Emmanuel Kowalski: Katalogdaten im Herbstsemester 2018

NameHerr Prof. Dr. Emmanuel Kowalski
LehrgebietMathematik
Adresse
Professur für Mathematik
ETH Zürich, HG G 64.1
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telefon+41 44 632 34 41
E-Mailemmanuel.kowalski@math.ethz.ch
URLhttp://www.math.ethz.ch/~kowalski
DepartementMathematik
BeziehungOrdentlicher Professor

NummerTitelECTSUmfangDozierende
401-0213-16LAnalysis II Information 5 KP2V + 2UE. Kowalski
KurzbeschreibungDifferential and Integral calculus in many variables, vector analysis.
LernzielDifferential and Integral calculus in many variables, vector analysis.
InhaltDifferential and Integral calculus in many variables, vector analysis.
LiteraturFür allgemeine Informationen, sehen Sie bitte die Webseite der Vorlesung: https://metaphor.ethz.ch/x/2017/hs/401-0213-16L/
401-2000-00LScientific Works in Mathematics
Zielpublikum:
Bachelor-Studierende im dritten Jahr;
Master-Studierende, welche noch keine entsprechende Ausbildung vorweisen können.
0 KPE. Kowalski
KurzbeschreibungIntroduction to scientific writing for students with focus on publication standards and ethical issues, especially in the case of citations (references to works of others.)
LernzielLearn the basic standards of scientific works in mathematics.
Inhalt- Types of mathematical works
- Publication standards in pure and applied mathematics
- Data handling
- Ethical issues
- Citation guidelines
SkriptMoodle of the Mathematics Library: https://moodle-app2.let.ethz.ch/course/view.php?id=519
Voraussetzungen / BesonderesWeisung https://www.ethz.ch/content/dam/ethz/common/docs/weisungssammlung/files-de/wiss-arbeiten-eigenst%C3%A4ndigkeitserklaerung.pdf
401-3113-68LExponential Sums over Finite Fields Information 8 KP4GE. Kowalski
KurzbeschreibungExponential sums over finite fields arise in many problems of number theory. We will discuss the elementary aspects of the theory (centered on the Riemann Hypothesis for curves, following Stepanov's method) and survey the formalism arising from Deligne's general form of the Riemann Hypothesis over finite fields. We will then discuss various applications, especially in analytic number theory.
LernzielThe goal is to understand both the basic results on exponential sums in one variable, and the general formalism of Deligne and Katz that underlies estimates for much more general types of exponential sums, including the "trace functions" over finite fields.
InhaltExamples of elementary exponential sums
The Riemann Hypothesis for curves and its applications
Definition of trace functions over finite fields
The formalism of the Riemann Hypothesis of Deligne
Selected applications
SkriptLectures notes from various sources will be provided
LiteraturKowalski, "Exponential sums over finite fields, I: elementary methods:
Iwaniec-Kowalski, "Analytic number theory", chapter 11
Fouvry, Kowalski and Michel, "Trace functions over finite fields and their applications"
401-5110-00LNumber Theory Seminar Information 0 KP1KÖ. Imamoglu, P. S. Jossen, E. Kowalski, P. D. Nelson, R. Pink, G. Wüstholz
KurzbeschreibungResearch colloquium
Lernziel
406-2005-AALAlgebra I and II
Belegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben.

Alle andere Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen.
12 KP26RM. Burger, E. Kowalski
KurzbeschreibungIntroduction and development of some basic algebraic structures - groups, rings, fields including Galois theory, representations of finite groups, algebras.

The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.
Lernziel
InhaltBasic notions and examples of groups;
Subgroups, Quotient groups and Homomorphisms,
Group actions and applications

Basic notions and examples of rings;
Ring Homomorphisms,
ideals, and quotient rings, rings of fractions
Euclidean domains, Principal ideal domains, Unique factorization
domains

Basic notions and examples of fields;
Field extensions, Algebraic extensions, Classical straight edge and compass constructions

Fundamentals of Galois theory
Representation theory of finite groups and algebras
SkriptFor a summary of the content and exercises with solutions of my lecture courses in HS2015 and FS2016 see:
https://www2.math.ethz.ch/education/bachelor/lectures/hs2015/math/algebra1/index-2.html
https://www2.math.ethz.ch/education/bachelor/lectures/fs2016/math/algebra2/
LiteraturS. Lang, Algebra, Springer Verlag
B.L. van der Waerden: Algebra I und II, Springer Verlag
I.R. Shafarevich, Basic notions of algebra, Springer verlag
G. Mislin: Algebra I, vdf Hochschulverlag
U. Stammbach: Algebra, in der Polybuchhandlung erhältlich
I. Stewart: Galois Theory, Chapman Hall (2008)
G. Wüstholz, Algebra, vieweg-Verlag, 2004
J-P. Serre, Linear representations of finite groups, Springer Verlag