**STUDENT PROJECTS IN BONN**

In general a Praktikum usually involves getting acquainted with a computer
algebra package like Maple and doing some computations with it related to
problems in elementary number theory. [If there is interest in a specific
field outside number theory and a suitable mathematical guest can be found
who is willing to supervise this, this is also possible.] For doing a Praktikum
no financial compensation is provided. However, if somebody lives so far away
from Bonn that this makes finding a place to stay in Bonn necessary, we usual
cover the rent. Due to lack of office place usually the Praktikant has to
work on some computer that is in the `free space'. This rarely proves to
be a problem. Furthermore, the MPIM does not have a cantine
(though a kitchen and microwave is available to warm up some food). However,
in the immediate surroundings there are plenty of places where one can get
food of all kinds of prices and qualities. For administrative purposes
the student is required to bring at some point a formal document involving
a picture (passport for example), so that our administration can make
a copy. The Praktikant gets also an own computer account. As to
working times, we are quite flexible.

Christine Jost (Dresden) did a Praktikum at MPI during the month March 2005.

She worked on some problems from elementary number theory and wrote a popular
account Die liebe
Verwandschaft on twin prime numbers. A modified and translated version (joint with
Jan van de Craats) of this appeared in the Dutch highschool journal
`Pythagoras'.

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Janina Muettel (Bonn) did a six week Praktikum at MPI during February-March 2005.

She worked on some problems from elementary
number theory and wrote a popular
account Die Riemannsche
Vermutung on the Riemann Hypothesis in collaboration
with me. A modified and translated version (joint with
Jan van de Craats) of this appeared in the Dutch highschool journal
`Pythagoras'.

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Alexander Blessing (Bonn) did a two week Praktikum at MPI in June 2006.

He considered congruence properties of the sequence v(n) with
v(n) the number of lines in hypersurfaces of degree 2n-3 in the n-dimensional
projective space.

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Pascal Cremer, (16 years),
Miriam Haegele (16 years),
and Linnea Passing (also 16 years old),
did a two week Praktikum at MPI in January 2007.

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Andreas Decker,
Alexander Bridi ,
Patrizia Dressler ,
Thorge Jensen and
Silke Glas
did a one-month Praktikum at MPI in August-September 2007. In October 2008 they all
start studying at some german universities. Here a picture of the group:

With from left to right: Thorge, Andreas, Patrizia, Pieter, Silke and Alexander.

They worked on various problems and Andreas, with some help of the others, managed
to solve one of those. I slightly improved and shortened his work. The results are
published in a note with the title
Counting RSA-integers,
which will appear in Resultate der Mathematik.

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In January 2008, 16 year old school boys
Lars Holzem,
Patrick Robinson ,
Christoph Lampe
and Armend Xhaferi ,
did a 2 week Praktikum (Patrick 3 weeks). They learned to work
with Maple and answered letters of amateurs.

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In March 2008 Patrick Embgenbroich,
did a 1 week Praktikum. Also in the spring of 2008
Jonas Reuters, a first year physics
student in Bonn, did a Praktikum.

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In June 2008 Nadina Baghina, Christian Budde, Benjamin
Juettner and Dennis Scully did a Praktikum.
Normally they are studying in Bremen, Kleve, Bonn and Bergheim, respectively.
They helped me computing tables
relevant for constructing counter-examples to the Sister Beiter conjecture.

With from left to right: Dennis, Pieter and Nadina.

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August/September 2008 Richard Cartwright and Andreas Decker did a
Praktikum. They studied the coefficients of divisors of x^n-1.
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In January 2008 Klara-Maria Boegle, Jonas Kaszian, Annette Streicher,
Inken Piekenbrock and Nils Solscheid did a Praktikum.
Here a picture of the group:

With from left to right: Annette, Klara-Maria, Inken (lower row), Pieter, Jonas and
Nils (upper row).
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During their Easter holidays Elena Meyer, Eva Neumann and Nicole Schmidt (from
left to right) did a Praktikum.

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August-September: Muriel Lang, Necla Kayaalp, Raluca Havarneanu and
Valentin Buciumas (from
left to right) did a Praktikum. They looked at a variant of the Erdos-Moser Diophantine equation.