Month: October 2022

Some countries have their own Mathematical Olympiad programs, and the status of IMO is kind of similar to other big international tournaments. Unlike other math competitions, competition in IMO is too high, all the high school students are eligible for IMO. It doesn’t matter to which country they belong. Every national program chooses its squad according to the performance of the exams. In major countries, problem-solving skill for IMO is like a serious business for some extraordinary students. The International Maths Challenge is one of the exams which is having the most popularity in the world. This exam aims to choose intelligent mathematics students who magnify their country’s pride and represent it at the international level.

Is It Difficult to Solve Maths Olympiad Problems?

The difficulty of the paper stems from the ease required to solve the maths olympiad questions. Problems are specially created to be solvable using elementary means using maths that students of high school can understand easily with some training. But it doesn’t mean problem-solving is easy with this sort of maths. It’s just an ability to use simple maths in ingenious ways & have insights into a problem to solve it. Here is an analogy, The International Mathematical Olympiad is that of painting in which It’s easy to learn all types of painting techniques and buy art tools that are required, but in the end, there are only a few people who will remain who can paint a masterpiece.

Tips For Preparation of International Maths Olympiad

1.     Understand the syllabus

Before starting your maths olympiad preparation you should introduce yourself with the syllabus. It is important to understand the syllabus’s structure, get the important resources, and start your maths olympiad preparation.

2.     Get the expert tutor

Hiring a well-experienced tutor can help you to prepare well for the exam. Someone who is at par with your ease level.

3.     Learn problem-solving skills

A problem-solving approach is the only one-stop solution for any exams. Thousands of students have already enrolled in IMO. It’s important to know for you to know how to solve difficult maths olympiad questions or you can consult with our expert trainers and get a brief idea of using problem-solving skills in the examination.

4.     Practice test papers

Practice online math olympiad test papers as much as you can it will help you to increase your speed and problem-solving ability.

5.     Check your progress

At last, revision is an important part of preparing for IMO. You can also make notes. They will help you to remember points while revising.

Studying and preparing for the maths Olympiad will enhance students’ logical reasoning and thinking abilities and make them move toward strong career opportunities. If you are confused about participating in the International Maths Challenge, we are here to guide you at every step of your success. Good luck!

Matrix multiplication – where two grids of numbers are multiplied together – forms the basis of many computing tasks, and an improved technique discovered by an artificial intelligence could boost computation speeds by up to 20 per cent.

Multiplying numbers is a fundamental task for computers

An artificial intelligence created by the firm DeepMind has discovered a new way to multiply numbers, the first such advance in over 50 years. The find could boost some computation speeds by up to 20 per cent, as a range of software relies on carrying out the task at great scale.

Matrix multiplication – where two grids of numbers are multiplied together – is a fundamental computing task used in virtually all software to some extent, but particularly so in graphics, AI and scientific simulations. Even a small improvement in the efficiency of these algorithms could bring large performance gains, or significant energy savings.

For centuries, it was believed that the most efficient way of multiplying matrices would be proportional to the number of elements being multiplied, meaning that the task becomes proportionally harder for larger and larger matrices.

But the mathematician Volker Strassen proved in 1969 that multiplying a matrix of two rows of two numbers with another of the same size doesn’t necessarily involve eight multiplications and that, with a clever trick, it can be reduced to seven. This approach, called the Strassen algorithm, requires some extra addition, but this is acceptable because additions in a computer take far less time than multiplications.

The algorithm has stood as the most efficient approach on most matrix sizes for more than 50 years, although some slight improvements that aren’t easily adapted to computer code have been found. But DeepMind’s AI has now discovered a faster technique that works perfectly on current hardware. The company’s new AI, AlphaTensor, started with no knowledge of any solutions and was presented with the problem of creating a working algorithm that completed the task with the minimum number of steps.

It found an algorithm for multiplying two matrices of four rows of four numbers using just 47 multiplications, which outperforms Strassen’s 49 multiplications. It also developed improved techniques for multiplying matrices of other sizes, 70 in total.

AlphaTensor discovered thousands of functional algorithms for each size of matrix, including 14,000 for 4×4 matrices alone. But only a small minority were better than the state of the art. The research builds on AlphaZero, DeepMind’s game-playing model, and has been two years in the making.

Hussein Fawzi at DeepMind says the results are mathematically sound, but are far from intuitive for humans. “We don’t really know why the system came up with this, essentially,” he says. “Why is it the best way of multiplying matrices? It’s unclear.”

“Somehow, the neural networks get an intuition of what looks good and what looks bad. I honestly can’t tell you exactly how that works. I think there is some theoretical work to be done there on how exactly deep learning manages to do these kinds of things,” says Fawzi.

DeepMind found that the algorithms could boost computation speed by between 10 and 20 per cent on certain hardware such as an Nvidia V100 graphics processing unit (GPU) and a Google tensor processing unit (TPU) v2, but there is no guarantee that those gains would also be seen on common devices like a smartphone or laptop.

James Knight at the University of Sussex, UK, says that a range of software run on supercomputers and powerful hardware, like AI research and weather simulation, is effectively large-scale matrix multiplication.
“If this type of approach was actually implemented there, then it could be a sort of universal speed-up,” he says. “If Nvidia implemented this in their CUDA library [a tool that allows GPUs to work together], it would knock some percentage off most deep-learning workloads, I’d say.”

Oded Lachish at Birkbeck, University of London, says the new algorithms could boost the efficiency of a wide range of software, because matrix multiplication is such a common problem – and more algorithms are likely to follow.

“I believe we’ll be seeing AI-generated results for other problems of a similar nature, albeit rarely something as central as matrix multiplication. There’s significant motivation for such technology, since fewer operations in an algorithm doesn’t just mean faster results, it also means less energy spent,” he says. If a task can be completed slightly more efficiently, then it can be run on less powerful, less power-intensive hardware, or on the same hardware in less time, using less energy.

But DeepMind’s advances don’t necessarily mean human coders are out of a job. “Should programmers be worried? Maybe in the far future. Automatic optimisation has been done for decades in the microchip design industry and this is just another important tool in the coder’s arsenal,” says Lachish.

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Matthew Sparkes*