UCC Mathematics Enrichment Programme




Math Notes






Maths circles


    MathS links 






Award for Irish Teachers of Mathematics

Do you know a Maths teacher who inspires and teaches with passion and knowledge? Nominate her or him for the Award for Irish Teachers of Mathematics! More details can be found on the homepage of the Irish Mathematical Trust.


 2018-2019 Mathematics Enrichment programme Registration: click here

   The Mathematics Enrichment Saturday classes will restart on 24th November 2018 and will be held in the Western Gateway Building, – building no 81 on this campus map. Here’s another map.  The rooms, class content and resources for each group can be found in the Schedules below.


Advanced Maths Enrichment

Intermediate Maths Enrichment

Junior Beginning Maths Enrichment

 Maths Circles

Who:  Most of the participants have attended the UCC Maths Enrichment Intermediary Classes in the previous year, but other students are welcome too.

Who:  4th and 5th year students as well as 3rd year students who have attended Junior Maths Enrichment in the past. Participants receive invitations through schools. Other places available upon request.

Who:  Most participants are students in their 2nd or 3rd Junior Cycle year who have attended a Maths Circle in their local school, or who have shown special interest and aptitude for Mathematics.

Who: Primary and Junior Cycle students in their first years of study, who are curious about mathematics and like maths games and puzzles.

Where: Western Gateway Building

  See schedule for room numbers.      

Where: Western Gateway Building

See schedule below for room numbers.

Where: Western Gateway Building

  See schedule for room numbers.

Where: Schools in the Cork area. If your school does not have a maths circle, ask your teacher to seek our help with setting up and running one.





 Including links to class-notes.




Including links to class notes

·         1st year maths circles Handbook

·          Primary school Maths Circles

         Using Math.EU resources.

When: Saturdays 10:00-13:00

November 2018 – May 2019


When: Saturdays 10:00-13:00

November 2018 – May 2019

When:  Sat 10:00-11:30

 November 2018 – May 2019

When: Throughout the school year.

Why: Now the topics you met last year start to feel more familiar, the ideas sink in, and you find yourself a better problem solver. Smaller group, more one-to-one interaction.

You get a chance to participate in events like Mathematical Olympiads

Why: You encounter deeper, more challenging and more interesting mathematical problems than those on the school syllabus.

 You get a chance to participate in the

Mathematical Olympiads

Leaving Cert results

Why: To continue on with the fun of Maths Circles.

To meet like-minded people from other schools around the Cork area. 

To participate in contests like Alcumus challenges, or the Purple Comet   

Why: Testimonials

Maths Circles in the news.

More info on the Maths Circles website.



UCC Mathematics Enrichment is


·         An outreach project the School of Mathematical Sciences;

·         a partner of Maths Circles Ireland and

·         a partner of the Irish Mathematical Trust.

·         home of the Boole2School Legacy.         

·         grateful for support from  SEFS, SFI Discover and Smart Futures.


Warm congratulations to team Ireland at the International Mathematical Olympiad 2017 in Rio de Janeiro for its best result

in 30 years, including 2 bronze medals and 4 honourable mentions!

UCC hosted two training camps for the team in August 2016 and July 2017, in addition to the training camp in Rio.

Warm congratulations to team Ireland at the European Girls Mathematical Olympiad 2017 in Zurich for its best result including one silver, one bronze medal and one honourable mention!





Irish team at IMO 2016 in Hong Kong




Irish team at EGMO 2015 in Belarus, Minsk, with leader, deputy and guide


Karen Briscoe, Keegan O’Mahoney and Gavin O’Driscoll received the

Accenture prize for most meritorious performance- Leaving Certificate

Mathematics 2014






EGMO 2016 in Busteni, Romania



   Mathematical Olympiads



What are Mathematical Olympiads? Contests for secondary school students, they are designed to test and stimulate the creativity, intuition and mathematical skills of the participants. They provide a competitive but friendly environment for students with an interest in mathematics. There are local, national and international mathematical Olympiads. The International Mathematical Olympiad is the pinnacle of mathematical competitions among school students.


How can I prepare?

·         Getting Started:

Here are some of the many fun competitions at local and national level for younger students to try before starting participating in a Mathematical Olympiad.




Achievement Awards based on Alcumus at Art of Problem Solving

All year

Primary, junior and senior secondary school

Irish Maths Teachers Association competitions

Contact IMTA at info@corkmaths.ie

Junior and senior secondary school

Prism competition


Junior and senior secondary school

Purple Comet international online team competition


Junior and senior secondary school


Most of these train your reasoning skills, speed and precision. In addition, Mathematical Olympiads are proof-based tests which typically require more advanced knowledge outside of school curriculum, along with perseverance and creativity. To practice this skill set, join one of our Mathematics Enrichment classes. Please check the schedules above.

·         For Mathematics Enrichment Programme participants:

Prior to the Irish Mathematical Olympiad (IrMO), you may review the lecture notes and exercise sets from our classes: click on the titles in the schedule page. As well, do check the resources offered by other centres in Ireland: the UCD Maths Enrichment as well as the Maynooth Olympiad manual. You can find more notes and practice with old Olympiad problems in the Maths Notes section of this website.


·         Students preparing for international olympiads: Here is a list of proposed free Olympiad Training Resources. Here is the  2018-2019 Calendar of Events

Every year we run three UCC based training camps for students who did well in IrMO. 

Here is the Schedule of the August 2017 camp and here the Schedule of the August 2016 Camp. Click on the session titles for lesson notes.


External links- useful resources for national and international Olympiads:

Olympiad Number Theory notes.  Olympiad Inequalities notes.  Yufei Zhaos Olympiad training notes.

Visit this Art of Problem Solving resource page for a large sample of international Olympiads.



Where can I get more information? Visit the official homepage of the Irish Mathematical Olympiad.


 International Mathematical Olympiad (IMO)

IMO is the most prestigious international mathematics competition for school age students. The first IMO was held in 1959 in Romania, with 7 countries participating. It has gradually expanded to over 100 countries from 5 continents.


Cork Maths Enrichment students at the International Mathematical Olympiad in recent years years:


IMO 2017 Rio de Janeiro, Brazil

Anna Mustata (Bronze Medal)

IMO 2016 Hong Kong

Ioana Teodora Grigoras from Mount Mercy Secondary School (Honourable Mention)

Liam Toebes from Carrigaline Community School

Anna Mustata from Bishopstown Community School (Honourable Mention)

IMO 2015 Chiang Mai, Thailand

Ioana Teodora Grigoras from Mount Mercy Secondary School,

Anna Mustata from Bishopstown Community School  (Honourable Mention)

IMO 2014 Cape Town, South Africa

Karen Briscoe from Kinsale Community School  (Honourable Mention)

IMO 2013 Columbia

Declan Manning from Ballincollig Community School  (Honourable Mention)

IMO 2012 Argentina

Jonathan Peters from Presentation Brothers College  (Honourable Mention)


Jonathan talks of Argentina 2012,  IMO 2015 Thailand retrospective.



 European Girls' Mathematical Olympiad (EGMO)

 is an international mathematics competition similar in style to the International Mathematical Olympiad, aimed at motivating girls to develop their mathematical talent, gain self-confidence and experience with international competitions. Participating countries send teams consisting of four female mathematicians of school age.


  The sixth EGMO took place in Zurich, Switzerland on 6-12 April 2017. The Irish team members were: Antonia Huang from Mount Anville Secondary School, Dublin (Bronze Medal), Anna Mustata from Bishopstown Community School, Cork   (Silver Medal),  Jean O’Brien from Castleknock Community College, Dublin (Honourable Mention) and Yuelin Xiong from Alexandra College, Dublin.


 The fifth EGMO took place in Busteni, Romania on April 10-16, 2016. The Irish team members were the same as at EGMO 2016 (see below). 

  Ioana won a Bronze Medal and Anna won a Silver Medal. Also in the news here.


The fourth EGMO took place in Minsk on April 14-20, 2015. The Irish team members were:  Antonia Huang from Mount Anville Secondary School, Dublin,  Ioana Teodora Grigoras from Mount Mercy Secondary School, Cork,  Anna Mustata from Bishopstown Community School, Cork   (Silver Medal),  Katie O’Connor from The High School, Dublin. The team leader was Dr. Mary Hanley and the deputy leader was Kieran Cooney.


The third EGMO took place Antalya on April 10-16, 2014. The Irish team was made of  Karen Briscoe from Kinsale Community School, Ioana Teodora Grigoras from                 Mount Mercy Secondary School and Anna Mustata from Bishopstown Community School.


The second EGMO took place Luxemburg in April 2013. Karen Briscoe from Kinsale Community School and Anna Mustata from Bishopstown Community School were awarded Honourable Mentions. Here is An Irish team member report by Jessica Weitbrecht and some photos.



 Irish Mathematical Olympiad (IrMO)

 Is the national mathematics competition design to select the Irish team to participate in the IMO. It takes place every year in two rounds: Round 1 in November in schools across Ireland, and Round 2 in the Mathematics Enrichment centres in UCC, UCD, Maynooth, Limerick, Galway.

The Final Round of the 31st Irish Mathematical Olympiad took place on Saturday,  12 May 2018. Here is the Roll of Honour.

The contest is used to select a team for the International Mathematical Olympiad. Here are the IMO Eligibility Rules

The Final Round of the 30th Irish Mathematical Olympiad took place on Saturday, 6 April 2017. Here is the Roll of Honour.

The Final Round of the 29th Irish Mathematical Olympiad took place on Saturday, 23 April 2016. Here is the Roll of Honour.

The Final Round of the 28th Irish Mathematical Olympiad took place on Saturday, 30 April 2015. Here is the Roll of Honour.

The Final Round of the 27th Irish Mathematical Olympiad took place on Saturday, 10 May 2014. Here is the Roll of Honour.

The Final Round of the 26th IrMO took place on Saturday, 11 May 2013. Here is the Roll of Honour

Short history:   Mathematics Enrichment Classes at University College Cork

     The programme was started in 1987 by Prof. Finbarr Holland and Donal Hurley, with the support of members of the Mathematics Department at UCC. These classes meet for three hours on Saturday mornings and around 100 students attend them. Students are invited to attend the classes based on their performance at the Junior Certificate Mathematics Examination and teacher recommendations. Invitations to attend these classes are highly valued. The topics covered are generally distinct from the Leaving Certificate Mathematics syllabus and the emphasis is on solving mathematical problems which require ingenuity and mathematical techniques.Programmes involving Mathematics Enrichment Classes are to be found in many countries. They are generally very extensive, meet more regularly and involve a large proportion of students. Generous sponsorship is readily available for such programmes as many of the leading scientists and engineers in these countries would have some of their early training at these activities.  


Here are some highlights of the previous season:

·         Three of our students have qualified to represent Ireland at the International Mathematical Olympiad IMO 2016. Here is the Irish Mathematical Olympiad roll of honour.

·         Our Cork girls brought home two medals from the European Girls Mathematical Olympiad (EGMO). And for the 1st time ever the IMO team Ireland is even 3 girls/3boys.

·         The junior students had their best yet result in the Purple Comet international online competition.

·         Last but not least, about 100,000 students from >40 countries found out about George Boole through our Boole2School lessons.


   Mathematics notes         

Irish Mathematical Olympiad

Compendium of IrMO papers 1988-2014.


    2015  Paper 1    /   Paper 2

    2016  Paper 1    /  Paper 2

    2017  Paper 1    /   Paper 2

    2018  Paper 1    /  Paper 2


EGMO selection tests:

 2012 UCD Selection Test

 2013 UCD Selection Test

 2014 Local and final test and UCD test.

 2015 UCD Selection Test

 2016 UCD Selection Test

 2017 UCD Selection Test

 2018 UCD Selection Test


Class notes, exercises, problem solving tips.

IMO geometry problems 1 and 4

IMO geometry problems 2 and 5


Geometry notes on symmetry by Andrei Mustata

Geometry notes by Sabin Tabirca: 
          1. Medial triangle
          2. Equilateral Triangles
          3. Inversion and Applications to Ptolemy and Euler
          4. Feuerbach's Theorem
          5. Orthic triangle
          6. Theorems of Ceva, Menelaus and Van Aubel
          7. Lemoine Point
          8. Lemoine Point and Circles

Geometry project1 and project2 by Prof Paddy Barry.        

  Notes on general problem solving: 


  Peng Shi’s notes on problem solving.

  The IMO compendium Group notes.

  Alcumus videos.


  Notes on Combinatorics:


  1. Course notes by Martin Stynes.

Basic Olympiad preparations: Chapters 1 and 6, begin 2 and 3.

  2. Repetitions and conditions.

  3. Binomial coefficients notes from UCD


  Notes on number theory:

 1. Modular arithmetic by Anca Mustata


                     Notes on Algebra: polynomials and inequalities


by Eugene Gath:

   1. Inequalities notes and problems

   2. Polynomial notes and problems


by Professor Finbarr  Holland:


 0. Beginning inequalities

 1. Trigonometrical identities and inequalities
 2. Complex numbers and polynomials
 3. Geometric and algebraic inequalities

 4. More inequalities -Variation on a common theme
 5. Solutions 1
 6. Solutions  2



Maths Circles also have their own new webpage.    Please make sure to check out the 1st year Maths Circles lesson plan Handbook written by Ciaran O’Conaill.

Sample Maths Circle activities: 

Getting Started

Matchstick puzzles:

Pdf     Rtf

Intro to probabilities and combinatorics.                 Pdf     

Logic puzzles, sequential thinking and graphs:   Pdf

Magic circles and sets    Pdf     

Triangular puzzle                  Pdf 

Slicing and guessing- powers of 2   Pdf    

Jumping lizard permutations                         Pdf 

Magic products Pdf  

Symmetry puzzles          Pdf         

Subtraction game   Pdf    

Chess board puzzles Pdf


Angles in triangle

Squares of sums

Multivariable action game

Binary numbers Pdf    


Triangular numbers      Pdf                    

Areas  Pdf

More challenging

Mastermind worksheet

Adding squares, cubes, etc.

Geometry without  compass or right angles




  A good source of nice puzzles, sorted by class: the  Kangaroo contest.              Problems with solutions: the Virtual Maths Club.                    A rich source of Maths puzzles and games, sorted by topic: Cut-the-knot.  

  A directory of e-books on maths games


Maths Circles on the Web: 

MSRI: How to start a math circle

AIM: Math teachers circle network             

The USA National Association of Math Circles             

A nice link  About math circles

 Some sites of maths circles containing problem sets, lesson Lesson plans or other useful information:  Toronto,  Stanford,  Berkeley.


Very rough sketch for lesson plan







Mathematics links

International Mathematical Olympiad   official site
International Mathematical Olympiad  Canadian site
Irish Mathematical Olympiad  

The Art of Problem Solving, including free interactive on-line learning
PRISM - Problem Solving for Irish Second Level.
Hamilton Mathematics Grand Challenge  - online mathematics contest, aimed at secondary school students of all ages.
The British Mathematical Olympiad 
The American Mathematics Competitions
The Canadian Mathematical Society competitions site

Millennium Mathematics Project  based at the University of Cambridge
              -   NRICH, on-line mathematics magazine 
              -   PLUS, on-line magazine featuring applications of mathematics to the sciences, arts, commerce and society
              -   MOTIVATE videoconferencing project for schools

David Joyce’s online version of Euclid’s Elements.

GeoGebra dynamic mathematics software for schools.
A. Bogomolny, Interactive Mathematics Activities from Interactive Mathematics Miscellany and Puzzles








Contact information

Email:  a.mustata@ucc.ie
Mathematics Enrichment Classes organizers:

Current:       Anca Mustata                              tel (021)  420 5852
Previous:      Dr. Donal Hurley                        
                      Professor Finbarr  Holland