Erich Walter Farkas: Catalogue data in Autumn Semester 2016

Name	Prof. Dr. Erich Walter Farkas (Professor Universität Zürich (UZH))
Address	Lehre Mathematik Plattenstrasse 14 8032 Zürich SWITZERLAND
Telephone	+41 44 634 39 53
Fax	+41 44 634 43 45
E-mail	farkas@math.ethz.ch
URL	http://www.math.ethz.ch/~farkas
Department	Mathematics
Relationship	Lecturer

Number	Title	ECTS	Hours	Lecturers
401-0291-00L	Mathematics I	6 credits	4V + 2U	E. W. Farkas
Abstract	Mathematics I/II is an introduction to one- and multidimensional calculus and linear algebra emphasizing on applications.
Learning objective	Students understand mathematics as a language for modeling and as a tool for solving practical problems in natural sciences. Students can analyze models, describe solutions qualitatively or calculate them explicitly if need be. They can solve examples as well as their practical applications manually and using computer algebra systems.
Content	Einführung in die Differential- und Integralrechnung von Funktionen einer Variablen und Anwendungen: Funktionen. Stetigkeit. Differentialrechnung. Anwendungen der Differentialrechnung. Integralrechnung. Potenzreihen. Komplexe Zahlen. Matrizen.
Literature	Siehe Lernmaterialien > Literatur L. Papula, Mathematik für Ingenieure und Naturwissenschaftler, 11. Auflage, Vieweg und Teubner Th. Wihler, Mathematik für Naturwissenschaften, 2 Bände: Einführung in die Analysis, Einführung in die Lineare Algebra; Haupt-Verlag Bern, UTB Ch. Blatter, Lineare Algebra; VDF H. H. Storrer: Einführung in die mathematische Behandlung der Naturwissenschaften I; Birkhäuser.
Prerequisites / Notice	Die Einschreibung in die Übungsgruppen erfolgt online. Alle unter http://mystudies.ethz.ch/ für die Vorlesung eingeschriebenen Studierenden können sich unter https://echo.ethz.ch/ in eine Übungsgruppe einschreiben. Der Zugang zu den Übungsserien erfolgt online. Vorlesungsverzeichnis > Lernmaterialien > Material zur Vorlesung
401-3913-01L	Mathematical Foundations for Finance	4 credits	3V + 2U	E. W. Farkas, M. Schweizer
Abstract	First introduction to main modelling ideas and mathematical tools from mathematical finance
Learning objective	This course gives a first introduction to the main modelling ideas and mathematical tools from mathematical finance. It aims at a double audience: mathematicians who want to learn the modelling ideas and concepts for finance, and non-mathematicians who need an introduction to the main tools from stochastics used in mathematical finance. The main emphasis will be on ideas, but important results will be given with (sometimes partial) proofs.
Content	Topics to be covered include - financial market models in finite discrete time - absence of arbitrage and martingale measures - valuation and hedging in complete markets - basics about Brownian motion - stochastic integration - stochastic calculus: Itô's formula, Girsanov transformation, Itô's representation theorem - Black-Scholes formula
Lecture notes	Lecture notes will be sold at the beginning of the course.
Literature	Lecture notes will be sold at the beginning of the course. Additional (background) references are given there.
Prerequisites / Notice	Prerequisites: Results and facts from probability theory as in the book "Probability Essentials" by J. Jacod and P. Protter will be used freely. Especially participants without a direct mathematics background are strongly advised to familiarise themselves with those tools before (or very quickly during) the course. (A possible alternative to the above English textbook are the (German) lecture notes for the standard course "Wahrscheinlichkeitstheorie".) For those who are not sure about their background, we suggest to look at the exercises in Chapters 8, 9, 22-25, 28 of the Jacod/Protter book. If these pose problems, you will have a hard time during the course. So be prepared.