UKMT maths challenges - how to?

It's a great achievement to get to BMO2. BMO2 only has four questions rather than six.

DS is thrilled to have gotten through to the Kangaroo round too, he scored 96!

Well done to the ones that got through, DS is pleased he is through to kangaroo.

Mine said he got high 90s, said he will go through with the next round (I assume it's optional) but not do any dedicated prep, I can live with that.

@Foxhasbigsocks yes, the old papers, and the answers, usually with worked solutions, will be available online. Make sure you get the Kangaroo that follows on from the JMC. Think the others have colours to distinguish them (pink and grey??).

It's very similar in style to the paper he's just sat just starts a bit harder!!

I think my Y 7 ds has been told he has gold and through to Kangaroo. He’s quite an anxious young man and I was a bit worried about him doing the Junior Challenge. What’s the best way to familiarise with Kangeroo to try to make it less daunting. Is it to just do past papers?

Again, I don’t think you followed the conversation. Their kids stopped there in the competition because they didn’t train/practise for it. But to go further in any competitions, they need to work hard for it.

some kids take these competitions as a bit of fun/challenge or because they have and that is fine. Others take them seriously and train for them and that is fine too. People should not judge the second group because their own kids do not care/got no where or that’s the limit of their ability.

Should have written: attempted 3 problems out of 6 and did not get any full mark for BMO2. The best thing about Olympiad is once you know the solution there is also an “art” to present it in the most concise, creative and new thinking.

It is possible to have loads of busy hobbies and still be able to be qualified for BMO from year 10.

Terence Tao on math competitions.

"I greatly enjoyed my experiences with high school mathematics competitions (all the way back in the 1980s!). Like any other school sporting event, there is a certain level of excitement in participating with peers with similar interests and talents in a competitive activity. At the Olympiad levels, there is also the opportunity to travel nationally and internationally, which is an experience I strongly recommend for all high-school students.

"Mathematics competitions also demonstrate that mathematics is not just about grades and exams. But mathematical competitions are very different activities from mathematical learning or mathematical research; don’t expect the problems you get in, say, graduate study, to have the same cut-and-dried, neat flavour that an Olympiad problem does. (While individual steps in the solution might be able to be finished off quickly by someone with Olympiad training, the majority of the solution is likely to require instead the much more patient and lengthy process of reading the literature, applying known techniques, trying model problems or special cases, looking for counterexamples, and so forth.)

"Also, the “classical” type of mathematics you learn while doing Olympiad problems (e.g. Euclidean geometry, elementary number theory, etc.) can seem dramatically different from the “modern” mathematics you learn in undergraduate and graduate school, though if you dig a little deeper you will see that the classical is still hidden within the foundation of the modern. For instance, classical theorems in Euclidean geometry provide excellent examples to inform modern algebraic or differential geometry, while classical number theory similarly informs modern algebra and number theory, and so forth. So be prepared for a significant change in mathematical perspective when one studies the modern aspects of the subject. (One exception to this is perhaps the field of combinatorics, which still has large areas which closely resemble its classical roots, though this is changing also.)

"In summary: enjoy these competitions, but don’t neglect the more “boring” aspects of your mathematical education, as those turn out to be ultimately more useful."

A different way of phrasing it might be that the material you cover in A Levels isn't particularly useful for the IMO. The facts you learn for GCSE are sufficient - if you really know how to apply them.

That said, a deep corpus of knowledge in the relevant areas of math really helps but you don't cover that in A Levels.

Terence Tao stopped doing the IMO because he lost eligibility when he enrolled in university. Before that, he'd participated for three years, which is more than the vast majority of kids who make it that far, plenty of time to burn out if IMO participation really causes that. Also, while he is of Chinese descent, he was educated in the Australian system, although I suspect he learned very little math in it.

Your DD sounds fantastic! Would be nice to know how she got on with JMC this year, participating in a challenge with children who are years older than her. Her school is very supportive!

Hello ChatGPT!

For BMO2, you must love it, my daughter could try to work out one single problem the whole week. It is NOT repetitive training. The BMO2 was very challenging this year, she attempted 3 and didnt get any full mark. In fact, it is not possible to train for BMO2 or IMO if the kids dont love them. It requires many hours deep thinking about ONE problem. That is what she loves the most.

to add to your excellent data gathering process: Ds (who is now studying maths and comp sci) did these - gold, got through to Olympiad, although silver ‘only’ at sixth form iirc, although he did well in step. He practiced a few past papers in class I think, and did a lot of programming/comp sci type maths for fun, but nothing else.

Following

DS is older now, and a Maths grad just finishing his Masters. He was a gifted Mathematician and used to love UKMT challenges - he was naturally drawn to the problem solving style. For him, practicing questions after he finished classwork was what kept him interested but there is a definite 'style' once you reach Kangaroo or Olympiad which I think are probably inaccessible other than to dc with a strong interest in Maths.
DS's view is that they are a great challenge that everyone should be encouraged to participate in as generally they can support greater depth in mathematical learning. And that learning can be applied to dc who want to go on and take the MAT or STEP papers. His proudest moment was reaching Senior BMO 02 and having a solution published.

The International Mathematical Olympiad (IMO) covers four main fields: number theory, combinatorics, geometry, and algebra. IMO primarily assesses problem-solving techniques rather than mere knowledge, unlike GCSE and A-level maths. Even university maths graduates may not necessarily be able to solve a single one of the six IMO questions. While these topics are included in GCSE maths, it's doubtful that many who got 9 could tackle a BMO2 question, let alone an IMO question.

IMO only need GCSE-level knowledge.

IMO aka International Maths Olympiad only needs GCSE-level knowledge? You must be joking. Have a look at past problems and guess what percentage of those who get 9 at GCSE Maths can understand the problems, let alone solve them.

and that’s why they stopped there Don't agree this. A kid has different way to progress to a good mathematician.

Not sure what your point was or if you were following the conversation. I have done enough IMO training and maths to a reasonable level to know the difference between the two.

Certainly, those who excel in the IMO are likely to thrive in their careers, as typically only around two or three newcomers are able to join the national IMO team each year. They represent the pinnacle of mathematical talent, after all.

I agree that not all young mathematicians are interested in competitions like the IMO, just as not all athletes/sports participants aim for the Olympics. However those who do dream of such achievements need to train hard to succeed. Challenges like the JMC, IMC, and SMC are there to get more students into math, not just to prepare for the IMO. Being good at the IMO isn’t necessary to be a great mathematician, since it focuses on quick problem-solving. But many who do well in the IMO succeed in careers where they use math and logic. And many also successfully in mathematics research career too.

That's my point. IMO only need GCSE-level knowledge. I wonder if it's worth spending so much time training for that. It may be beneficial for children who enjoy competition, but not for all young mathematicians.

That just shows IMO and Fields are very different thing. T Tao has start his maths rigorous training as early as 5 years old when his parents his parents discovered his prodigious talent in maths. He started attending university-level mathematics courses at the age of 9 before he participate in IMO.