
The Irish Mathematical Trust
![]() DSC_4122 | ![]() honeycomb | ![]() IMO2013 | ![]() Formula Mathematics Equation Mathematical Symbol Geometry Information Concept | ![]() Irish_IMO_team_2014 | ![]() rectified_icosahedral_honeycomb |
---|---|---|---|---|---|
![]() EGMO2017IrishTeam | ![]() MurlHoleSurfaceKnot-large | ![]() IMO2019Flags |
Welcome to Mathematics Enrichment Ireland!
This programme was first offered online in 2021 and consists of weekly video-lessons and problem sets, which can now be used for individual study at any time. You can also send your written solutions to the lecturers who offered each lesson for feedback.
The beginner level and Geometry lessons can be used as first steps in preparation for the Irish Mathematical Olympiad (IrMO) which usually takes place annually in early May and for the EGMO selection test and local olympiads which usually take place in Feb-March in Mathematics Enrichment Centres around the country. The Geometry and advanced level lessons are useful first steps in preparing for international competitions like the International Mathematical Olympiad (IMO) and the European Girls Mathematical Olympiad (EGMO).
The Mathematics Enrichment Ireland online is a collaborative project of Mathematics Enrichment centres across the country:
NUI Galway, Maynooth University, University College Cork, University College Dublin, University of Limerick, Sligo Institute of Technology,
as well as by former members of team Ireland at the International Mathematical Olympiad and other members of the Irish Mathematical Trust. We hope you may use these materials as complements to the live lessons taking place every Spring in the centres listed above.
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9
Week 10
Week 11
Week 12
Welcome!
We will start the online Mathematics Enrichment Programme with a weekly course on Geometry, suitable for both beginners and more advanced students. The course will run weekly for the duration of 12 weeks. The problem sets are essential for progress. Try them! The starred problems are aimed at the more advanced students.
In the following weeks, more varied Maths Topics will be added for the beginner and advanced levels.
Geometry:
​
-
Lecturer: Anca Mustata, (UCC). Send your written solutions to a.mustata@ucc.ie.
-
Preliminaries: Here is a short video Introduction. Here are some first tips on how to build a proof. Here are a Preliminary Problem Set and Sample Solutions.
-
Learn: Lesson on parallelograms: video and slides and lesson on applications: video and slides.
-
Solve: Please practice on this Problem Set. Try at least 3 problems by yourself. Problem solutions sample 1 and sample 2.
-
Problem Solving Meeting: Solutions for Q1, Q2, Q10 video and slides, Solutions for Q6, Q12 video and slides.
​
Notes on video quality: To watch the videos online, you might be prompted to download an app first. If you experience sound or image problems:​
-
To play full-screen, click Fullscreen [ ] in the bottom right.
-
To adjust image quality while playing the video, in the bottom right Options, choose 480p or try other options to find the ideal one.
-
If the sound quality is poor, you might want to turn volume up to max.
​
Geometry for General Maths Enrichment and the Irish Squad:
​
-
Lecturer: Anca Mustata (UCC). Send your written solutions to a.mustata@ucc.ie.
-
Learn: Important lines and centre in a triangle: video 1, video 2 and slides.
-
Solve: Please practice on this Problem Set. Try at least 3 problems by yourself. Problem solutions sample 1.
-
Problem Solving Meeting: Here is the video and here are the slides: sample 2.
​
Combinatorics for beginners:
-
Learn: Introduction to Counting video 1, video 2 and Inclusion-Exclusion: video 1, video 2 and slides for all lessons.
-
Solve: Please practice on this Problem Set.
​
Combinatorics for the advanced level:
​
-
Lecturer: Mark Flanagan (UCD)
-
Online resources: Viktoria Krakovna's handout VK, Yufei Zhao's handout YZ,
-
Solve: Please attempt Problems 8 in handout YZ, Problem 2 in handout VK, and Problem 11 in handout YZ. Homework hints/solutions.
-
Problem Solving Meeting: Submit your solutions to mark.flanagan@ucd.ie.
​
​
​
​
​
​
Geometry:
​
-
Lecturer: Anca Mustata (UCC). Send you written solutions for feedback to a.mustata@ucc.ie
-
Learn: Special configurations in a triangle: Euler's Line video 1, Incentre-Excentres video 2 and slides for both lessons.
-
Solve: Please practice on this Problem Set. Try at least 3 problems by yourself. Problem solutions sample 1.
-
Problem Solving Meeting: Here is the video and here are the slides: sample 2.
​
Number Theory for beginners:
​
-
Lecturers: Mayya Golitsyna (UCD).
-
Learn: GCD and Euclid's Algorithm. Here are the class notes-start @page 5.
-
Solve: Please work on the problems on the last page of this handout.
-
Problem Solving Feedback: Please submit your solutions to mayya.golitsyna@ucdconnect.ie or by telegram app on the number 0861007821 for written feedback.
​
Number Theory for the advanced level:
​
-
Lecturer: David Malone (Maynooth)
-
Solve: The homework Problems can be found in Alexander Remorov's notes. Here are some hints.
-
Problem Solving Feedback: Please submit your solutions to David.Malone@mu.ie for written feedback.
​
​
​
​
​
Geometry:
​
-
Lecturer: Anca Mustata (UCC). Send you written solutions for feedback to a.mustata@ucc.ie
-
Learn: Circles: video 1 on chords, arcs and angles and notes; video 2 on cyclic quadrilaterals, and notes.
-
Solve: Please practice on this Problem Set. Hints for all problems are on page 3. Problem solutions sample 1.
-
Problem Solving Meeting: Here are the slides: sample 2.
​
Algebra for beginners:
​
-
Lecturer: Myrto Manolaki (UCD).
-
Learn: Introduction to Induction and Recurrence video (Passcode: uLvd=+7G) and notes, ​
-
Resources: Intro video, slides and Tower of Hanoi game, Induction video by Zach Starr,
-
Solve: Homework Problem Set.​
-
Problem Solving Feedback: Please submit solutions to Myrto Manolaki at myrto.manolaki@ucd.ie.
​
Algebra for the advanced level:
​
-
Lecturer: Myrto Manolaki (UCD).
-
Learn: Advanced Induction video (Passcode: e.n3L29c) and notes. ​
-
Resources: Goldbach conjecture.
-
Solve: Homework Problem Set.​
-
Problem Solving Feedback: Please submit solutions to Myrto Manolaki at myrto.manolaki@ucd.ie.
​
​
​
​
​
Geometry:
​
-
Lecturer: Anca Mustata (UCC). Send your written solutions to a.mustata@ucc.ie.
-
Learn: video 1, notes 1: tangents, video 2: circle configurations, video 3: complete quads, video 4: starred pentagons; notes 2-4.
-
Solve: Please practice on this Problem Set. See sample solutions 2.
-
Problem Solving Meeting: Here is the video and here are the slides: solutions1.
​
Combinatorics for beginners:
​
-
Lecturers: Jessica Weitbrecht (AIMS).
-
Learn: nPk,nCk: intro video, video 1, video 2, video 3, video 4 and notes for all videos.
-
Solve: Please practice on this Problem Set. First watch the introduction video, then do all of Question 1. Then watch video 1. Then do Question 2, then watch video 2 etc.
​
Combinatorics for the advanced level:
​
-
Lecturer: Mark Flanagan (UCD)
-
Online resources: Here are the Example Problems discussed in the videos. Here are additional notes by David Arthur.
-
Solve: Here is the Homework Problem Set. Submit your solutions by Saturday 20 March to mark.flanagan@ucd.ie.
-
Problem Solving Meeting: A live Zoom session was held on Saturday 27th March. Here is homework problems solutions/feedback.
​
​
​​
​
​
​
​
Geometry:
​
-
Lecturer: Anca Mustata (UCC). Send your written solutions to a.mustata@ucc.ie.
-
Learn: video 1, notes 1 on use of Areas; video 2, notes 2 on Sines and Ceva's Theorems.
-
Solve: Please practice on this Problem Set. See sample solutions 1.
-
Problem Solving Meeting: Here is the video and here are the slides.
​
Number Theory for beginners:
​
-
Lecturer: Andrew Smith (UCD)
-
Learn: Modular Arithmetic notes.
-
Solve: Practice on this Problem Set.
​
Number Theory for the advanced level:
​
-
Lecturers: John Murray (Maynooth) and Seoirse Murray (Cambridge)
-
Learn: Quadratic Reciprocity: video 1 and notes 1. Using Quadratic Residues in some Olympiad problems video 2 and notes 2 Jacobi symbols and more problems: video 3 and notes 3.
-
Online resources: These notes by P. Stoienescu and T.D.Popescu also include examples and a problem set.
-
Problem Solving: For written feedback, please send your solutions to John.Murray@mu.ie
​
​
​
​
​
​
​​
​
Geometry:
​
-
Lecturer: Anca Mustata (UCC). Send your written solutions to a.mustata@ucc.ie.
-
Learn: The Power of a Point wrt a Circle: video and notes. Radical Axes: video and notes.
-
Solve: Please practice on this Problem Set. See sample solutions 1.
-
Problem Solving Meeting: Here is the video and here are the slides.
​
Algebra for beginners:
​
-
Lecturer: Eugene Gath (UL).
-
Learn: Introduction to Inequalities: video 1, video 2, video 3 snd video 4. Here are the notes: part I and part II.
-
Solve: Please practice on this Problem Set.
-
Problem Solving Feedback please submit your solutions to eugene.gath@ul.ie for feedback.
​
Algebra for the advanced level:
​
-
Lecturer: Andrew Smith (UCD)
-
Learn: Functional Equations notes.
-
Resources: Notes and problem sets by Evan Chen, James Rickards, David Arthur.
​
​
​​
​
Geometry:
​
-
Lecturer: Anca Mustata (UCC). Send your written solutions to a.mustata@ucc.ie.
-
Learn: The Power of a Point is so great in Olympiad geometry that it's worthwhile spending another week on it. Please review the video lectures from last week: The Power of a Point wrt a Circle: video and notes. Radical Axes: video and notes.
-
Resources: Yufei Zhao's notes and problems.
-
Solve: Please practice on this Problem Set. Please send solutions to a.mustata@ucc.ie.
-
Problem Solving Meeting: Here is the video and here are the slides.
​
​
Notes on video quality: By now you have probably played some of our videos online. If you experience sound or image problems:​
-
To play full-screen, click Fullscreen [ ] in the bottom right.
-
To adjust image quality while playing the video, in the bottom right Options/Settings, choose 720p or 480p or try options to find the ideal one.
-
If the sound quality is poor, you might want to turn volume up to max.
​
​Calculus and Combinatorics for Advanced level
-
Lecturer: Finbarr Holland (UCC Emeritus)
-
Learn and Solve: Lecture notes with problems.
​
​
Geometry:
​
-
Lecturer: Anca Mustata (UCC). Send your written solutions to a.mustata@ucc.ie.
-
Learn: Isogonal Pairs video and notes. Symmedian: video and notes.
-
Solve: Try at least 3 problems from Yufei Zhao's problem set below.
-
Resources: Yufei Zhao's notes and problems.
-
Problem Solving Meeting: Here are the slides.
​
Algebra for beginners:
​
-
Lecturer: Mark Fortune (TCD).
-
Learn: Factorisation problems: video 1, video 2, Rearrangement: video 3 Factorisation formulas: video 4. Here are the notes
-
Solve: Please practice on this Problem Set.
-
Problem Solving Feedback please submit your solutions to fortunma@tcd.ie for feedback.
​
Algebra for the advanced level:
​
-
Lecturer: Jonathan Grant Peters (Oxford).
-
Learn: Jensen's Inequality. Here are the lesson slides.
-
Solve: Please practice on this Problem Set.
-
Problem Solving Feedback: Send your written solutions to jonathan@peters7.net.
​​
​​
​
​
​
​
​
​
Geometry:
​
-
Lecturer: Andrei Mustata (UCC).
-
Resources: IMO Math page on Inversion.
-
Solve: Please practice on this Problem Set.
-
Problem Solving Feedback: For written feedback, please send solutions to a.mustata@ucc.ie or andrei.mustata@ucc.ie.
​
​
Number Theory for beginners and advanced level:
​
-
Lecturer: Rob Sparkes (Cambridge).
-
Learn: Diophantine Equations handout.
-
Solve: included in the notes above.
-
Resources: For background reading on Linear Diophantine Equations, see here and here. You may also review the Week 3 notes on Euclid's algorithm.
-
Problem Solving Feedback: For feedback, email your written solutions to robertsparkes@live.ie
​
Geometry:
​
-
Lecturer: Anca Mustata (UCC). Send your written solutions to a.mustata@ucc.ie.
-
Learn: Homothety: video, Menelaus' Theorem video and notes. Spiral similarity: video and notes.
-
Solve: Please practice on this Problem Set.
-
Resources: Yufei Zhao's notes and problems. Mathematical Excalibur Homothety problems
-
Problem Solving Meeting: Here is the video and here are the slides.
​
Number Theory for beginners:
​
-
Lecturers: Seoirse Murray (Cambridge) and John Murray (Maynooth).
-
Online resources: These notes by Evan Chen also include examples and a problem set.
-
Problem Solving: For written feedback, please send your solutions to murray@seoire.net or John.Murray@mu.ie
​
​​
Number Theory for the advanced level:
​
-
Lecturer: Kazim Buyukboduk (UCD)
-
Learn: Here are the notes.
​
​
Geometry:
​
-
Lecturer: Tianyiwa Xie (Cambridge).
-
Learn: Orthocentre configurations: handout.
-
Solve: Please practice on this Problem Set.
-
Problem Solving Feedback: For written feedback, please send solutions to a.mustata@ucc.ie or andrei.mustata@ucc.ie.
​
Combinatorics for beginners and advanced level:
​
-
Lecturer: Adam Kelly (Cambridge).
-
Learn: Introduction to Graphs: handout. Hall's theorem: handout.
-
Solve: The problems are included at the end of each handout.
-
Problem Solving Feedback: For written feedback, please send solutions to ak2316@cam.ac.uk.
​
To prepare for the Irish Mathematical Olympiad: study our lessons in weeks 1-12 above, and try to work on as many problems as possible. If you would like feedback on your solutions or if you are unsure on how to proceed with a specific problem, please do not hesitate the contact the lecturers at the addresses provided. You can find more information including past IrMO papers on the IrMO website.