus in a mathematically rigorous way. | |||||

Literature | H. Amann, J. Escher: Analysis I https://link.springer.com/book/10.1007/978-3-7643-7756-4 J. Appell: Analysis in Beispielen und Gegenbeispielen https://link.springer.com/book/10.1007/978-3-540-88903-8 R. Courant: Vorlesungen über Differential- und Integralrechnung https://link.springer.com/book/10.1007/978-3-642-61988-5 O. Forster: Analysis 1 https://link.springer.com/book/10.1007/978-3-658-00317-3 H. Heuser: Lehrbuch der Analysis https://link.springer.com/book/10.1007/978-3-322-96828-9 K. Königsberger: Analysis 1 https://link.springer.com/book/10.1007/978-3-642-18490-1 W. Walter: Analysis 1 https://link.springer.com/book/10.1007/3-540-35078-0 V. Zorich: Mathematical Analysis I (englisch) https://link.springer.com/book/10.1007/978-3-662-48792-1 A. Beutelspacher: "Das ist o.B.d.A. trivial" https://link.springer.com/book/10.1007/978-3-8348-9599-8 H. Schichl, R. Steinbauer: Einführung in das mathematische Arbeiten https://link.springer.com/book/10.1007/978-3-642-28646-9 | |||||

Compulsory Courses | ||||||

Examination Block I In Examination Block I either the course unit 402-2883-00L Physics III or the course unit 402-2203-01L Classical Mechanics must be chosen and registered for an examination. (Students may also enrol for the other of the two course units; within the ETH Bachelor's programme in mathematics, this other course unit cannot be registered in myStudies for an examination nor can it be recognised for the Bachelor's degree.) | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-2303-00L | Complex Analysis | O | 6 credits | 3V + 2U | R. Pandharipande | |

Abstract | Complex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, index of closed curves, analytic continuation, special functions, conformal mappings, Riemann mapping theorem. | |||||

Objective | Working Knowledge with functions of one complex variables; in particular applications of the residue theorem | |||||

Literature | Th. Gamelin: Complex Analysis. Springer 2001 E. Titchmarsh: The Theory of Functions. Oxford University Press D. Salamon: "Funktionentheorie". Birkhauser, 2011. (In German) L. Ahlfors: "Complex analysis. An introduction to the theory of analytic functions of one complex variable." International Series in Pure and Applied Mathematics. McGraw-Hill Book Co. B. Palka: "An introduction to complex function theory." Undergraduate Texts in Mathematics. Springer-Verlag, 1991. R.Remmert: Theory of Complex Functions. Springer Verlag | |||||

401-2333-00L | Methods of Mathematical Physics I | O | 6 credits | 3V + 2U | H. Knörrer | |

Abstract | Fourier series. Linear partial differential equations of mathematical physics. Fourier transform. Special functions and eigenfunction expansions. Distributions. Selected problems from quantum mechanics. | |||||

Objective | ||||||

Prerequisites / Notice | Die Einschreibung in die Übungsgruppen erfolgt online. Melden Sie sich im Laufe der ersten Semesterwoche unter echo.ethz.ch mit Ihrem ETH Account an. Der Übungsbetrieb beginnt in der zweiten Semesterwoche. | |||||

402-2883-00L | Physics III | W | 7 credits | 4V + 2U | J. Home | |

Abstract | Introductory course on quantum and atomic physics including optics and statistical physics. | |||||

Objective | A basic introduction to quantum and atomic physics, including basics of optics and equilibrium statistical physics. The course will focus on the relation of these topics to experimental methods and observations. | |||||

Content | Evidence for Quantum Mechanics: atoms, photons, photo-electric effect, Rutherford scattering, Compton scattering, de-Broglie waves. Quantum mechanics: wavefunctions, operators, Schrodinger's equation, infinite and finite square well potentials, harmonic oscillator, hydrogen atoms, spin. Atomic structure: Perturbation to basic structure, including Zeeman effect, spin-orbit coupling, many-electron atoms. X-ray spectra, optical selection rules, emission and absorption of radiation, including lasers. Optics: Fermat's principle, lenses, imaging systems, diffraction, interference, relation between geometrical and wave descriptions, interferometers, spectrometers. Statistical mechanics: probability distributions, micro and macrostates, Boltzmann distribution, ensembles, equipartition theorem, blackbody spectrum, including Planck distribution | |||||

Lecture notes | Lecture notes will be provided electronically during the course. | |||||

Literature | Quantum mechanics/Atomic physics/Molecules: "The Physics of Atoms and Quanta", H. Hakan and H. C. Wolf, ISBN 978-3-642-05871-4 Optics: "Optics", E. Hecht, ISBN 0-321-18878-0 Statistical mechanics: "Statistical Physics", F. Mandl 0-471-91532-7 | |||||

402-2203-01L | Classical Mechanics | W | 7 credits | 4V + 2U | N. Beisert | |

Abstract | A conceptual introduction to theoretical physics: Newtonian mechanics, central force problem, oscillations, Lagrangian mechanics, symmetries and conservation laws, spinning top, relativistic space-time structure, particles in an electromagnetic field, Hamiltonian mechanics, canonical transformations, integrable systems, Hamilton-Jacobi equation. | |||||

Objective | ||||||

252-0851-00L | Algorithms and Complexity | O | 4 credits | 2V + 1U | A. Steger | |

Abstract | Introduction: RAM machine, data structures; Algorithms: sorting, median, matrix multiplication, shortest paths, minimal spanning trees; Paradigms: divide & conquer, dynamic programming, greedy algorithms; Data Structures: search trees, dictionaries, priority queues; Complexity Theory: P and NP, NP-completeness, Cook's theorem, reductions. | |||||

Objective | After this course students know some basic algorithms as well as underlying paradigms. They will be familiar with basic notions of complexity theory and can use them to classify problems. | |||||

Content | Die Vorlesung behandelt den Entwurf und die Analyse von Algorithmen und Datenstrukturen. Die zentralen Themengebiete sind: Sortieralgorithmen, Effiziente Datenstrukturen, Algorithmen für Graphen und Netzwerke, Paradigmen des Algorithmenentwurfs, Klassen P und NP, NP-Vollständigkeit, Approximationsalgorithmen. | |||||

Lecture notes | Ja. Wird zu Beginn des Semesters verteilt. | |||||

Examination Block II | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-2003-00L | Algebra I | O | 7 credits | 4V + 2U | E. Kowalski | |

Abstract | Introduction and development of some basic algebraic structures - groups, rings, fields. | |||||

Objective | Introduction to basic notions and results of group, ring and field theory. | |||||

Content | Group Theory: basic notions and examples of groups; Subgroups, Quotient groups and Homomorphisms, Sylow Theorems, Group actions and applications Ring Theory: basic notions and examples of rings; Ring Homomorphisms, ideals and quotient rings, applications Field Theory: basic notions and examples of fields; finite fields, applications | |||||

Literature | J. Rotman, "Advanced modern algebra, 3rd edition, part 1" http://bookstore.ams.org/gsm-165/ J.F. Humphreys: A Course in Group Theory (Oxford University Press) G. Smith and O. Tabachnikova: Topics in Group Theory (Springer-Verlag) M. Artin: Algebra (Birkhaeuser Verlag) R. Lidl and H. Niederreiter: Introduction to Finite Fields and their Applications (Cambridge University Press) B.L. van der Waerden: Algebra I & II (Springer Verlag) | |||||

Core Courses | ||||||

Core Courses: Pure Mathematics | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-3531-00L | Differential Geometry I At most one of the three course units (Bachelor Core Courses) 401-3461-00L Functional Analysis I 401-3531-00L Differential Geometry I 401-3601-00L Probability Theory can be recognised for the Master's degree in Mathematics or Applied Mathematics. | W | 10 credits | 4V + 1U | D. A. Salamon | |

Abstract | Submanifolds of R^n, tangent bundle, embeddings and immersions, vector fields, Lie bracket, Frobenius' Theorem. Geodesics, exponential map, completeness, Hopf-Rinow. Levi-Civita connection, parallel transport, motions without twisting, sliding, and wobbling. Isometries, Riemann curvature, Theorema Egregium. Cartan-Ambrose-Hicks, symmetric spaces, constant curvature, Hadamard's theorem. | |||||

Objective | Introduction to Differential Geometry. Submanifolds of Euclidean space, tangent bundle, embeddings and immersions, vector fields and flows, Lie bracket, foliations, the Theorem of Frobenius. Geodesics, exponential map, injectivity radius, completeness Hopf-Rinow Theorem, existence of minimal geodesics. Levi-Civita connection, parallel transport, Frame bundle, motions without twisting, sliding, and wobbling. Isometries, the Riemann curvature tensor, Theorema Egregium. Cartan-Ambrose-Hicks, symmetric spaces, constant curvature, nonpositive sectional curvature, Hadamard's theorem. | |||||

Literature | Joel Robbin and Dietmar Salamon "Introduction to Differential Geometry", https://people.math.ethz.ch/~salamon/PREPRINTS/diffgeo.pdf | |||||

401-3461-00L | Functional Analysis I At most one of the three course units (Bachelor Core Courses) 401-3461-00L Functional Analysis I 401-3531-00L Differential Geometry I 401-3601-00L Probability Theory can be recognised for the Master's degree in Mathematics or Applied Mathematics. | W | 10 credits | 4V + 1U | A. Carlotto | |

Abstract | Baire category; Banach and Hilbert spaces, bounded linear operators; basic principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces; Fourier transform and applications. | |||||

Objective | Acquire a good degree of fluency with the fundamental concepts and tools belonging to the realm of linear Functional Analysis, with special emphasis on the geometric structure of Banach and Hilbert spaces, and on the basic properties of linear maps. | |||||

Lecture notes | Lecture Notes on "Funktionalanalysis I" by Michael Struwe | |||||

Literature | A primary reference for the course is the textbook by H. Brezis: Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011. Other useful, and recommended references are the following: Elias M. Stein and Rami Shakarchi. Functional analysis (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011. Peter D. Lax. Functional analysis. Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002. Walter Rudin. Functional analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991. | |||||

Prerequisites / Notice | Solid background on the content of all Mathematics courses of the first two years of the undergraduate curriculum at ETH (most remarkably: fluency with measure theory, Lebesgue integration and L^p spaces). | |||||

401-3001-61L | Algebraic Topology I | W | 8 credits | 4G | W. Merry | |

Abstract | This is an introductory course in algebraic topology. Topics covered include: the fundamental group, covering spaces, singular homology, cell complexes and cellular homology and the Eilenberg-Steenrod axioms. Along the way we will introduce the basics of homological algebra and category theory. | |||||

Objective | ||||||

Lecture notes | I will produce full lecture notes, available on my website at www.merry.io/algebraic-topology | |||||

Literature | "Algebraic Topology" (CUP, 2002) by Hatcher is excellent and covers all the material from both Algebraic Topology I and Algebraic Topology II. You can also download it (legally!) for free from Hatcher's webpage: www.math.cornell.edu/%7ehatcher/AT/ATpage.html Another classic book is Spanier's "Algebraic Topology" (Springer, 1963). This book is very dense and somewhat old-fashioned, but again covers everything you could possibly want to know on the subject. | |||||

Prerequisites / Notice | You should know the basics of point-set topology (topological spaces, and what it means for a topological space to be compact or connected, etc). Some (very elementary) group theory and algebra will also be needed. | |||||

401-3132-00L | Commutative Algebra | W | 10 credits | 4V + 1U | P. D. Nelson | |

Abstract | This course provides an introduction to commutative algebra as a foundation for and first steps towards algebraic geometry. | |||||

Objective | We shall cover approximately the material from --- most of the textbook by Atiyah-MacDonald, or --- the first half of the textbook by Bosch. Topics include: * Basics about rings, ideals and modules * Localization * Primary decomposition * Integral dependence and valuations * Noetherian rings * Completions * Basic dimension theory | |||||

Literature | Primary Reference: 1. "Introduction to Commutative Algebra" by M. F. Atiyah and I. G. Macdonald (Addison-Wesley Publ., 1969) Secondary Reference: 2. "Algebraic Geometry and Commutative Algebra" by S. Bosch (Springer 2013) Tertiary References: 3. "Commutative algebra. With a view towards algebraic geometry" by D. Eisenbud (GTM 150, Springer Verlag, 1995) 4. "Commutative ring theory" by H. Matsumura (Cambridge University Press 1989) 5. "Commutative Algebra" by N. Bourbaki (Hermann, Masson, Springer) | |||||

Prerequisites / Notice | Prerequisites: Algebra I (or a similar introduction to the basic concepts of ring theory). | |||||

401-3581-67L | Symplectic Geometry | W | 8 credits | 4V + 1U | A. Cannas da Silva | |

Abstract | This course is an introduction to symplectic geometry -- the geometry of manifolds equipped with a closed non-degenerate 2-form. We will discuss symplectic manifolds and transformations, the relation of symplectic to other geometries and some of the interplay with dynamics, eventually in the presence of symmetry groups. Guided homework assignments will complement the exposition. | |||||

Objective | Introduction to symplectic geometry | |||||

» Core Courses: Pure Mathematics (Mathematics Master) | ||||||

Core Courses: Applied Mathematics and Further Appl.-Oriented Fields vollständiger Titel: Kernfächer aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-3651-00L | Numerical Methods for Elliptic and Parabolic Partial Differential Equations (University of Zurich)Course audience at ETH: 3rd year ETH BSc Mathematics and MSc Mathematics and MSc Applied Mathematics students. Other ETH-students are advised to attend the course "Numerical Methods for Partial Differential Equations" (401-0674-00L) in the CSE curriculum during the spring semester. No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH. UZH Module Code: MAT802 Mind the enrolment deadlines at UZH: https://www.uzh.ch/cmsssl/en/studies/application/mobilitaet.html | W | 10 credits | 4V + 1U + 1P | S. Sauter | |

Abstract | This course gives a comprehensive introduction into the numerical treatment of linear and non-linear elliptic boundary value problems, related eigenvalue problems and linear, parabolic evolution problems. Emphasis is on theory and the foundations of numerical methods. Practical exercises include MATLAB implementations of finite element methods. | |||||

Objective | Participants of the course should become familiar with * concepts underlying the discretization of elliptic and parabolic boundary value problems * analytical techniques for investigating the convergence of numerical methods for the approximate solution of boundary value problems * methods for the efficient solution of discrete boundary value problems * implementational aspects of the finite element method | |||||

Content | A selection of the following topics will be covered: * Elliptic boundary value problems * Galerkin discretization of linear variational problems * The primal finite element method * Mixed finite element methods * Discontinuous Galerkin Methods * Boundary element methods * Spectral methods * Adaptive finite element schemes * Singularly perturbed problems * Sparse grids * Galerkin discretization of elliptic eigenproblems * Non-linear elliptic boundary value problems * Discretization of parabolic initial boundary value problems | |||||

Lecture notes | Course slides will be made available to the audience. | |||||

Literature | n.a. | |||||

Prerequisites / Notice | Practical exercises based on MATLAB |

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