Search result: Catalogue data in Autumn Semester 2017

Mathematics Bachelor Information
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.)
NumberTitleTypeECTSHoursLecturers
401-2303-00LComplex Analysis Information O6 credits3V + 2UR. Pandharipande
AbstractComplex 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.
ObjectiveWorking Knowledge with functions of one complex variables; in particular applications of the residue theorem
LiteratureTh. 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
401-2333-00LMethods of Mathematical Physics IO6 credits3V + 2UH. Knörrer
AbstractFourier series. Linear partial differential equations of mathematical physics. Fourier transform. Special functions and eigenfunction expansions. Distributions. Selected problems from quantum mechanics.
Objective
Prerequisites / NoticeDie 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.
402-2883-00LPhysics IIIW7 credits4V + 2UJ. Home
AbstractIntroductory course on quantum and atomic physics including optics and statistical physics.
ObjectiveA 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.
ContentEvidence 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 notesLecture notes will be provided electronically during the course.
LiteratureQuantum 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
402-2203-01LClassical MechanicsW7 credits4V + 2UN. Beisert
AbstractA 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
252-0851-00LAlgorithms and ComplexityO4 credits2V + 1UA. Steger
AbstractIntroduction: 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.
ObjectiveAfter 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.
ContentDie 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 notesJa. Wird zu Beginn des Semesters verteilt.
Examination Block II
NumberTitleTypeECTSHoursLecturers
401-2003-00LAlgebra I Information O7 credits4V + 2UE. Kowalski
AbstractIntroduction and development of some basic algebraic structures - groups, rings, fields.
ObjectiveIntroduction to basic notions and results of group, ring and field
theory.
ContentGroup 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
LiteratureJ. Rotman, "Advanced modern algebra, 3rd edition, part 1"
Link
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)
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