Math olympiad blog

Olympiad examinations at school level are competitive examination, based on the school syllabus, which are conducted through various independent organizations.

These exams give exposure to students about competition and make them ready to face any competitive challenge that would be thrown open to them in the future. They also bring out the areas needing attention so that proper orientation can be given in areas lacking prof iciency. In a nutshell, they are a platform for realistic assessment to prepare a child to face the modern competitive world.

Competition is a healthy concept. Competition helps a student to strive for better. It creates a feeling of excitement.

Math Olympiad

Moreover, it leads to success. Without competition, students would be lazy, and they would become incompetent. Competition is good for children. It helps children to develop healthy attitudes about winning and losing.

Children become competitive as they ref ine and practice skills and develop coordination and cognitive abilities. Competition can encourage growth and push a child to excel. When Kid s compete with another Kid s, they work harder, in the process all the students improve their knowledge. The competition should be healthy, not harmful.

There are many Olympiad Examinations are happening all across the year. These exams are conducted through various organizations. To participate in these exams, you need to talk to your school. Most of these exams are conducted through schools only. If you are interested in conducting olympiad exams in your school, please contact the organisers of the exam.Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao.

My student, Jaume de Dioshas set up a web site to collect upcoming mathematics seminars from any institution that are open online. For instance, it has a talk that I will be giving in an hour.

There is a form for adding further talks to the site; please feel free to contribute or make other suggestions in order to make the seminar list more useful. Perhaps further links of this type could be added in the comments. It would perhaps make sense to somehow unify these lists into a single one that can be updated through crowdsourcing.

CA Tags: Kakeya conjecturemultilinear analysismultilinear Kakeya conjecturerestriction theorems by Terence Tao 81 comments. This set of notes focuses on the restriction problem in Fourier analysis.

math olympiad blog

Introduced by Elias Stein in the s, the restriction problem is a key model problem for understanding more general oscillatory integral operators, and which has turned out to be connected to many questions in geometric measure theory, harmonic analysis, combinatorics, number theory, and PDE.

Only partial results on the problem are known, but these partial results have already proven to be very useful or influential in many applications. We work in a Euclidean space. Recall that is the space of -power integrable functionsquotiented out by almost everywhere equivalence, with the usual modifications when.

If then the Fourier transform will be defined in this course by the formula. From the dominated convergence theorem we see that is a continuous function; from the Riemann-Lebesgue lemma we see that it goes to zero at infinity.

Thus lies in the space of continuous functions that go to zero at infinity, which is a subspace of. Indeed, from the triangle inequality it is obvious that. Because of this, there is a unique way to extend the Fourier transform from toin such a way that it becomes a unitary map from to itself. By abuse of notation we continue to denote this extension of the Fourier transform by.

By 23and the Riesz-Thorin interpolation theoremwe also obtain the Hausdorff-Young inequality. One can improve this inequality by a constant factor, with the optimal constant worked out by Becknerbut the focus in these notes will not be on optimal constants. As a consequence, the Fourier transform can also be uniquely extended as a continuous linear map from. The situation with is much worse; see below the fold. The restriction problem asks, for a given exponent and a subset ofwhether it is possible to meaningfully restrict the Fourier transform of a function to the set.

If the set has positive Lebesgue measure, then the answer is yes, since lies in and therefore has a meaningful restriction to even though functions in are only defined up to sets of measure zero. But what if has measure zero? Ifthen is continuous and therefore can be meaningfully restricted to any set. It was observed by Stein as reported in the Ph. Theorem 1 Preliminary restriction theorem If andthen one has the estimate.

In particular, the restriction can be meaningfully defined by continuous linear extension to an element of. Proof: Fix. We expand out. Since the sphere have bounded measure, we have from the triangle inequality that. Also, from the method of stationary phase as covered in the previous class Aor Bessel function asymptotics, we have the decay.Updates on my research and expository papers, discussion of open problems, and other maths-related topics.

By Terence Tao. The actual project will be run on the polymath blog ; this blog will host the discussion threads and post-experiment analysis. After two or three days of somewhat chaotic activity, multiple solutions to this problem were obtained, and have been archived on this page. In the post-mortem discussion of this experimentit became clear that the project could have benefited from some more planning and organisation, for instance by setting up a wiki page early on to try to collect strategies, insights, partial results, etc.

math olympiad blog

Also, the project was opened without any advance warning or prior discussion, which led to an interesting but chaotic opening few hours to the project. About a month from now, the 51st International Mathematical Olympiad will be held in Kazahkstanwith the actual problems being released on July 7 and 8.

Traditionally, the sixth problem of the Olympiad which would thus be made public on July 8 is the hardest, and often the most interesting to solve. So in the interest of getting another data point for the polymath process, I am thinking of setting up another mini-polymath for this question though I of course do not know in advance what this question will be! But this time, I would like to try to plan things out well in advance, to see if this makes much of a difference in how the project unfolds.

So I would like to open a discussion among those readers who might be interested in such a project, regarding the logistics of such a project.

Some basic issues include:. Anyway, I hope that this project will be interesting, and am hoping to get some good suggestions as to how make it an instructive and enjoyable experience for all. NTpaper Tags: international mathematical olympiad by Terence Tao 9 comments. I have now converted the slides from that talk into a more traditional paper 7 pages in lengthfor submission to a Festschrift for the Bremen Olympiad.

The content is much the same as the slides, but some references have been added. COpolymathquestion Tags: international mathematical olympiadmini-polymath1 by Terence Tao comments.

The International Mathematical Olympiad IMO consists of a set of six problems, to be solved in two sessions of four and a half hours each. Traditionally, the last problem Problem 6 is significantly harder than the others. Problem 6 of the IMOwhich was given out last Wednesday, reads as follows:. Problem 6. Let be distinct positive integers and let be a set of positive integers not containing.Math Olympiad questions can seem rather daunting.

So how do you tackle this. Now, start reading the test.

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Whatever approach you are comfortable with is fine. Spend as much time you need on this part. Let me repeat this — read the question carefully and completely. Take careful note of all the values and data provided in the quesion.

Second, keep track of the time. Keep a general idea of how much time you have per question. Then try those. The next tip is on using your spare paper effectively. You could use a grid kind of structure if that helps — but the aim is to use it effectively and neatly. Double check it, and triple check. Do the same thing while copying the answer back. Kids are getting numerous days off school with the holidays, snow days, sick days off.

Everyone needs a break of course, but some kids get sucked into the electronic world of texting, movies, cartoons, and gaming. I have found with my own school aged kids that girls are very much self-motivated to keep on learning.

I actually, banned all electronic games in my household. I encourage my son to work on the things that are giving him the most difficulty right now : writing and math Olympiad. Get the hard things done, hard writing assignments, etc. This holiday we are starting to prep for the Kangaroo Math Olympiad. If you have not heard of this competition, check out the Kangaroo Math site. This is an international math Olympiad that takes place around the world in late March.

Practicing the test questions is a great way to enrich your in-home math curriculum. Math Olympiad questions are on par with international math standards which unfortunately are much more advanced than the U. Thirteen children are playing hide and seek. After a while nine children have been found.

How many children are still hiding? What would the sum of their ages be after one year?So it sure looks that way. My primary agenda is to run a summer program that is good for its participants, and we get funding for N of them. If anything, what I would hope to select for is the people who would get the most out of attending. This is correlated with, but not exactly the same as, score. Anyways, given my mixed feelings on meritocracy, I sometimes wonder whether MOP should do what every other summer camp does and have an application, or even a lottery.

Some reasons I can think of behind using score only:. Honestly, the core issue might really be cultural, rather than an admissions problem.

I wish there was a way we could do the MOP selection as we do now without also implicitly sending the unintentional and undesirable message that we value students based on how highly they scored. You can grab the direct link to the file below:.

My hope is that this can be useful in a couple ways. The other is that the hardness scale contains a very long discussion about how I judge the difficulty of problems. While this is my own personal opinion, obviously, I hope it might still be useful for coaches or at least interesting to read about. I held off on posting this for a few months, but eventually decided to at least try it and see for myself, and just learn from it if it turns out to be a mistake.

But I suspect much of it applies to communicating hard ideas in general. The premise of this post is that understanding math well is largely about having the concept resonate with your S1, rather than your S2.

58th International Mathematical Olympiad (IMO 2017)

Then I claim that. Verifying a solution to a hard olympiad problem by having S2 check each individual step is straightforward in principle, albeit time-consuming. The tricky part is to get this solution to resonate with S1.

Hence my advice to never read a solution line by line. First, giving good concrete examples. Similarly, drawing picturesso your S1 can actually see the object. For example, my Napkin features the following picture of cardinal collapse when forcing. Third, write like you talkand share your feelings. S1 is emotional. These S1 reactions you get are the things you want to pass on. In particular, avoid standard formal college-textbook-bleed-your-eyes-dry-in-boredom style. Even the mechanics on the page can be made to accommodate S1 in this way.

But S1 can pick out section headers, or bolded phrases like this oneand so on and so forth. This way S1 naturally puts its attention there. Usually this ends up in S2 getting tired and not actually reading the proof after the third or fourth iteration. For the Chinese remainder theorem the right thing to do is ask yourself why any arithmetic progression with common difference 7 must contain multiples of 3: credits to Dominic Yeo again for that.

Usually I just ask my friends what is going on, or give up for now and come back later.

math olympiad blog

Because we sure do an awful job of being supportive of the students, or, well, really doing anything at all. Just three unreasonably hard problems each month, followed by a score report about a week later, starting in December and dragging in to April. Here is my commentary for the International Math Olympiad, consisting of pictures and some political statements about the problem.

I thought it might be nice to share on this blog. And since I am not actually director of MOP, the speech was never given. People sometimes ask me, why do we have international students at MOP?Last month the leadership from our student center, Semillitas de Fe Student Center GU in Guatemala City, invited me to come up with a program to encourage our sponsored kids in their academic achievement. A couple of years ago, I taught many of the kids from this student center, and I was excited to be back, even if it was for a little while.

So I asked the Lord for His guidance in prayer. I used to coordinate the spiritual development program at GU and shared lots of time, through lessons, camps and vacation bible study programs, with these kids. I knew them well enough to know that when I ask them for their favorite subject, they say math, over half the time, but also that they often get bored and discouraged with monotonous homework.

Knowing this and having a degree in math and physics myself, I proposed conducting a Math Olympiad for them on August 15, a local holiday, and right in the middle of the Summer Olympics. I wanted to get the kids excited about math and academics in general. I had a great time preparing all the workbooks and problems, diplomas, medals, arranging for the food, inviting the teachers to come and help, and on the morning of August 15 we were ready to serve the 46 kids that showed up to participate 16 boys, 30 girls, ages Families in poverty have no safety net in times of crisis.

Help provide food, medical care and support during this pandemic. I also invited a local doctor to encourage and challenge the kids to study a lot. It was amazing to see these little brothers and sisters of mine, all of whom are sponsored through Compassion, showing up courageously to participate in this event armed with their pencils and erasers and a big smile. We actually conducted two different contests, one for elementary and another for middle school students.

The contest itself lasted around 30 minutes, but the kids stayed for a couple more hours to have some pizza, playtime, and participate in the award ceremony. We started the day in prayer and reminded them that this was just a contest, as we tried to help ease any nervousness among them. After the contest, every child was recognized with a certificate of participation. And during the award ceremony, they all also got a chance to hear from this young doctor who grew up in the community and at this church.

Finally, the top 12 scorers were called to the front to receive their medals and diplomas. Then we sung the national anthem. It was a moving time for the teachers.

We congratulated all the kids and once again encouraged them to study their math and give their best at their schools. We closed with our theme verse for the event, which was also printed in the diplomas and certificates — Mark NIV.

Then in prayer we thanked the Lord for the experiences of the day and for all the sponsors who funded this event, and asked Him for His blessing upon all of us.

Since the Olympiad we have heard testimonies of parents in disbelief when their kids showed up at home with a medal.Updates on my research and expository papers, discussion of open problems, and other maths-related topics.

What's new

By Terence Tao. The actual project will be run on the polymath blog ; this blog will host the discussion threads and post-experiment analysis. After two or three days of somewhat chaotic activity, multiple solutions to this problem were obtained, and have been archived on this page.

In the post-mortem discussion of this experimentit became clear that the project could have benefited from some more planning and organisation, for instance by setting up a wiki page early on to try to collect strategies, insights, partial results, etc. Also, the project was opened without any advance warning or prior discussion, which led to an interesting but chaotic opening few hours to the project. About a month from now, the 51st International Mathematical Olympiad will be held in Kazahkstanwith the actual problems being released on July 7 and 8.

Traditionally, the sixth problem of the Olympiad which would thus be made public on July 8 is the hardest, and often the most interesting to solve.

So in the interest of getting another data point for the polymath process, I am thinking of setting up another mini-polymath for this question though I of course do not know in advance what this question will be! But this time, I would like to try to plan things out well in advance, to see if this makes much of a difference in how the project unfolds.

So I would like to open a discussion among those readers who might be interested in such a project, regarding the logistics of such a project.

Some basic issues include:. Anyway, I hope that this project will be interesting, and am hoping to get some good suggestions as to how make it an instructive and enjoyable experience for all. NTpaper Tags: international mathematical olympiad by Terence Tao 9 comments.

I have now converted the slides from that talk into a more traditional paper 7 pages in lengthfor submission to a Festschrift for the Bremen Olympiad. The content is much the same as the slides, but some references have been added. COpolymathquestion Tags: international mathematical olympiadmini-polymath1 by Terence Tao comments.

The International Mathematical Olympiad IMO consists of a set of six problems, to be solved in two sessions of four and a half hours each. Traditionally, the last problem Problem 6 is significantly harder than the others. Problem 6 of the IMOwhich was given out last Wednesday, reads as follows:. Problem 6. Let be distinct positive integers and let be a set of positive integers not containing. A grasshopper is to jump along the real axis, starting at the point and making jumps to the right with lengths in some order.

Prove that the order can be chosen in such a way that the grasshopper never lands on any point in. I myself worked it out about seven hours after first hearing about the problem, though I was preoccupied with other things for most of that time period. To keep with the spirit of the polymath approach, I would however like to impose some ground rules:. Blog at WordPress. Ben Eastaugh and Chris Sternal-Johnson. Subscribe to feed. What's new Updates on my research and expository papers, discussion of open problems, and other maths-related topics.


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