International Summer School on Advanced Methods in Applied Mathematics,
Wiesbaden 2016

An Introduction to Functional Analysis Through Applications  


September 23, 2016 (Friday) – September 29, 2016 (Thursday)

University of Applied Sciences, Wiesbaden, Germany

Target Audience:
Mathematics students approaching their bachelor’s degrees

Participation Fee:
90 EUR (covering lectures, coffee breaks, meals, excursions)

What is the Summer School about?

The summer school is geared towards mathematics students in the final phase of their bachelor’s studies, and the topic was chosen accordingly. The development of functional analysis at the beginning of the 20th century marks a change towards a more abstract approach to mathematics, which is also felt in neighboring areas such as point-set topology and integration theory and which is well motivated by applications in many areas both within mathematics (especially analysis) and outside (especially in physics). Such a change to a more abstract approach is also characteristic for the change from a bachelor’s to a master’s programme, and it is well worth motivating this change by emphasizing similar mathematical structures occurring in different application areas. The idea of the summer school is to motivate and lead up to the core ideas underlying functional analysis (dealing with coupled algebraic and topological structures) by typical examples and applications in analysis, physics, and financial mathematics. No previous knowledge of functional analysis is required.

Abstracts of the lectures

Preliminary Programme

Thursday, September 22 (arrival day)

     17:00 get-together (grill party)

Friday, September 23

    09:00 Lecture 1: From Linear Algebra and Calculus to Functional Analysis, Part 1 (Karlheinz Spindler)
    11:00 Lecture 2: From Linear Algebra and Calculus to Functional Analysis, Part 2 (Karlheinz Spindler)

    Presentations: Lectures 1 + 2 (Printversion)

     Afternoon: Neroberg
     Evening: opera (La Traviata)

Saturday, September 24

      09:45 Sightseeing tour of Wiesbaden

     13:30 Lecture 3: Reproducing Kernel Hilbert Spaces (Hagen Knaf)
     15:00 Lecture 4: Kernel methods in Data Mining (Hagen Knaf)

     Report: Kernel-Fisher Discriminant Analysis
     Presentation: Lecture 3
     Presentation: Lecture 4
     Article: A primer on reproducing kernel Hilbert spaces

Sunday, September 25

     09:30 Whole-day excursion: boat trip to Rüdesheim, Niederwalddenkmal, hike to Aßmannshausen

     A collection of pictures will be available here after the summer school has ended.

Monday, September 26

     09:30 Lecture 5: Functional Analysis and Partial Differential Equations (Thomas Lorenz)
     11:30 Lecture 6: Functional Analytic Foundations of Numerical Methods (Thomas Lorenz)
     14:00 Lecture 7: Computer Workshop on Numerical Methods (Alexander Ekhlakov)

     Script: Lectures 5 and 6

Tuesday, September 27

     09:30 Lecture  8: Hilbert Space Methods in Quantum Mechanics, Part 1 (Detlef Lehmann)
     11:30 Lecture 9: Hilbert Space Methods in Quantum Mechanics, Part 2 (Detlef Lehmann)

     Presentation: Lectures 8 and 9
     Notes: Wave-function Collapse Models: The Basic Mechanism

     Meeting after lunch at 13:30 at the entrance of the C-building, bus to Neroberg,
     Guided tour from 15:00 to 17:00.

Wednesday, September 28

     09:30 Lecture 10: Martingales and Their Application in Mathematical Finance, Part 1 (Claas Becker)
     11:30 Lecture 11: Martingales and Their Application in Mathematical Finance, Part 2 (Claas Becker)

     Scan: Lecture 10
     Scan: Lecture 11

Thursday, September 29 (departure day)

     09:30 Lecture 12: The Historical Development of Functional Analysis (Karlheinz Spindler)
     11:30 Lecture 13: Functional Analysis and Control (Karlheinz Spindler)

     Presentation: Lecture 12 (Printversion)
     Presentation: Lecture 13 (Printversion)

     Farewell brunch

Contact Address

Prof. Dr. Karlheinz Spindler
University of Applied Sciences
Applied Mathematics
Kurt-Schumacher-Ring 18
D – 65197 Wiesbaden, Germany


The organizers can provide accommodation in a nearby youth hostel (two- and three-bed rooms). This youth hostel is within walking distance of the summer school location. If you need other accommodation, please contact the organizers.


To register as a participant of the summer school please use the

Registration Form (Summer School already started)

If you need additional information, please contact the organizers.

After registration, please transfer the participation fee of 90 EUR to the following account:

Account: Hochschule Rhein Main

IBAN: DE62 5005 0000 0001 0065 19; BIC: HELA DE FFXXX
Keyword: 40140137 Mathematical Summer School

Financial Support

Financial support for travel and accommodation costs can be provided on a limited basis. Please contact the organizers if you need such support. In this case we ask you to send us a résumé of your academic records and a little essay describing your motivation to participate in the summer school.