Menny Akka Ginosar: Catalogue data in Spring Semester 2017 |
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 | |
---|---|---|---|---|---|
401-0242-00L | Analysis II | 7 credits | 5V + 2U | M. Akka Ginosar | |
Abstract | Mathematical tools of an engineer | ||||
Objective | Mathematics as a tool to solve engineering problems, mathematical formulation of problems in science and engineering. Basic mathematical knowledge of an engineer | ||||
Content | Multi variable calculus: gradient, directional derivative, chain rule, Taylor expansion. Multiple integrals: coordinate transformations, path integrals, integrals over surfaces, theorems of Green, Gauss and Stokes, applications in physics. | ||||
Lecture notes | M. Akveld, R. Sperb. Analysis II. vdf, 2015 | ||||
Literature | - M. Akveld, R. Sperb. Analysis II. vdf, 2015 - James Stewart: Multivariable Calculus, Thomson Brooks/Cole - Papula, L.: Mathematik für Ingenieure 2, Vieweg Verlag - Smirnow, W. I.: Lehrgang der höheren Mathematik, Bd. II - William L. Briggs / Lyle Cochran: Calculus: Early Transcendentals: International Edition, Pearson Education | ||||
Prerequisites / Notice | Analysis I | ||||
401-3370-17L | Arithmetic of Quadratic Forms Number of participants limited to 12. Registration to the seminar will only be effective once confirmed by the organisers. Please contact Link . This seminar is fully occupied. Unconfirmed registrations have been deleted. | 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. | ||||
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. | ||||
406-0242-AAL | Analysis 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. | 7 credits | 15R | M. Akka Ginosar | |
Abstract | Mathematical tools of an engineer | ||||
Objective | Mathematics as a tool to solve engineering problems, mathematical formulation of problems in science and engineering. Basic mathematical knowledge of an engineer | ||||
Content | Multi variable calculus: gradient, directional derivative, chain rule, Taylor expansion. Multiple integrals: coordinate transformations, path integrals, integrals over surfaces, divergence theorem, applications in physics. | ||||
Literature | - James Stewart: Multivariable Calculus, Thomson Brooks/Cole - William L. Briggs / Lyle Cochran: Calculus: Early Transcendentals: International Edition, Pearson Education (Chapters 10 - 14) | ||||
406-0243-AAL | Analysis 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. | 14 credits | 30R | M. Akka Ginosar | |
Abstract | Mathematical tools for the engineer | ||||
Objective | Mathematics as a tool to solve engineering problems. Mathematical formulation of technical and scientific problems. Basic mathematical knowledge for engineers. | ||||
Content | Short introduction to mathematical logic. Complex numbers. Calculus for functions of one variable with applications. Simple types of ordinary differential equations. Simple Mathematical models in engineering. Multi variable calculus: gradient, directional derivative, chain rule, Taylor expansion. Multiple integrals: coordinate transformations, path integrals, integrals over surfaces, divergence theorem, applications in physics. | ||||
Literature | Textbooks in English: - J. Stewart: Calculus, Cengage Learning, 2009, ISBN 978-0-538-73365-6 - J. Stewart: Multivariable Calculus, Thomson Brooks/Cole (e.g. Appendix G on complex numbers) - V. I. Smirnov: A course of higher mathematics. Vol. II. Advanced calculus - W. L. Briggs, L. Cochran: Calculus: Early Transcendentals: International Edition, Pearson Education Textbooks in German: - M. Akveld, R. Sperb: Analysis I, vdf - M. Akveld, R. Sperb: Analysis II, vdf - L. Papula: Mathematik für Ingenieure und Naturwissenschaftler, Vieweg Verlag - L. Papula: Mathematik für Ingenieure 2, Vieweg Verlag |