The spring semester 2021 will generally take place online. New presence elements as of April 26 will be communicated by the lecturers.

Erich Walter Farkas: Catalogue data in Autumn Semester 2018

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-mailfarkas@math.ethz.ch
URLhttp://www.math.ethz.ch/~farkas
DepartmentMathematics
RelationshipLecturer

NumberTitleECTSHoursLecturers
401-0291-00LMathematics I Information 6 credits4V + 2UE. W. Farkas
AbstractMathematics I/II is an introduction to one- and multidimensional calculus
and linear algebra emphasizing on applications.
ObjectiveStudents 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.
ContentEinführung in die Differential- und Integralrechnung von Funktionen einer Variablen und Anwendungen:

Funktionen. Stetigkeit. Differentialrechnung. Anwendungen der Differentialrechnung. Integralrechnung. Potenzreihen. Komplexe Zahlen. Matrizen.
LiteratureSiehe 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 / NoticeDie Übungsaufgaben sind ein wichtiger Bestandteil
der Lehrveranstaltung. Der Prüfungsstoff ist eine Auswahl von Themen aus der Vorlesung und den Übungen. Für
eine erfolgreiche Prüfung ist die konzentrierte Bearbeitung der Aufgaben
unerlässlich.

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 über https://metaphor.ethz.ch/x/2018/hs/401-0291-00L/.
401-3913-01LMathematical Foundations for Finance Information 4 credits3V + 2UE. W. Farkas, M. Schweizer
AbstractFirst introduction to main modelling ideas and mathematical tools from mathematical finance
ObjectiveThis course gives a first introduction to the main modelling ideas and mathematical tools from mathematical finance. It mainly aims at non-mathematicians who need an introduction to the main tools from stochastics used in mathematical finance. However, mathematicians who want to learn some basic modelling ideas and concepts for quantitative finance (before continuing with a more advanced course) may also find this of interest.. The main emphasis will be on ideas, but important results will be given with (sometimes partial) proofs.
ContentTopics 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 notesLecture notes will be sold at the beginning of the course.
LiteratureLecture notes will be sold at the beginning of the course. Additional (background) references are given there.
Prerequisites / NoticePrerequisites: 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.