Emmanuel Kowalski: Catalogue data in Spring Semester 2018 |
Name | Prof. Dr. Emmanuel Kowalski |
Field | Mathematics |
Address | Professur für Mathematik ETH Zürich, HG G 64.1 Rämistrasse 101 8092 Zürich SWITZERLAND |
Telephone | +41 44 632 34 41 |
emmanuel.kowalski@math.ethz.ch | |
URL | http://www.math.ethz.ch/~kowalski |
Department | Mathematics |
Relationship | Full Professor |
Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|
401-0212-16L | Analysis I | 7 credits | 4V + 2U | E. Kowalski | |
Abstract | Real and complex numbers, vectors, functions, limits, sequences, series, power series, differentiation and integration in one variable | ||||
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 | ||||
Literature | Michael Struwe: Analysis für Informatik Christian Blatter: Ingenieur-analysis Tom Apostol: Mathematical Analysis Teaching materials and further information is available through the course website (https://metaphor.ethz.ch/x/2018/fs/401-0212-16L/) | ||||
401-2000-00L | Scientific Works in Mathematics Target audience: Third year Bachelor students; Master students who cannot document to have received an adequate training in working scientifically. | 0 credits | E. Kowalski | ||
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.) | ||||
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 | This 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 Directive https://www.ethz.ch/content/dam/ethz/common/docs/weisungssammlung/files-en/declaration-of-originality.pdf | ||||
401-3104-18L | Diophantine Equations and Hilbert's 10th Problem Does not take place this semester. | 8 credits | 4G | E. Kowalski | |
Abstract | The 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. | ||||
Objective | |||||
Content | The 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. | ||||
Literature | J. 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). | ||||
Prerequisites / Notice | Prerequisites: Algebra I+II | ||||
401-3146-12L | Algebraic Geometry | 10 credits | 4V + 1U | E. Kowalski | |
Abstract | This course is an Introduction to Algebraic Geometry (algebraic varieties and schemes). | ||||
Objective | Learning Algebraic Geometry. | ||||
Literature | Primary 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. | ||||
Prerequisites / Notice | Requirement: Some knowledge of Commutative Algebra. | ||||
401-5110-00L | Number Theory Seminar | 0 credits | 1K | Ö. Imamoglu, P. S. Jossen, E. Kowalski, P. D. Nelson, R. Pink, G. Wüstholz | |
Abstract | Research colloquium | ||||
Objective | Talks on various topics of current research. | ||||
Content | Research seminar in algebra, number theory and geometry. This seminar is aimed in particular to members of the research groups in these areas and their graduate students. | ||||
406-2005-AAL | Algebra 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 credits | 26R | M. Burger, E. Kowalski | |
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. | ||||
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 |