## Marc Burger: Catalogue data in Spring Semester 2021 |

Name | Prof. Dr. Marc Burger |

Field | Mathematics |

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 |

marc.burger@math.ethz.ch | |

URL | http://www.math.ethz.ch/~burger |

Department | Mathematics |

Relationship | Full Professor |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-0212-16L | Analysis I | 7 credits | 4V + 2U | M. Burger | |

Abstract | Real and complex numbers, vectors, functions, limits, sequences, series, power series, differentiation and integration in one variable | ||||

Learning objective | Real and complex numbers, vectors, functions, limits, sequences, series, power series, differentiation and integration in one variable | ||||

Content | Real and complex numbers, vectors, functions, limits, sequences, series, power series, differentiation and integration in one variable | ||||

Lecture notes | Analysis I, Marc Burger | ||||

Literature | Tom Apostol: Mathematical Analysis Teaching materials and further information will be available through the course website. | ||||

401-2000-00L | Scientific Works in MathematicsTarget audience: Third year Bachelor students; Master students who cannot document to have received an adequate training in working scientifically. | 0 credits | M. Burger | ||

Abstract | Introduction to scientific writing for students with focus on publication standards and ethical issues, especially in the case of citations (references to works of others.) | ||||

Learning objective | Learn 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 | ||||

Lecture notes | Moodle of the Mathematics Library: https://moodle-app2.let.ethz.ch/course/view.php?id=519 | ||||

Prerequisites / Notice | Directive https://www.ethz.ch/content/dam/ethz/common/docs/weisungssammlung/files-en/declaration-of-originality.pdf | ||||

401-2004-00L | Algebra II | 5 credits | 2V + 2U | M. Burger | |

Abstract | The main topics are field extensions and Galois theory. | ||||

Learning objective | Introduction to fundamentals of field extensions, Galois theory, and related topics. | ||||

Content | The 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. | ||||

Literature | Joseph 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. | ||||

401-5530-00L | Geometry Seminar | 0 credits | 1K | M. Burger, M. Einsiedler, P. Feller, A. Iozzi, U. Lang, University lecturers | |

Abstract | Research colloquium | ||||

Learning objective | |||||

406-2004-AAL | Algebra IIEnrolment 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 credits | 11R | M. Burger | |

Abstract | Galois theory and related topics. The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. | ||||

Learning objective | Introduction to fundamentals of field extensions, Galois theory, and related topics. | ||||

Content | The 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. | ||||

Literature | Joseph 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 / Notice | Algebra I, in Rotman's book this corresponds to the topics treated in the Chapters A3 and A4. | ||||

406-2005-AAL | Algebra I and IIEnrolment 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 credits | 26R | M. Burger, M. Einsiedler | |

Abstract | Introduction 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. | ||||

Learning objective | |||||

Content | Basic 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 | ||||

Literature | Joseph J. Rotman, "Advanced Modern Algebra" third edition, part 1, Graduate Studies in Mathematics,Volume 165 American Mathematical Society |