Real Olympiads versus Fake Olympiads: Recommended by Cheenta

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Mathematical Olympiads began with a noble objective: promote non-routine problem solving and a culture of research among school students. The real International Math Olympiad is a 9 - hour marathon examination consisting of only 6 problems. Here is an example of a problem from IMO 2023. Notice its difference from the 'multiple choice problems' found in hundreds of so called private olympiads that operate all around the world.

IMO 2023, Problem 1.

Determine all composite integers $n>1$ that satisfy the following property: if $d_1, d_2, \ldots, d_k$ are all the positive divisors of $n$ with $1=d_1<d_2<\cdots<d_k=n$, then $d_i$ divides $d_{i+1}+d_{i+2}$ for every $1 \leqslant i \leqslant k-2$.

How can I participate in the real IMO?

In order to qualify for IMO, a student goes through a rigorous, multi-step process. These steps are different in every country. For example, India has a 4 step process:

  1. IOQM [Starts at 8th grade]
  2. RMO [For those who qualify in IOQM]
  3. INMO [For those who qualify in RMO]
  4. IMO Training Camp

At the end of this 4-step process, only 6 students from India are sent to the actual International Math Olympiad.

Similarly, the United States has a 4 step process:

  1. American Math Competition 10 or 12
  2. AIME
  3. USAMO / USAJMO
  4. MOSP

What topics are tested in the real math olympiads?

Mathematical Olympiads test ingenuity and problem solving skill of young mathematicians. This is usually developed over several years, through consistent hard work. In particular, the problems are derived from the following four areas of pre-college mathematics.

  1. Number Theory
  2. Geometry
  3. Algebra
    • Polynomials
    • Complex Numbers
    • Functional Equations
    • Inequalities
  4. Combinatorics

What contests are recommended in elementary school or middle school if I am not ready for real IMO?

The rule of the thumb is: go for olympiads created by real mathematicians, who are usually part of Mathematical Teacher's Association of a particular country. Here are some of the recommended contests:

India (upto Grade 7 --> After that you should focus on IOQM)
  • NMTC Contests
  • Australian Math Competition
  • Math Kangaroo
  • American Math Competition 8
United States (upto Grade 7 --> After that you should focus on AMC 10)
  • Australian Math Competition
  • Math Kangaroo
  • American Math Competition 8
  • MOEMS
  • University of Waterloo Contests
United Kingdom
  • UKMT
  • American Math Competition 8
  • University of Waterloo Contests
Why should you avoid other private olympiads?

There are hundreds of private olympiads run by publishing houses and coaching centers who are interested in selling books and courses. They have created their own contests. They use the buzzword 'olympiad', 'imo' to lure students and parents. Unfortunately these private contests add little to no value to a student's academic development. In order to become popular they keep the difficulty level of their questions quite low. Students who do well in those poor-quality problems, are handed out with gold and silver medals (certainly if your child gets a 'gold' in so-and-so 'olympiad', chances are, you will spread the word).

In most cases the private olympiads play a negative role. Since most of the problems in a private contest requires the students to remember some extra formulae, it defeats the central philosophy of the real mathematical olympiads: to think out-of-the-box. We often hear a third grader's parent boasting, 'my child knows tenth grade math'. However when challenged with some non-routine problem from their own standard, these students fumble desperately. Indeed the private olympiads can change the focus of a student from ingenuity to rote learning.

Another issue that often comes up is this: students who received 'gold' and 'silver' in the private competitions, develop a false sense of complacency. They lose valuable time for preparation for the real contests. When faced with the real olympiads, they find themselves completely unprepared.

What books should you follow for real math olympiad preparation?
  • Math Circle by the Bay: Topics for Grades $1-5$ by Ilya Zakharevich, Laura Givental, and Maria Nemirovskaya
  • Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers by Alexander K. Zvonkin Mathematics can be fun by Yakov Perelman
  • Math Circles for Elementary School Students by Natasha Rozhkovskaya
  • Mathematical Circles: (Russian Experience) by Dmitrii Vladimirovich Fomin, Ilia Itenberg, and Sergei Aleksandrovich Genkin
  • Algebra by Alexander Shen and Israel Gelfand
  • Kiselev's Geometry: Planimetry by Alexander Givental
  • Challenge and Thrill of Pre-College Mathematics by C. R. Pranesachar and V Krishnamurthy
  • An Excursion In Mathematics. by M. R. Modak
  • Trigonometry by Israel Gelfand and Mark Saul
  • Complex Numbers from A to …Z by Dorin Andrica and Titu Andreescu Euclidean Geometry in Mathematical Olympiads by Evan Chen Principles and Techniques in Combinatorics by Chuan Chong Chen and KOH KHEE MENG
  • Secrets in Inequalities by Pham Kim Hung
  • Functional Equations by Venkatachala Test of Mathematics at the 10+2 Level by East West Press (useful for ISI-CMI Entrances.Polynomials by Edward Barbeau
Watch more videos on this topic.

Fake versus real Math Olympiads. Let's Talk Math

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4 comments on “Real Olympiads versus Fake Olympiads: Recommended by Cheenta”

  1. I disagree with some points.

    1.I don't think that the objective of Mathematical Olympiads is to promote a culture of research among school students. Actual math research and Olympiads are very different. Indeed, if that were true, all IMO (the real one) participants would go on to do research in math, but we know that is not the case. If I were forced to compare them to research, I would say that Olympiads are more of an Erdős approach than a Grothendieck one.

    2. Just pointing some small errors:
    The IMO (real one) is not a marathon examination; it is split over two days, with 4 and a half hours each day, which is 9 hours in total.
    The abbreviation MOSP is no longer official; the program has been MOP from 2017.

    3. This one is more personal, but I would not recommend Challenges and Thrills for 9-12. The choice of problems in it is quite wild; it will suddenly jump from trivial school-level to "i-have-no-clue-how-to-start" level without warning if you're a beginner. The theory is also quite unpolished and is arranged in an awkward way (for instance, Radical axes should be mentioned in the circles chapter, but they are mentioned in the circles section in the Coordinate Geometry chapter. While the proof of the existence of radical axes uses coordinates, they have more synthetic applications than analytic ones). Moreover, a lot of the exercise problems are really bashy and uninstructive, which is not expected from a math Olympiad book. There are better books, and their PDFs can be easily obtained online for free if you do not want to buy them.

    Other than these, I wholeheartedly agree with this message and we should definitely discourage participation in private Olympiads and promote the real ones. This will help to flourish a culture of mathematics in the country.

  2. Surprised you haven't recommended the AOPS books given they are specially designed for students who are preparing for Maths contest - AMCs in particular.

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