# Search result: Catalogue data in Autumn Semester 2017

Mathematics Bachelor | ||||||

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. | |||||

Learning 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. | |||||

Learning 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. | |||||

Learning 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. | |||||

Learning 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. | |||||

Learning 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. | |||||

Learning 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) |

- Page 1 of 1