## Menny Akka Ginosar: Catalogue data in Spring Semester 2022 |

Name | PD Dr. Menny Akka Ginosar |

Field | Dynamic systems |

Address | Professur für Mathematik ETH Zürich, HG J 67 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 70 24 |

menny.akka@math.ethz.ch | |

URL | https://people.math.ethz.ch/~menashea/ |

Department | Mathematics |

Relationship | Privatdozent |

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

401-3370-17L | Arithmetic of Quadratic Forms Number of participants limited to 12. Registration to this seminar is closed, the participants have been selected. There is no waiting list. | 4 credits | 2S | M. Akka Ginosar | |

Abstract | Introductory seminar about rational quadratic forms. P-adic numbers, Hasse's local to global principle and the finiteness of the genus will be discussed. | ||||

Learning objective | Quadratic forms and the numbers they represent have been of interest to mathematicians for a long time. For example, which integers can be expressed as a sum of two squares of integers? Or as a sum of three squares? Lagrange's four-squares theorem for instance states that any positive integer can be expressed as a sum of four squares. Such questions motivated the development of many aspects of algebraic number theory. In this seminar we follow the beautiful monograph of Cassels "Rational quadratic forms" and will treat the fundamental results concerning quadratic forms over the integers and the rationals such as Hasse's local to global principle and finiteness of the genus. | ||||

Content | The seminar will mostly follow the book "Rational quadratic forms" by J.W.S. Cassels, particularly Chapters 1-9. Exercises in this book are an integral part of the seminar. Towards the end of the semester additional topics may be treated. | ||||

Lecture notes | Cassels, John William Scott. Rational quadratic forms. Vol. 13. Academic Pr, 1978. | ||||

Literature | Main reference: Cassels, John William Scott. Rational quadratic forms. Vol. 13. Academic Pr, 1978. Additional references: Kitaoka, Yoshiyuki. Arithmetic of quadratic forms. Vol. 106. Cambridge University Press, 1999. Schulze-Pillot, Rainer. "Representation by integral quadratic forms - a survey." Contemporary Mathematics 344 (2004): 303-322. | ||||

Prerequisites / Notice | The student is assumed to have attended courses on linear algebra and algebra (as taught at ETH for instance). Previous knowledge on p-adic numbers is not assumed. | ||||

401-5370-00L | Ergodic Theory and Dynamical Systems | 0 credits | 1K | M. Akka Ginosar, M. Einsiedler, University lecturers | |

Abstract | Research colloquium | ||||

Learning objective | |||||

406-0141-AAL | Linear AlgebraEnrolment 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. Akka Ginosar | |

Abstract | Introduction to Linear Algebra and Numerical Analysis for Engineers. The contents of the course are covered in the book "Introduction to Linear Algebra" by Gilbert Strang (SIAM, 2003). MATLAB is used as a tool to formulate and implement numerical algorithms. | ||||

Learning objective | To acquire basic knowledge of Linear Algebra and of a few fundamental numerical techniques. The course is meant to hone analytic and algorithmic skills. | ||||

Content | 1. Vectors and vector spaces 2. Solving linear systems of equations (Gaussian elimination) 3. Orthogonality 4. Determinants 5. Eigenvalues and eigenvectors 6. Linear transformations 7. Numerical linear algebra in MATLAB 8. (Piecewise) polynomial interpolation 9. Splines | ||||

Literature | G. Strang, "Introduction to linear algebra", Third edition, 2003, ISBN 0-9614088-9-8, http://math.mit.edu/linearalgebra/ T. Sauer. "Numerical analysis", Addison-Wesley 2006 |