Maths Olympiad: theory building and problem solving from junior to intermediate

Can you solve a difficult problem about something which you've only just been introduced to?

That's a key skill for mathematicians: to be able to step by step relate the unknown to what is familiar. In this book we familiarise ourselves with certain core high school topics, such as Algebra, Number Theory, Geometry and Combinatorics which are at the heart of the math Olympiad curriculum, not just to memorise them but to build theory profoundly and to gain skill in the art of investigation and familiarisation. Part of this involves the tackling of challenging problems that one might initially have no idea how to solve but eventually after exploring many approaches and making many observations one reaches a solution. One might then cap it off by writing an elegant proof of the discovery!

There are also QR codes and links to playlists that are designed to keep the book alive in terms of updates, feedback, supplements and other extra materials to help the reader.

Contents

• Preface
• Introduction
• Chapter 1. Combinatorics I: Choices and Probability
• Chapter 2. Number theory I: Bases and Modular Arithmetic
• Chapter 3. Algebra I: Factorisation and Expansion
• Chapter 4. Geometry I: Circumcircles and Incircles
• Chapter 5. Examples of Proofs
• Chapter 6. Number theory II: Linear (Diophantine) equations
• Chapter 7. Combinatorics II: Graph theory
• Chapter 8. Algebra II: Trigonometry and Complex numbers
• Chapter 9. Geometry II
• Chapter 10. Maths Olympiads
• Chapter 11. More exams and preparation materials
• Index
• Bibliography

About the Author

Dr Sun received his M.Sc in Sydney, his PhD in the USA, completed postdoctoral research in Germany and did research in China, publishing his work along the way in top research journals, before returning to Australia where he now lives with his wife and three children in Carlingford NSW teaching students who love maths.

Dr Michael Sun's school of maths uses the AIMO as its end of term 3 exam to assess its Junior and Intermediate students externally (hosted by their day schools), and since 2018 his students have achieved 7 Perfect scores, 9 Prizes and numerous High Distinctions and Distinctions, with Prizes or better accounting for almost all of the year 10 graduates from the Junior/Intermediate program of the school. Many students have received invitations into the national training program for math Olympiads and some have even been selected to represent Australia at the International Maths Olympiad, including Haibing Wang who was the only NSW member of the Australian team in 2021.