## December 3

Saturday *from 4pm to 7pm and 9pm to midnight*, In room 102, Bethlen ter

*Putnam Mathematical Competition*

as has been announced several times, the Putnam exam will be offered
at Budapest for the registered BSM students.

Venue: BSM headquarters, Bethlen ter 2, room 102

Time: Saturday, December 4th, 4pm to 7pm ("morning session") and 9pm
to midnight ("afternoon session")

If you plan to participate, be there 10 minutes prior the beginning of each session.

You are not permitted to bring in any paper, books, slide rulers,
rulers, calculators, computers, etc., in the exam room. CELL PHONES
SHOULD BE TURNED OFF COMPLETELY. Participants should bring sharpened
pencils (or pens) and erasers.

## November 10

Thursday at *16:30*, at Eotvos University, (Pazmany Peter setany
1/A - north building, "Északi tömb" - room 7-14; see remark below)

*Prof. Miklós Laczkovich*, Eötvös University: **Tilings with similar or congruent pieces**

*Abstract:* Decomposing geometric figures into similar or congruent pieces
is a popular topic of recreational mathematics. Puzzles of this kind
have motivated extensive research in geometry and raised many
difficult questions. The talk gives a brief survey of the topic
presenting several unsolved problems as well.

*REMARK:*Another exceptional, out of the building colloquium lecture. The venue will be at the Eötvös University, Faculty of Sciences campus, north building (Északi tömb, 1/A on this map).

You find the Eotvos University campus by taking trams 4 or 6 southbound from Blaha Lujza, go with them across the Danube and leave the trams immediately on the Buda side. Walk along the Danube southbound until you reach the first of the two huge buildings of the Faculty of Sciences (North building)

A more detailed map of the immediate neighborhood .

Once you reach the north building ("Északi tömb") - which is the one closer to the bridge (and trams 4 and 6), you go to the elevators found in the center of the building (see blue arrows on this picture ), go to the 7th floor (push button 7) and the room will be just in front of you leaving the elevator.

The time is 4:30pm, allowing all of you to reach the place.

You will have a chance to meet some of the faculty and math students of the Institute of Mathematics over there.

## November 3

Thursday at *16:30*, at the Central European University (Zrinyi utca 14. 3. floor, room 310/A , Budapest, Hungary)

*Prof. Pál Hegedűs*, Central European University :
**Maximality in Algebra**

*Abstract:* A problem: Describe those proper subsets A of the rational numbers Q that are closed under the operations (., +, -) but there is no intermediate subset B (that is A subset of B subset of Q with this property. In abstract language: Describe maximal subrings of the field of rational numbers. A natural example is {p/q| q odd}. Note that this construction uses the prime 2 and it works for any prime. Is it true that every such subset A can be characterised by a prime?
We shall see many examples of such questions going from the simplest to quite complicated and examine what maximality (one of the most intriguing concepts of algebra) depends on.

*REMARK:*This will be the first lecture in the sequence introducing fine Hungarian higher education mathematics centers. CEU is an international graduate level university in the truest sense: Its students come from more than 80 countries; its faculty, from more than 30 countries--with the mix of nationalities increasing every year. The language of instruction and communication is English. It has it's own mathematics department and MSc and PhD math programs, which will also be shortly introduced. The venue of the lecture is the headquarters of the Department of Mathematics and it's Application at Zrinyi utca, downtown Budapest. You are assumed to find the location by yourself, with the following help: general directions general directions and map of the neighborhood.

## October 22

Saturday 9:00am to 14:00 pm:*BSM Local Mathematics Competition*In room 102, Bethlen ter

## October 6

Thursday 16.30 pm:*"N is a number", a movie about Paul Erdős.*Please note that the movie will be shown in the Main Lecture Hall of the Renyi Institute, which you can find according to this map.

## September 30

Friday at *16:45 (apprx.)*, at Bolyai Institute (Aradi vertanuk tere 1, Szeged, Hungary)

*Prof. Péter Hajnal *, Bolyai Institute, University of Szeged:
**Combinatorics of finite planar point sets**

*Abstract: * Paul Erdos proposed many questions having the same setup: "Take n points on the plane, what is the minimum/maximum number of ..." These extremal questions consider natural parameters of palanar point sets, like the number of distinct distances determined, the number of Gallai lines (lines incident exactly two points from our set). These questions are mostly older than 50 years, but still provide a main driving force of research.

We survey some classical and recent developments in the area. We will concentrate the two examples, above mentioned.

*REMARK:*This will be an exceptional, out of the town colloquium lecture at an exceptional time, Friday afternoon. This Friday the last classes (from noon) will be canceled (and made up later) and the group will leave from Nyugati railway station at 13:53 with TÖMÖRKÉNY intercity train. You will be met at the Szeged railway station at the arrival time, at quarter past 4 and be ushered to the site of the lecture. Mariann takes care of the train ticket (to Szeged) and the dormitory type accommodation, see her in case you intend to attend the lecture and visit Szeged.

## September 29

Feedback Session

Thursday at *14:15*, in Room *102*

Having any
problems in organizing your life in Budapest? We all come together on Thursday to help each other.

This is the perfect opportunity to discuss your first
impression about the courses, instructors, and the BSM program. Your opinion can be valuable to us, as well as to
others in making the big decision.

Also, this late afternoon is the deadline for registration. If you are uncertain what to
keep and what to drop, the 'Feedback' will help to solve this clue. In any case, we finally have to form the classes, decide the fate of ones with low/high audience.

## September 5

Monday*16:15*in the

*Main Lecture Hall*of the Renyi Institute, which you can find according to this map .

*Prof. Béla Bollobás*, University of Cambridge and University of Memphis:

**Sums of sets**

*Abstract:*The

*sum*of two subsets of integers,

*A*and

*B*, say, is

*A+B*={

*a+b*:

*a∈A, b∈B*};

sums of several sets are defined similarly. If there are

*a*elements in

*A*and

*b*in

*B*, at least how many elements are in

*A+B*? And what about the sum of three or more finite summands? Questions like these were first considered by Cauchy almost two hundred years ago, but the deeper study of the field was started only a few decades ago. In the talk I shall present some of the classical results, together with recent surprising developments.

*REMARK:*This will be an extraordinary colloquium lecture before the beginning of the semester, but still all of those who are already in the city are welcome.

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