Month: October 2021

The IMOC stands for International Mathematical Olympiad Challenge and is a well-renowned world championship mathematics competitive examination. It occurs every year, similar to another competitive exam. You can get ready for the International Maths Olympiad once you get familiar with the mathematical concepts and ideas, get into the mock tests, and try to give as many mock tests as you can.

Here are a few points that will help you prepare for the International Maths Olympiad:

Understand The Syllabus

While beginning to prepare for the International Maths Olympiad exam, it is necessary to introduce yourself to the syllabus. The syllabus for the exam is a bit different from your academic syllabus and you can find out all about it here.

Get The Expert Tutor

As your trainer will play a major part in your learning method, just be sure that you choose someone who is experienced and at par with your ease level. Generally, your school maths trainer can make your competition worthy. If you can’t find an experienced Maths Olympiad trainer near your location, look for the best online tutoring.

Learn Problem-Solving Skills

The IMC problem-solving approach is a one-stop solution for math competition practices and materials, thousands of students have already enrolled in the mission to crack the International Maths Olympiad. We have resources to learn how you can solve difficult types of math problems. Consult with our expert trainers and get a brief idea to use problem-solving skills in the examination.

Practice past papers

We do not wish to tutor your child; their teachers are doing a great job at it. We believe that students should be taught in only one way and not be confused with multiple styles of teaching. So while your child covers conceptual learning of math topics in school, we help you by providing exhaustive and fully solved Test Practice Papers (10 of them). These practice test papers are replicas of the Olympiad. Do not worry about the approach we have in our explanatory solutions. Our subject experts simply explain the basics using logical techniques which helps students to get well acquainted with the topics. Knowledge of these topics will eventually help students to ace their school curriculum as well.

Study Smart

Following your timetable, you also need to focus on sample papers and the previous year’s questions. Schedule mock tests that will let you track your progress report. Practice is the only key to success that will help in developing your skills. However, smart studying is just as essential as studying energetically. Find the sequence in the sample papers and utilize them to your greatest advantage.

Check Your Progress

Revision is an immensely significant part of preparing for the International Maths Olympiad. As you are learning, use note cards for writing down the major points. When you begin with revision, the note cards will let you remember the pointers that you have written down on the cards. The notes are an effective way of recalling what you have learned. Hence, if you are preparing for the International Mathematics Olympiad exam then you should always think that these revisions are the progress standard. If any such topics require you to check those pointers in the notes again and again, then go back to revise and focus on those questions a bit more.

Final Thoughts

The method of IMC preparation and taking part in our examination is a great learning experience apart from the result. This exam assists students to be skilled at school levels and provides them the opportunity to know the structure and timetable of international-level competitive exams. The IMO Challenge helps students throughout the world to determine their strengths and capabilities. 

This St Patrick’s Day, revellers around the world will crowd the streets seeking one of Ireland’s national drinks: a pint of Guinness. But besides this tasty stout, one of the most fundamental and commonly used tools of science also has its origins at the Guinness brewery.

Towards the end of the 19th century, Guinness was scaling up its operations, and was interested in applying a scientific approach to all aspects of Guinness production: from barley growth right through to the Guinness taste.

Before adopting a scientific approach, brewers at Guinness relied on subjective methods, such as the appearance and scent of hops, to assess produce quality.

Once scientific brewers were recruited, a more objective approach was taken. The first scientific brewer, Thomas Bennett Case, was hired in 1893 and he believed that the amount of soft resins in hops was related to the quality of Guinness. He was therefore keen to estimate the amount of soft resin in particular crops of hops.

The challenge facing Case was that he, like any scientist, could not measure everything at once. It was not possible for him to assess the amount of soft resin in every single one of the countless hop flowers (added by the thousands to enormous vats of soon-to-be Guinness) in his charge.

Instead, he took a sample of hops (11 measurements of 50 grams each) and calculated the average soft resin content. His hope was that the average soft resin content of his small sample could be used to estimate the soft resin content of the entire crop (what statisticians would call “the population”) of hops.

For comparison, a colleague took a further 14 measurements of 50 grams each from the same lot of hops. Case found a small difference in the average amount of soft resins between these samples.

He was stumped. Were these differences in hop content due to real differences across the whole hop crop, or were they due to random error introduced by using small sample sizes?

Size matters

At the time, statistics relied on what is called “large-sample theory”, which unsurprisingly requires large samples (150 or more) to work. Applying it to problems involving small samples (like those faced by Case at Guinness) was difficult.

William Sealy Gosset. Wikimedia

This was the problem that William Sealy Gosset, a recent graduate of chemistry and mathematics at Oxford University, was keen to address. Gosset began work as an apprentice brewer at the Guinness factory in Dublin in 1899.

In 1906, Gosset, now a self-taught statistician, went to study with Karl Pearson, a leading figure in statistics, at University College London.

Gosset was keen to adapt Pearson’s large-sample methods to deal with the small samples they used at Guinness. There, he developed his ideas and readied them for publication.

However, until the late 1930s, Guinness would not allow employees to publish under their own names for fear that other brewers would learn of their scientific approaches to beer. As a result, Gosset published his most important paper, The Probable Error of a Mean, under the pseudonym “Student” in the journal Biometrika in 1908.

The ultimate ‘Student’ author’s journal paper. Biometrika (screen grab)

This was the origin of Student’s t-test, a fundamental statistical method that is widely used to this day.

Student’s t-test

The problem that Case faced was that using small samples of hops introduces a new source of uncertainty into the analysis, leaving him less able to distinguish between real, true differences between two batches of hops and differences due to this uncertainty.

Gosset’s genius was to devise a way of accounting for this: the t-distribution. This mathematically defines the relationship between the size of sample and the amount of uncertainty this imposes.

Basically, when carrying out experiments, the t-distribution (and the famous t-test that depends upon it) allows beer brewers and scientists alike to account for the size of the sample they have used in their work, and then define just how confident they are in their findings.

Sticking with the brewers’ case, you would have information from the two samples, such as the average soft resin content of the hops and the spread of each measurement around the average of each sample.

Without going into too much detail, the t-test helps to determine whether there is evidence of a difference between the two averages based on the sample size (that is, the number of measurements taken from a particular hop crop). In the brewers’ case they were looking for zero difference between their two samples.

A lasting legacy

Gosset’s method did not draw the attention of the statistical community until another leading statistical figure, Ronald Aylmer Fisher, enthusiastically embraced the method and provided a mathematical proof.

Since that time, the t-test has been used to tackle a huge range of scientific problems, from the assessment of brain function in stroke patients , to the measurement of carbon and nitrogen content in coastal ocean-dwelling bacteria, to how the behaviour of coal miners may or may not lead to accidents (the consumption of Guinness by these miners was, perhaps unsurprisingly, not a focus of the study).

In fact, Student’s t-test has been employed in essentially every field of scientific endeavour: biology, physics, psychology, biometrics, economics and medicine.

It is a staple of undergraduate statistics taught across these disciplines, but few may be aware of Gosset’s role in creating the t-test and his beery reasons for doing so.

Gosset remained at Guinness throughout his life as Head Experimental Brewer, then Head of the Statistics Department he formed at Guinness, before his promotion to Head Brewer for the new Guinness brewery in London in 1935. He published several papers as “Student” but his true identity was only publicly revealed upon his death in 1937.

So, if you’re drinking a Guinness this St Patrick’s day, raise a glass to the little-known character who played a pivotal role in beer, statistics and indeed, modern science: William Sealy Gosset.

For more insights like this, visit our website at www.international-maths-challenge.com.
Credit of the article given to Karen Lamb, David Farmer

Elegant new visualization maps the digits of pi as a star catalogue

The mind of Martin Krzywinski is a rich and dizzying place, teeming with fascinating questions, ideas, and inspiration. Krzywinski is a scientist and data visualizer whose primary line of work involves genome analysis for cancer research. In his spare time, though, he explores his many different interests as a scientific and visual thinker through creative projects. For the past few years, one such project has occupied him on a recurring basis each March: reimagining the digits of pi in a novel, science-based, and visually compelling way.

Today, this delightful March 14th (“Pi Day”) tradition brings us the digits of pi mapped onto the night sky, as a star catalogue. Like the infinitely long sequence of pi, space has no discernible end, but we earthbound observers can only see so far. So Krzywinski places a cap at 12 million digits and groups each successive series of 12 numerals to define a latitude, longitude and brightness, resulting in a field of a million stars, randomly arranged.

Just as humans throughout history have found figures and narratives among the stars, this new array of celestial bodies also yields a story. As a way to honor our evolutionary ancestors, Krzywinski connects the dots to create shapes of extinct animals from around the globe.

Carée projection of “Pi in the Sky” star chart
Credit: Martin Krzywinski

But he couldn’t possibly stop there, so Krzywinski takes the visualization a step further, experimenting with different projections to re-create the map in various spatial iterations.

Azimuthal projections of “Pi in the Sky” star chart
Credit: Martin Krzywinski

Hammer/Aitoff projection of “Pi in the Sky” star chart
Credit: Martin Krzywinski

To read more about the visualization, including descriptions of the animals depicted, and a poem written by the artist’s collaborator Paolo Marcazzan, visit Martin Krzywinski’s website. There, you can also explore his previous Pi Day visualizations and even purchase them as posters.

For more insights like this, visit our website at www.international-maths-challenge.com.

Credit of the article given to Amanda Montañez