Marc Burger: Catalogue data in Autumn Semester 2021

Name Prof. Dr. Marc Burger
FieldMathematik
Address
Dep. Mathematik
ETH Zürich, HG G 37.1
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telephone+41 44 632 49 73
Fax+41 44 632 10 85
E-mailmarc.burger@math.ethz.ch
URLhttp://www.math.ethz.ch/~burger
DepartmentMathematics
RelationshipFull Professor

NumberTitleECTSHoursLecturers
401-0213-16LAnalysis II Information 5 credits2V + 2UM. Burger
AbstractDifferential and Integral calculus in many variables, vector analysis.
Objective
LiteratureFür allgemeine Informationen, sehen Sie bitte die Webseite der Vorlesung
401-2000-00LScientific Works in Mathematics
Target audience:
Third year Bachelor students;
Master students who cannot document to have received an adequate training in working scientifically.
0 creditsM. Burger
AbstractIntroduction to scientific writing for students with focus on publication standards and ethical issues, especially in the case of citations (references to works of others.)
ObjectiveLearn the basic standards of scientific works in mathematics.
Content- Types of mathematical works
- Publication standards in pure and applied mathematics
- Data handling
- Ethical issues
- Citation guidelines
Prerequisites / NoticeDirective https://www.ethz.ch/content/dam/ethz/common/docs/weisungssammlung/files-en/declaration-of-originality.pdf
401-5530-00LGeometry Seminar Information 0 credits1KM. Burger, M. Einsiedler, P. Feller, A. Iozzi, U. Lang, University lecturers
AbstractResearch colloquium
Objective
406-2004-AALAlgebra II
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
5 credits11RM. Burger
AbstractGalois theory and related topics.

The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.
ObjectiveIntroduction to fundamentals of field extensions, Galois theory, and related topics.
ContentThe main topic is Galois Theory. Starting point is the problem of solvability of algebraic equations by radicals. Galois theory solves this problem by making a connection between field extensions and group theory. Galois theory will enable us to prove the theorem of Abel-Ruffini, that there are polynomials of degree 5 that are not solvable by radicals, as well as Galois' theorem characterizing those polynomials which are solvable by radicals.
LiteratureJoseph J. Rotman, "Advanced Modern Algebra" third edition, part 1,
Graduate Studies in Mathematics,Volume 165
American Mathematical Society

Galois Theory is the topic treated in Chapter A5.
Prerequisites / NoticeAlgebra I, in Rotman's book this corresponds to the topics treated in the Chapters A3 and A4.
406-2005-AALAlgebra I and II
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
12 credits26RM. Burger, M. Einsiedler
AbstractIntroduction 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.
Objective
ContentBasic 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
LiteratureJoseph J. Rotman, "Advanced Modern Algebra" third edition, part 1,
Graduate Studies in Mathematics,Volume 165
American Mathematical Society