TCD Problem Solving Group
This page summarises some past and the current activities of the problem-solving group at School of Maths, Trinity College Dublin.We strongly encourage students to attend. Problem-solving is the main business of mathematicians, problem-solving leads to innovation, and the great problem solvers are our heroes: Tartaglia, Newton, Euler, Abel, Galois, Hermite, Ramanujan, Einstein, Gödel, Cohen, Matiyasevich, Wiles, Perelman... but down here on earth, it should be possible to get a lot from the sessions if you simply attend, without taking the work home. Of course, some students will be interested in competitions, and that will require more commitment.
It is expected that the sessions will explore diverse approaches to problem-solving, with several mathematicians from Dublin area (currently there are five: Vladimir Dotsenko, Sergey Mozgovoy, Timothy Murphy, Colm O Dunlaing and Masha Vlasenko), as well as some senior students who are experienced in maths competitions, taking different sessions, in rotation.
The sessions have three aims:
- To introduce students to the experience of discussing and solving problems such as are posed in mathematics competitions.
- Periodically, to work on problems posed in American Mathematical Monthy (AMM) and submit solutions under the name `TCDmath problem group.'
- For the more committed student participants, to help them prepare for the IMC (international mathematics competition).
All information about problem-solving sessions will eventually appear on this webpage. To receive all the updates promptly, we recommend to join the mailing list, through this http URL. Any e-mail sent to the mailing list (by someone on the list) will be automatically sent to all people subscribed; please use this functionality wisely.
Arrangements for Hilary 2014
Meeting time/venue: Wednesday, 6pm, Synge Lecture Theatre, Hamilton buildingFirst meeting: January 22. Run by Colm O Dunlaing.
Second meeting: January 29. Run by Vladimir Dotsenko. Handout from the meeting.
Third meeting: February 5. Run by Tim Murphy.
Fourth meeting: February 12. Preparations for a maths battle. Run by Padraig Condon.
Maths battle: February 20, 6pm, MacNeill Lecture Theatre, Hamilton Building. Problem sheet for the battle.
Photos from the battle (courtesy of Masha Vlasenko)
Solution to the most difficult problem from the battle.
Maths battles
In 2012/13, we had two Maths battles (see here if you want to know what it is). This is the protocol of the first battle, photo taken on the spot:
Materials related to AMM problems
Current problem set:
AMM problems due by 2014-09-30
AMM problems due by 2014-08-31
AMM problems due by 2014-06-30
AMM problems due by 2014-04-30
AMM problems due by 2014-03-31
AMM problems due by 2014-02-28
AMM problems due by 2013-11-30
Old problem sets:
AMM problems due by 2013-10-31
AMM problems due by 2013-09-30
AMM problems due by 2013-08-31
AMM problems due by 2013-06-30
AMM problems due by 2013-05-31
AMM problems due by 2013-04-30
AMM problems due by 2013-02-28
AMM problems due by 2012-12-31
Solutions we submitted:
Solutions to AMM problems 11628, 11631, and 11636
Solutions to AMM problems 11637 and 11641
Solution to AMM problem 11651
Solution to AMM problem 11653
Solutions to AMM problems 11658, 11659, 11660, and 11661
Solution to AMM problem 11674
Solution to AMM problem 11687
Solution to AMM problem 11688
Solutions to AMM problems 11692 and 11693
Solutions to AMM problem 11698 and 11703
Archive of the academic year 2012/2013
Handout from the meeting on October 2, 2012
Handout from the meeting on October 16, 2012
Handout from the meeting on October 23, 2012
Maths battle 1, November 2, 2012
Maths battle 2, December 13, 2012
Handout from the meeting on January 15, 2013
Archive of the academic year 2011/2012
Problem set 1
Problem set 2
Problem set 3
Problem set 4
Problem set 5
Problem set 6
Problem set 7
Problem set 8
Problem set 9
Problem set 10
Problem set 11
Problem set 12
Problem set 13
Problem set 14
Problem set 15
Problem set 16
Problem set 17
Problem set 18
Problem set 19
Problem set 20
Problem set 21
Problem set 22
Answer set 1
Answer set 2
Answer set 3
Answer set 4
Answer set 5
Answer set 6
Answer set 7
Answer set 8
Answer set 9
(Incomplete) archive of the academic year 2010/2011
First handout for Freshmen problem sessions, October 5, 2010Addendum to the first handout for Freshmen problem sessions (hints and intermediate steps), November 16, 2010
Second handout for Freshmen problem sessions, November 23, 2010
First handout for Sophister problem sessions, October 7, 2010
Problem solving group before 2010
Systematic meetings of the problem solving group have been taking place since 2008. In the academic year 2008/09, each meeting included just 6-10 people, and those meetings took place in an informal atmosphere of a pub (Messrs Maguire, now known as J.W.Sweetman). An incomplete list of problems we discussed is available on Mathsoc Wiki. In the academic year 2009/10, meeting have been somewhat more sporadic and undocumented, unfortunately. (Please contact me if you have some materials from back then, and I shall gladly post them here. --Vlad)Past materials of the IMC
IMC problems from the year 1994
IMC problems from the year 1999
IMC problems from the year 2000
IMC problems from the year 2001
IMC problems from the year 2002
IMC problems from the year 2007
IMC problems from the year 2008
IMC problems from the year 2010
IMC problems from the year 2011
IMC problems from the year 2012