Emmanuel Kowalski: Katalogdaten im Frühjahrssemester 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
401-0212-16LAnalysis I Information 7 KP4V + 2UE. Kowalski
KurzbeschreibungFunktionen, Grenzwerte, Folgen, Reihen, Potenzreihen, Differential- und Integralrechnung einer Variablen,
LernzielFunktionen, Grenzwerte, Folgen, Reihen, Potenzreihen, Differential- und Integralrechnung einer Variablen,
InhaltFunktionen, Grenzwerte, Folgen, Reihen, Potenzreihen, Differential- und Integralrechnung einer Variablen,
LiteraturMichael Struwe: Analysis für Informatik
Christian Blatter: Ingenieur-analysis
Tom Apostol: Mathematical Analysis
Lernmaterialien und weitere Informationen sind auf der Webseite des Kurses (https://metaphor.ethz.ch/x/2018/fs/401-0212-16L/) erhältlich
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 / BesonderesThis course is completed by the optional course "Recherchieren in der Mathematik" (held in German) by the Mathematics Library. For more details see: http://www.math.ethz.ch/library/services/schulungen

Weisung https://www.ethz.ch/content/dam/ethz/common/docs/weisungssammlung/files-de/wiss-arbeiten-eigenst%C3%A4ndigkeitserklaerung.pdf
401-3104-18LDiophantine Equations and Hilbert's 10th Problem
Findet dieses Semester nicht statt.
8 KP4GE. Kowalski
KurzbeschreibungThe course presents the solution by Davis, Putnam, Robinson and Matijasevich of Hilbert's Tenth Problem, concerning the non-existence of an algorithm to determine the solubility of a general diophantine equation. All necessary ingredients from logic and number theory will be covered in the class.
We will then discuss similar questions in other contexts, such as the word problem in group theory.
Lernziel
InhaltThe course will present in full details the solution by Davis, Putnam, Robinson and Matijasevich of Hilbert's Tenth Problem, concerning the non-existence of an algorithm to determine the solubility in integers of a general diophantine equation.
All necessary ingredients from logic, computability theory and number theory will be covered in the class.
If time allows, we will then discuss some similar questions in other contexts, for instance the word problem in group theory.
LiteraturJ. Robinson, Collected Works, especially papers 9, 10, 19, 24.

M. Davis, "Hilbert's Tenth Problem is Unsolvable", The American Mathematical Monthly, Vol. 80, 233-269.

J. Rotman, "An introduction to the theory of groups", chapter 12 (Springer, 1995).
Voraussetzungen / BesonderesPrerequisites: Algebra I+II
401-3146-12LAlgebraic Geometry Information 10 KP4V + 1UE. Kowalski
KurzbeschreibungThis course is an Introduction to Algebraic Geometry (algebraic varieties and schemes).
LernzielLearning Algebraic Geometry.
LiteraturPrimary reference:
* Ulrich Görtz and Torsten Wedhorn: Algebraic Geometry I, Advanced Lectures in Mathematics, Springer.

Secondary reference:
* Qing Liu: Algebraic Geometry and Arithmetic Curves, Oxford Science Publications.
* Robin Hartshorne: Algebraic Geometry, Graduate Texts in Mathematics, Springer.
* Siegfried Bosch: Algebraic Geometry and Commutative Algebra (Springer 2013).

Other good textbooks and online texts are:
* David Eisenbud, Joe Harris: The Geometry of Schemes, Graduate Texts in Mathematics, Springer.
* Ravi Vakil, Foundations of Algebraic Geometry, http://math.stanford.edu/~vakil/216blog/
* Jean Gallier and Stephen S. Shatz, Algebraic Geometry http://www.cis.upenn.edu/~jean/algeom/steve01.html

"Classical" Algebraic Geometry over an algebraically closed field:
* Joe Harris, Algebraic Geometry, A First Course, Graduate Texts in Mathematics, Springer.
* J.S. Milne, Algebraic Geometry, http://www.jmilne.org/math/CourseNotes/AG.pdf

Further readings:
* Günter Harder: Algebraic Geometry 1 & 2
* I. R. Shafarevich, Basic Algebraic geometry 1 & 2, Springer-Verlag.
* Alexandre Grothendieck et al.: Elements de Geometrie Algebrique EGA
* Saunders MacLane: Categories for the Working Mathematician, Springer-Verlag.
Voraussetzungen / BesonderesRequirement: Some knowledge of Commutative Algebra.
401-5110-00LNumber Theory Seminar Information 0 KP1KÖ. Imamoglu, P. S. Jossen, E. Kowalski, P. D. Nelson, R. Pink, G. Wüstholz
KurzbeschreibungForschungskolloquium
LernzielVorträge über neue Themen aus der Forschung.
InhaltForschungsseminar in Algebra, Zahlentheorie und Geometrie, richtet sich insbesondere an Mitarbeiterinnen und Mitarbeiter sowie Doktorandinnen und Doktoranden.
406-2005-AALAlgebra I and II
Belegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben.

Alle anderen 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
LiteraturJoseph J. Rotman, "Advanced Modern Algebra" third edition, part 1,
Graduate Studies in Mathematics,Volume 165
American Mathematical Society