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The lecture is focused on fundamental principles in analysis which are of great importance for application in stochastic and financial mathematics.

The main topics are:

• Normed and metric spaces
• Measure and integration
• Hilbert spaces
• Fourier transform and characteristic functions

For an overview, see also the lecture notes by Markus Kunze on the website for the course Applied Analysis in WS 2011/2012.

• Bartle: The elements of integration and Lebesgue measure
• Conway: A course in functional analysis
• Jost: Postmodern analysis
• Lang: Undergraduate analysis
• Varadhan: Probability theory
• Stein and Shakarchi: Real analysis – measure theory, integration, and Hilbert spaces

The 2 hour written exam will take place on 28 Feburary 2014, room He. 18 E.20, from 10 am to noon. In order to take the exam, you will have to register in LSF-QISPOS at the latest 4 days before the exam. More details about the exam will be announced here.

Only participants of the first exam who did not pass will be admitted to the second exam. The second exam takes the form of an oral exam.

Mock exams and other relevant material:

1. A first mock exam based on half of the relevant material is given as Exercise Sheet 10. (Suggested solutions)
2. A second mock exam can be found here. (Suggested solution).
3. A third mock exam is available here. We will not provide a solution for this mock exam, but you are welcome to arrange an appointment for discussion or to give us your solution for correction.
4. Two checklists
5. You are always welcome to ask questions!

Both lectures and exercises will take place the Helmholtzstrasse 18. The lectures take place in Room E.60 and the exercises in Room E.20.  Don't hesitate to ask questions during the lecture and the exercise lessons, or drop us an email.

Lectures (E.60)

• Tuesday, 12–14
• Friday, 8–10

Exercises (E.20)

• Thursday, 16–18

Time for questions (O28, room 2002)

• Wednesday, 16–18

SheetDiscussion

ExerciseSheet01.pdf ExerciseSheet02.pdf ExerciseSheet03.pdf ExerciseSheet04.pdf ExerciseSheet05.pdf ExerciseSheet06.pdf ExerciseSheet07.pdf ExerciseSheet08.pdf ExerciseSheet09.pdf ExerciseSheet10.pdf ExerciseSheet11.pdf ExerciseSheet12.pdf ExerciseSheet13.pdf ExerciseSheet14.pdf ExerciseSheet15.pdf	2013-10-24 2013-10-31 2013-11-07 2013-11-14 2013-11-21 2013-11-28 2013-12-05 2013-12-12 2013-12-19 2014-01-09 2014-01-16 2014-01-23 2014-01-30 2014-02-06 2014-02-13