Lớp 9 năm học 2022-2023: Một số đề luyện tập

Trong bài này tôi sẽ giới thiệu một số đề luyện tập cho học sinh lớp 9 năm học 2022-2023.

Học sinh lớp 8 có thể làm được cả 4 bài trong đề này.

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The Trifference Problem January 23, 2023

Originally posted on Anurag's Math Blog: What is the largest possible size of a set of ternary strings of length , with the property that for any three distinct strings in , there is a position where they all…

Gil Kalai

Greatest Hits 2015-2022, Part II January 5, 2023

This is the second part of Greatest Hits 2015-2022, Part I. Here are popular and favorite posts published in 2019-2022. 2019 Supremacy and Sensitivity (and Sunflowers) Test your intuition 38 was contributed in March 2019 by my youngest son Lior. … Continue reading →

Gil Kalai

Greatest Hits 2015-2022, Part I January 1, 2023

In February 2015 I wrote a post on the blog’s greatest hits in the first seven years, and its time to write a similar post for the eight years that followed. Quick updates: In recent months I took part in … Continue reading →

Gil Kalai

Tel Aviv University Theory Fest is Starting Tomorrow December 25, 2022

Tel Aviv University Theory Fest, December 26-December 28 2022. Cryptography workshop @ TAU TheoryFest December 29, 2022 TAU 2022 TheoryFest, December 26-28, 2022 The Theory of Computing was born as a purely mathematical investigation into the notion of computation. From … Continue reading →

Gil Kalai

Alef’s Corner December 19, 2022

Gil Kalai

A Nice Example Related to the Frankl Conjecture November 30, 2022

Update: Peter Frankl brought to my attention that the very same example appeared in a paper by Dynkin and Frankl “Extremal sets of subsets satisfying conditions induced by a graph“. The example As a follow up to my previous post … Continue reading →

Gil Kalai

Amazing: Justin Gilmer gave a constant lower bound for the union-closed sets conjecture November 17, 2022

Frankl’s conjecture (aka the union closed sets conjecture) asserts that if is a family of subsets of [n] (=: ) which is closed under union then there is an element such that Justin Gilmer just proved an amazing weaker form … Continue reading →

Gil Kalai

Barnabás Janzer: Rotation inside convex Kakeya sets November 16, 2022

Barnabás Janzer studied the following question: Suppose we have convex body in that contains a copy of a convex body in every orientation. Is it always possible to move any one copy of to another copy of , keeping inside … Continue reading →

Gil Kalai

Inaugural address at the Hungarian Academy of Science: The Quantum Computer – A Miracle or Mirage November 5, 2022

(Picture: János Pach) The Quantum Computer – A Miracle or Mirage inaugural address of Gil Kalai honorary member of the MTA, Budapest, 15 June, 2022, 15:00 Abstract: On February 12, 2002, Michel Devoret’s lecture entitled “The Quantum Computers: Miracle or … Continue reading →

Gil Kalai

Remarkable: “Limitations of Linear Cross-Entropy as a Measure for Quantum Advantage,” by Xun Gao, Marcin Kalinowski, Chi-Ning Chou, Mikhail D. Lukin, Boaz Barak, and Soonwon Choi October 25, 2022

In this post I would like to report about an important paper (posted Dec. 2021) by Xun Gao, Marcin Kalinowski, Chi-Ning Chou, Mikhail D. Lukin, Boaz Barak, and Soonwon Choi. (I am thankful to Xun Gao and Boaz Barak for … Continue reading →

Gil Kalai

Terence Tao

Infinite partial sumsets in the primes January 26, 2023

Tamar Ziegler and I have just uploaded to the arXiv our paper “Infinite partial sumsets in the primes“. This is a short paper inspired by a recent result of Kra, Moreira, Richter, and Robertson (discussed for instance in this Quanta article from last December) showing that for any set of natural numbers of positive upper […]

Terence Tao

Illustrating the Impact of the Mathematical Sciences January 12, 2023

Over the last few years, I have served on a committee of the National Academy of Sciences to produce some posters and other related media to showcase twenty-first century and its applications in the real world, suitable for display in classrooms or math departments. Our posters (together with some associated commentary, webinars on related topics, […]

Terence Tao

Special relativity and Middle-Earth December 19, 2022

This post is an unofficial sequel to one of my first blog posts from 2007, which was entitled “Quantum mechanics and Tomb Raider“. One of the oldest and most famous allegories is Plato’s allegory of the cave. This allegory centers around a group of people chained to a wall in a cave that cannot see […]

Terence Tao

An improvement to Bennett’s inequality for the Poisson distribution December 13, 2022

If , a Poisson random variable with mean is a random variable taking values in the natural numbers with probability distribution One is often interested in bounding upper tail probabilities for , or lower tail probabilities for . A standard tool for this is Bennett’s inequality: Proposition 1 (Bennett’s inequality) One has for and for […]

Terence Tao

Postdoctoral Research Positions in Mathematics and AI at the Sydney Mathematics Research Institute December 5, 2022

[The following information was provided to me by Geordie Williamson, who is Director of the Sydney Mathematics Research Institute – T.] We are currently advertising two positions in math and AI: Both positions are for three years and are based at the Sydney Mathematical Research Institute. The positions are research only, but teaching at the […]

Terence Tao

A counterexample to the periodic tiling conjecture November 30, 2022

Rachel Greenfeld and I have just uploaded to the arXiv our paper “A counterexample to the periodic tiling conjecture“. This is the full version of the result I announced on this blog a few months ago, in which we disprove the periodic tiling conjecture of Grünbaum-Shephard and Lagarias-Wang. The paper took a little longer than […]

Terence Tao

Trying out Mathstodon November 21, 2022

It’s been a while since I’ve actively participated in social media outside of this blog – I was active in Google Buzz/Google+ for a while, until that service closed – but I’ve decided to try out Mathstodon, one of the servers of the open source social media software platform Mastodon. As I understand it, Mastodon […]

Terence Tao

UCLA Math Undergraduate Merit Scholarship for 2023 November 5, 2022

In 2010, the UCLA mathematics department launched a scholarship opportunity for entering freshman students with exceptional background and promise in mathematics. This program was unfortunately suspended for a while due to technical reasons, but we are once again able to offer one scholarship each year. The UCLA Math Undergraduate Merit Scholarship provides […]

Terence Tao

Upcoming workshop on “Machine assisted proofs” at IPAM October 21, 2022

Just a short post to advertise the workshop “Machine assisted proofs” that will be held on Feb 13-17 next year, here at the Institute for Pure and Applied Mathematics (IPAM); I am one of the organizers of this event together with Erika Abraham, Jeremy Avigad, Kevin Buzzard, Jordan Ellenberg, Tim Gowers, and Marijn Heule. The […]

Terence Tao

A Bayesian probability worksheet October 7, 2022

This is a spinoff from the previous post. In that post, we remarked that whenever one receives a new piece of information , the prior odds between an alternative hypothesis and a null hypothesis is updated to a posterior odds , which can be computed via Bayes’ theorem by the formula where is the likelihood […]

Terence Tao

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