Category: Uncategorized

It’s a dilemma that many a regular bettor probably faces often—deciding when to place a sports bet. In a study entitled, “A statistical theory of optimal decision-making in sports betting,” Jacek Dmochowski, Associate Professor in the Grove School of Engineering at The City College of New York, provides the answer. His original finding appears in the journal PLOS One.

“The central finding of the work is that the objective in sports betting is to estimate the median outcome. Importantly, this is not the same as the average outcome,” said Dmochowski, whose expertise includes machine learning, signal processing and brain-computer interfaces. “I approach this from a statistical point-of-view, but also provide some intuitive results with sample data from the NFL that can be digested by those without a background in math.”

To illustrate one of the findings, he presents a hypothetical example. “Assume that Kansas City has played Philadelphia three times previously. Kansas City has won each of those games by margins of 3, 7, and 35 points. They are playing again, and the point spread has been posted as ‘Kansas City -10.’ This means that Kansas City is favoured to win the game by 10 points according to the sportsbooks.”

For a bettor, Dmochowski added, the optimal decision in this scenario is to bet on Philadelphia (+10), even though they have lost the last three games by an average margin of 15 points. The reason is that the median margin of victory in those games was only 7, which is less than the point spread of 10.

He noted that because a bettor’s intuition may sometimes be more linked to an average outcome rather than the median, the utilization of some data, or even better, a model, is strongly encouraged.

On his new findings, Dmochowski said he was surprised that the derived theorems have not been previously presented, although it is possible that sports books and some statistically-minded bettors have understood at least the basic intuitions that are conveyed by the math.

Moreover, other investigators have reported findings that align with what’s in the paper, principally Fabian Wunderlich and Daniel Memmert at the German Sports University of Cologne.

With a Pew Research poll establishing that one in five Americans have placed a sports bet in the last year, Dmochowski’s study should be of interest to many bettors in this growing enterprise.

He had other advice for potential bettors. Firstly, “Avoid betting on matches for which the sports book has produced estimates that are ‘very close’ to the median outcome. In the case of the National Football League, the analysis shows that ‘very close’ is equivalent to the point spread being within one point of the true median.”

“Secondly, understand that the sports books are incredibly skilled at setting the odds. At the same time, they only need to make a small error to allow a profitable bet. So the goal is to seek out those opportunities.”

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to Jay Mwamba, City College of New York

 

Whether it’s physical phenomena, share prices or climate models—many dynamic processes in our world can be described mathematically with the aid of partial differential equations. Thanks to stochastics—an area of mathematics which deals with probabilities—this is even possible when randomness plays a role in these processes.

Something researchers have been working on for some decades now are so-called stochastic partial differential equations. Working together with other researchers, Dr. Markus Tempelmayr at the Cluster of Excellence Mathematics Münster at the University of Münster has found a method which helps to solve a certain class of such equations.

The results have been published in the journal Inventiones mathematicae.

The basis for their work is a theory by Prof. Martin Hairer, recipient of the Fields Medal, developed in 2014 with international colleagues. It is seen as a great breakthrough in the research field of singular stochastic partial differential equations. “Up to then,” Tempelmayr explains, “it was something of a mystery how to solve these equations. The new theory has provided a complete ‘toolbox,’ so to speak, on how such equations can be tackled.”

The problem, Tempelmayr continues, is that the theory is relatively complex, with the result that applying the ‘toolbox’ and adapting it to other situations is sometimes difficult.

“So, in our work, we looked at aspects of the ‘toolbox’ from a different perspective and found and proved a method which can be used more easily and flexibly.”

The study, in which Tempelmayr was involved as a doctoral student under Prof. Felix Otto at the Max Planck Institute for Mathematics in the Sciences, published in 2021 as a pre-print. Since then, several research groups have successfully applied this alternative approach in their research work.

Stochastic partial differential equations can be used to model a wide range of dynamic processes, for example, the surface growth of bacteria, the evolution of thin liquid films, or interacting particle models in magnetism. However, these concrete areas of application play no role in basic research in mathematics as, irrespective of them, it is always the same class of equations which is involved.

The mathematicians are concentrating on solving the equations in spite of the stochastic terms and the resulting challenges such as overlapping frequencies which lead to resonances.

Various techniques are used for this purpose. In Hairer’s theory, methods are used which result in illustrative tree diagrams. “Here, tools are applied from the fields of stochastic analysis, algebra and combinatorics,” explains Tempelmayr. He and his colleagues selected, rather, an analytical approach. What interests them in particular is the question of how the solution of the equation changes if the underlying stochastic process is changed slightly.

The approach they took was not to tackle the solution of complicated stochastic partial differential equations directly, but, instead, to solve many different simpler equations and prove certain statements about them.

“The solutions of the simple equations can then be combined—simply added up, so to speak—to arrive at a solution for the complicated equation which we’re actually interested in.” This knowledge is something which is used by other research groups who themselves work with other methods.

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

Credit of the article given to Kathrin Kottke, University of Münster

In teaching mathematics, the challenge often lies in making abstract concepts and problem-solving strategies explicit to students. Students often struggle to grasp the underlying reasoning and processes that drive mathematics. Explicit Teaching in Mathsprovides strategies for the teacher which help them to design and present instruction and learning to students in a meaningful way.

Teacher modelling is a way we can intentionally make clear the reasoning and processes behind mathematical ideas and concepts. Listen to our podcast, Explicit modelling of reasoning and processes behind actions , for more, where Allan Dougan (AAMT) and Dr Kristen Trippet (Australian Academy of Science) discuss how we model the reasoning and processes behind actions.

This article answers the questions:

• What do we mean by modelling in maths?
• How do we model the reasoning and processes behind actions in maths?
• How do we make the most of modelling in classroom teaching?

What is Teacher modelling in mathematics?

Mathematics is a subject where concepts can easily remain invisible to students. Teacher modelling allows teachers to showcase and explain the reasoning and processes behind mathematical concepts and practices. It often involves breaking down complex problems, strategies and skills into manageable steps that students can understand and replicate.

Teacher modelling is about thinking aloud and making visible those practices that are often concealed within a mathematician’s mind.

 

What is mathematical reasoning?

According to the Australian Curriculum V9.0: Understand this learning area , students are reasoning mathematically when they can:

• explain their thinking
• deduce and justify strategies used and conclusions reached
• adapt the known to the unknown
• transfer learning from one context to another
• prove that something is true or false.

Explicit modelling is a powerful tool for developing students’ mathematical reasoning abilities. Model mathematical reasoning by analysing, generalising and justifying mathematical situations. By thinking aloud, teachers can model this process effectively.

Start by analysing a problem: 7+8, I can do that with 5+2+8!

Then generalise the approach: It doesn’t matter what order I add these numbers up in, I will get the same result.

Justify the learning: I can use this approach to solve other problems too.

Using mathematical reasoning helps build patterns of thinking and mathematical fluency.

Beyond worked examples

Worked examples are the prime example of modelling and mathematical reasoning in action, but they are just the tip of the iceberg. While they provide a helpful starting point for students, relying solely on worked examples will not lead to a comprehensive understanding of mathematical concepts.

Fade in/Fade out

The idea of Fade in/Fade out support refers to when and why support is provided. This concept is useful when thinking about modelling.

Teachers will often start a lesson with a worked example and then fade out their modelling while students proceed with their learning. This approach doesn’t allow for the flexibility and responsiveness required for the most effective modelling. Modelling should not be a one-time occurrence. Instead, it should be scaffolded throughout a lesson. Build your modelling up through your lesson and fade in with instruction and modelling as students need it.

What does explicit modelling and mathematical reasoning look like?

Let’s unpack it with an example.

Example 1:

Problem: A student is asked to solve the equation 7+8 and to explain how they did it.

Student: I added 2 to 8, which made 10, and then added 5.

This strategy is called ‘bridging to 10’ and involves children using their knowledge of addition up to 10 as a base to then work out sums with totals over 10. A modelled response to this student’s work might look like this:

Teacher: Hang on a second, you said you added 2 to the 8, let’s take a look at that. So, 7+8 is the same as 5+2+8, where did the 7 go in that? Oh yes! (5+2)+8 also equals 15! What happens if we change the order of the numbers?

Student: 8+5+2, that also equals 15.

In this example, the student has modelled their own mathematical awareness, and this has then been extended with the teacher modelling both equivalence and the associative property in the working out of the problem.

Planning for modelling

Modelling is most effective when it is intentional and focused. Before teaching a lesson, ask yourself:

• What is the mathematical concept I want students to understand?
• What is the important mathematical skill I want them to see?
• What are the most effective ways I can model these strategies to students?
• How can I be responsive in my modelling (for example, fading in)?

There is so much more to maths than just getting the right answer! Explicit modelling is a powerful tool for making mathematical concepts and practices accessible to students. By incorporating modelling, educators empower students to not only find the right answers, but also to develop their mathematical reasoning skills, as well as their understanding of the underlying processes and strategies that mathematics is built upon. Modelling helps students to develop their thinking and come up with efficient strategies for tackling unknown mathematical problems. And this is the work of a true mathematician!

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to The Mathematics Hub

One hundred years ago, in the 1924 Paris Olympics, American Johnny Weissmuller won the men’s 100m freestyle with a time of 59 seconds. Nearly 100 years later, in the most recent Olympics, the delayed 2020 Games in Tokyo, Caeleb Dressel took home the same event with a time that was 12 seconds faster than Weissmuller’s.

Swimming times across the board have become much faster over the past century, a result of several factors, including innovations in training, recovery strategy, nutrition, and some equipment advances.

One component in the improvement in swimming performances over the years is the role of biomechanics—that is, how swimmers optimize their stroke, whether it’s the backstroke, breaststroke, butterfly, or freestyle.

Swimmers for decades have experimented with different techniques to gain an edge over their competitors. But in more recent years, the application of mathematics and science principles as well as the use of wearable sensor technology in training regimens has allowed some athletes to elevate their performances to new heights, including members of the University of Virginia’s swim team.

 

In a new research paper, a UVA professor who introduced these concepts and methods to the team and some of the swimmers who have embraced this novel approach to training lay out how the use of data is helping to transform how competitive swimmers become elite. The paper is published in The Mathematical Intelligencer journal.

‘Swimming in data’

Ken Ono thought his time working with swim teams was over. Ono—a UVA mathematics professor, professor of data science by courtesy, and STEM advisor to the University provost—had spent years working with competitive swimmers, first during his time at Emory University in Atlanta and then with other college teams, including Olympians, over the years.

However, he didn’t plan to continue that aspect of his work when he arrived at UVA in 2019. But after a meeting with Todd DeSorbo, who took over the UVA swim program in 2017, Ono soon found himself once again working closely with athletes, beginning his work as a consultant for the team during the 2020-21 season. The UVA women’s swim team would win their first of four consecutive national championships that year.

“One of the things that WElike quite a bit about this work is that swimming is crazy hard,” Ono said. “We were never meant to be swimmers, and it is both an athletic challenge as well as a scientific challenge—it has it all.”

Last fall, following a suggestion from DeSorbo, Ono offered a class that outlined the science-focused approach to improving swimming performances that had proven so successful at UVA, but he wanted to make sure there were no misconceptions about the seriousness of the material.

“We don’t want people thinking that it’s a cupcake course that’s offered for the swimmers,” Ono said.

So, Ono teamed up with UVA students Kate Douglass, August Lamb, and Will Tenpas, as well as MIT graduate student Jerry Lu, who had worked with Ono and the UVA swim team while an undergraduate at the University, to produce a paper that covered the key elements of the class and Ono’s work with swimmers.

Tenpas and Lamb both recently completed the residential master’s program at the School of Data Science as well as their careers as competitive collegiate swimmers. Douglass, who finished her UVA swim career in 2023 as one of the most decorated swimmers in NCAA history, is a graduate student in statistics at the University and is set to compete in the Paris Olympics after winning a bronze medal in the 2020 games.

The group drafted the paper, which they titled “Swimming in Data,” over the course of two months, and it was quickly accepted by The Mathematical Intelligencer. There, Ono said, it has become one of the most-read papers on a STEM subject since tracking began. In July, a version of the paper will also be published in Scientific American.

“It seems to have taken off,” Ono said.

The impact of digital twins

After outlining the evolution of swimming over the past 100 years, the paper explains how an understanding of math and physics, combined with the use of technology to acquire individual-level data, can help maximize performances.

Essential to understanding the scientific principles involved with the swimming stroke, the paper says, are Newton’s laws of motion. The laws—which cover inertia, the idea that acceleration depends on an object’s mass and the amount of force applied, and the principle that an action exerted by an object on another elicits an equal and opposite reaction—help simplify how one should think about the many biomechanical factors involved with swimming, according to Tenpas.

“There are all sorts of flexibility limitations. You have water moving at you, you have wakes, you have currents—it’s easy to kind of get paralyzed by the number of factors,” said Tenpas, who after four years at Duke, where he studied mechanical engineering, enrolled in UVA’s data science program and joined the swim team with a fifth year of eligibility.

“WEthink having Newton’s laws is nice as it gives you this baseline we can all agree on,” he added.

It’s a way to understand pool mechanics given the counterintuitive motion swimmers must use to propel themselves forward, according to Ono.

“The reason that we go to great extent to recall Newton’s laws of motion is so that we can break down the factors that matter when you test a swimmer,” he said.

To conduct these tests, Ono and his team use sensors that can be placed on swimmers’ wrists, ankles, or backs to gather acceleration data, measured as inertial measurement units. That information is then used to generate what are called digital twins, which precisely replicate a swimmer’s movements.

These twins reveal strengths and weaknesses, allowing Ono and the coaching staff to make recommendations on technique and strategy—such as how to reduce drag force, a swimmer’s true opponent—that will result in immediate improvement. In fact, through the analysis of data and the use of Newton’s laws, it is possible to make an accurate prediction about how much time a swimmer can save by making a given adjustment.

Lamb, who swam for UVA for five years while a computer science undergrad, then as a data science master’s student, likened digital twins to a feature in the popular Nintendo game Mario Kart where you can race against a ghost version of yourself.

“Being able to have this resource where you can test for one month and then spend a month or two making that adjustment and then test again and see what the difference is—it’s an incredibly valuable resource,” he said.

To understand the potential of digital twins, one need only look at the example of Douglass, one of the co-authors, who is cited in the paper.

A flaw was identified in her head position in the 200m breaststroke. Using her digital twin, Ono and the coaching staff were able to quantify how much time she could save per streamline glide by making a modification, given her obvious talent and aerobic capacity. She did, and the results were remarkable. In November 2020, when her technique was tested, the 200m breaststroke wasn’t even on her event list. Three years later, she held the American record.

‘Everyone’s doing it now’

Swimming will be front and center in the national consciousness this summer. First, the U.S. Olympic Team Trials will be held in Indianapolis in June, leading up to the Paris Olympics in July and August, where DeSorbo, UVA’s coach who embraced Ono’s data-driven strategic advice, will lead the women’s team.

Many aspiring swimmers will undoubtedly be watching over the coming weeks, wondering how they might realize their full athletic potential at whatever level that might be.

For those who have access to technology and data about their technique, Tenpas encourages young swimmers to take advantage.

He noted the significant amount of time a swimmer must put in to reach the highest levels of the sport, estimating that he had been swimming six times per week since he was 12 years old.

“If you’re going to put all of this work in, at least do it smart,” Tenpas said.

At the same time, Lamb urged young swimmers who may not yet have access to this technology to not lose faith in their potential to improve.

“While this is an incredibly useful tool to make improvements to your technique and to your stroke, it’s not the end all, be all,” he said.

“There are so many different ways to make improvements, and we’re hopeful that this will become more accessible as time goes on,” Lamb said of the data methods used at UVA.

As for where this is all going, with the rapidly expanding use and availability of data and wearable technology, Ono thinks his scientific approach to crafting swimming strategies will soon be the norm.

“We think five years from now, our story won’t be a story. It’ll be, “Oh, everyone’s doing it now,'” he said.

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to Cooper Allen, University of Virginia

 

Graphic novels can help make math and physics more accessible for students, parents or teachers in training. Metamorworks/iStock via Getty Images

Post-pandemic, some educators are trying to reengage students with technology – like videos, computer gaming or artificial intelligence, just to name a few. But integrating these approaches in the classroom can be an uphill battle. Teachers using these tools often struggle to retain students’ attention, competing with the latest social media phenomenon, and can feel limited by using short video clips to get concepts across.

Graphic novels – offering visual information married with text – provide a means to engage students without losing all of the rigor of textbooks. As two educators in math and physics, we have found graphic novels to be effective at teaching students of all ability levels. We’ve used graphic novels in our own classes, and we’ve also inspired and encouraged other teachers to use them. And we’re not alone: Other teachers are rejuvenating this analog medium with a high level of success.

In addition to covering a wide range of topics and audiences, graphic novels can explain tough topics without alienating student averse to STEM – science, technology, engineering and math. Even for students who already like math and physics, graphic novels provide a way to dive into topics beyond what is possible in a time-constrained class. In our book “Using Graphic Novels in the STEM Classroom,” we discuss the many reasons why graphic novels have a unique place in math and physics education. Here are three of those reasons:

Explaining complex concepts with rigor and fun

Increasingly, schools are moving away from textbooks, even though studies show that students learn better using print rather than digital formats. Graphic novels offer the best of both worlds: a hybrid between modern and traditional media.

This integration of text with images and diagrams is especially useful in STEM disciplines that require quantitative reading and data analysis skills, like math and physics.

For example, our collaborator Jason Ho, an assistant professor at Dordt University, uses “Max the Demon Vs Entropy of Doom” to teach his physics students about entropy. This topic can be particularly difficult for students because it’s one of the first times when they can’t physically touch something in physics. Instead, students have to rely on math and diagrams to fill in their knowledge.

 

Rather than stressing over equations, Ho’s students focus on understanding the subject more conceptually. This approach helps build their intuition before diving into the algebra. They get a feeling for the fundamentals before they have to worry about equations.

After having taken Ho’s class, more than 85% of his students agreed that they would recommend using graphic novels in STEM classes, and 90% found this particular use of “Max the Demon” helpful for their learning. When strategically used, graphic novels can create a dynamic, engaging teaching environment even with nuanced, quantitative topics.

 

Combating quantitative anxiety

Students learning math and physics today are surrounded by math anxiety and trauma, which often lead to their own negative associations with math. A student’s perception of math can be influenced by the attitudes of the role models around them – whether it’s a parent who is “not a math person” or a teacher with a high level of math anxiety.

Graphic novels can help make math more accessible not only for students themselves, but also for parents or students learning to be teachers.

In a geometry course one of us (Sarah) teaches, secondary education students don’t memorize formulas and fill out problem sheets. Instead, students read “Who Killed Professor X?”, a murder mystery in which all of the suspects are famous mathematicians. The suspects’ alibis are justified through problems from geometry, algebra and pre-calculus.

While trying to understand the hidden geometry of suspect relationships, students often forget that they are doing math – focusing instead on poring over secret hints and notes needed to solve the mystery.

Although this is just one experience for these students, it can help change the narrative for students experiencing mathematical anxiety. It boosts their confidence and shows them how math can be fun – a lesson they can then impart to the next generation of students.

 

Helping students learn and readers dream big

In addition to being viewed favourably by students, graphic novels can enhance student learning by improving written communication skills, reading comprehension and critical literacy skills. And even outside the classroom, graphic novels support long-term memory for those who have diagnoses like dyslexia.

Pause and think about your own experience – how do you learn about something new in science?

If you’re handed a textbook, it’s extremely unlikely that you’d read it cover to cover. And although the internet offers an enormous amount of math and physics content, it can be overwhelming to sift through hours and hours of videos to find the perfect one to get the “aha!” moment in learning.

Graphic novels provide a starting point for such a broad range of niche topics that it’s impossible for anyone to be experts in them all. Want to learn about programming? Try the “Secret Coders” series. Want to understand more about quantum physics? Dive into “Suspended in Language: Niels Bohr’s life, discoveries, and the century he shaped.” Searching for more female role models in science? “Astronauts: Women on the Final Frontier” could be just what you’re looking for.

With all that they offer, graphic novels provide a compelling list of topics and narratives that can capture the attention of students today. We believe that the right set of graphic novels can inspire the next generation of scientists as much as any single individual can.

For more such insights, log into our website https://international-maths-challenge.com

A new study into classroom practices, led by Dr. Steve Murphy, has found extensive research fails to uncover how teachers can remedy poor student engagement and perform well in math.

More than 3,000 research papers were reviewed over the course of the study, but only 26 contained detailed steps for teachers to improve both student engagement and results in math. The review is published in the journal Teaching and Teacher Education.

Dr. Murphy said the scarcity of research involving young childrenwas concerning.

“Children’s engagement in math begins to decline from the beginning of primary school while their mathematical identity begins to solidify,” Dr. Murphy said.

“We need more research that investigates achievement and engagement together to give teachers good advice on how to engage students in mathematics and perform well.

“La Trobe has developed a model for research that can achieve this.”

While teachers play an important role in making decisions that impact the learning environment, Dr. Murphy said parents are also highly influential in children’s math education journeys.

“We often hear parents say, ‘It’s OK, I was never good at math,’ but they’d never say that to their child about reading or writing,” Dr. Murphy said.

La Trobe’s School of Education is determined to improve mathematical outcomes for students, arguing it’s an important school subject that is highly applicable in today’s technologically rich society.

Previous research led by Dr. Murphy published in Educational Studies in Mathematics found many parents were unfamiliar with the modern ways of teaching math and lacked self-confidence to independently assist their children learning math during the COVID-19 pandemic.

“The implication for parents is that you don’t need to be a great mathematician to support your children in math, you just need to be willing to learn a little about how schools teach math today,” Dr. Murphy said.

“It’s not all bad news for educators and parents. Parents don’t need to teach math; they just need to support what their children’s teacher is doing.

“Keeping positive, being encouraging and interested in their children’s math learning goes a long way.”

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article to be given La Trobe Universit

 

For Michel Talagrand, who won the Abel mathematics prize on Wednesday, math provided a fun life free from all constraints—and an escape from the eye problems he suffered as a child.

“Math, the more you do it, the easier it gets,” the 72-year-old said in an interview with AFP.

He is the fifth French Abel winner since the award was created by Norway’s government in 2003 to compensate for the lack of a Nobel prize in mathematics.

Talagrand’s career in functional analysis and probability theorysaw him tame some of the incredibly complicated limits of random behaviour.

But the mathematician said he had just been “studying very simple things by understanding them absolutely thoroughly.”

Talagrand said he was stunned when told by the Norwegian Academy of Science and Letters that he had won the Abel prize.

“I did not react—I literally didn’t think for at least five seconds,” he said, adding that he was very happy for his wife and two children.

Fear of going blind

When he was young, Talagrand only turned to math “out of necessity,” he said.

By the age of 15, he had endured multiple retinal detachments and “lived in terror of going blind”.

Unable to run around with friends in Lyon, Talagrand immersed himself in his studies.

His father had a math degree and so he followed the same path. He said he was a “mediocre” student in other areas.

Talagrand was particularly poor at spelling, and still lashes out at what he calls its “arbitrary rules”.

Especially in comparison to math, which has “an order in which you do well if you are sensitive to it,” he said.

In 1974, Talagrand was recruited by the French National Centre for Scientific Research (CNRS), before getting a Ph.D. at Paris VI University.

He spent a decade studying functional analysis before finding his “thing”: probability.

It was then that Talagrand developed his influential theory about “Gaussian processes,” which made it possible to study some random phenomena.

Australian mathematician Matt Parker said that Talagrand had helped tame these “complicated random processes”.

Physicists had previously developed theories on the limits of how randomness behaves, but Talagrand was able to use mathematics to prove these limits, Parker said on the Abel Prize website.

‘Monstrously complicated’

“In a sense, things are as simple as could be—whereas mathematical objects can be monstrously complicated,” Talagrand said.

His work deepening the understanding of random phenomena “has become essential in today’s world,” the CNRS said, citing algorithms which are “the basis of our weather forecasts and our major linguistic models”.

Rather than creating a “brutal transformation”, Talagrand considers his discoveries as a collective work he compared to “the construction of a cathedral in which everyone lays a stone”.

He noted that French mathematics had been doing well an elite level, notching up both Abel prizes and Fields medals—the other equivalent to a math Nobel, which is only awarded to mathematicians under 40.

“But the situation is far less brilliant in schools,” where young people are increasingly less attracted to the discipline, he lamented.

The new Abel winner admitted that math can be daunting at first, but re-emphasized his belief that it gets easier the more you do it.

He advised aspiring mathematicians not to worry about failure.

“You can fail to solve a problem 10 times—but that doesn’t matter if you succeed on the 11th try,” he said.

It can also be hard work.

“All my life I worked to the point of exhaustion—but I had such fun!” he said.

“With math, you have all the resources within yourself. You work without any constraints, free from concerns about money or bosses,” he added.

“It’s marvelous.”

Talagrand will receive his prize, including a 7.5-million-kroner ($705,000) check, in Oslo on May 21.

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to Juliette Collen

 

A George Washington University research team has created a novel formula that demonstrates how, why, and when hate speech spreads throughout social media. The researchers put forth a first-principles dynamical theory that explores a new realm of physics in order to represent the shockwave effect created by bigoted content across online communities.

This effect is evident in lightly moderated websites, such as 4Chan, and highly regulated social platforms like Facebook. Furthermore, hate speech ripples through online communities in a pattern that non-hateful content typically does not follow.

The new theory considers recently gained knowledge on the pivotal role of in-built communities in the growth of online extremism. The formula weighs the competing forces of fusion and fission, accounting for the spontaneous emergence of in-built communities through the absorption of other communities and interested individuals (fusion) and the disciplinary measures moderators take against users and groups that violate a given platform’s rules (fission).

Researchers hope the formula can serve as a tool for moderators to project the shockwave-like spread of hateful content and develop methods to delay, divert, and prevent it from spiraling out of control. The novel theory could also be applied beyond social mediaplatforms and online message boards, potentially powering moderation strategies on blockchain platforms, generative AI, and the metaverse.

“This study presents the missing science of how harms thrive online and, hence, how they can be overcome,” Neil Johnson, professor of physics at the George Washington University and co-author of the study, said. “This missing science is a new form of shockwave physics.”

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to George Washington University

When President Ronald Reagan proclaimed the first National Math Awareness Week in April 1986, one of the problems he cited was that too few students were devoted to the study of math.

“Despite the increasing importance of mathematics to the progress of our economy and society, enrollment in mathematics programs has been declining at all levels of the American educational system,” Reagan wrote in his proclamation.

Nearly 40 years later, the problem that Reagan lamented during the first National Math Awareness Week—which has since evolved to become “Mathematics and Statistics Awareness Month”—not only remains but has gotten worse.

Whereas 1.63%, or about 16,000, of the nearly 1 million bachelor’s degrees awarded in the U.S. in the 1985–1986 school year went to math majors, in 2020, just 1.4%, or about 27,000, of the 1.9 million bachelor’s degrees were awarded in the field of math—a small but significant decrease in the proportion.

Post-pandemic data suggests the number of students majoring in math in the U.S. is likely to decrease in the future.

A key factor is the dramatic decline in math learning that took place during the lockdown. For instance, whereas 34% of eighth graders were proficient in math in 2019, test data shows the percentage dropped to 26% after the pandemic.

These declines will undoubtedly affect how much math U.S. students can do at the college level. For instance, in 2022, only 31% of graduating high school seniors were ready for college-level math—down from 39% in 2019.

These declines will also affect how many U.S. students are able to take advantage of the growing number of high-paying math occupations, such as data scientists and actuaries. Employment in math occupations is projected to increase by 29% in the period from 2021 to 2031.

About 30,600 math jobs are expected to open up per year from growth and replacement needs. That exceeds the 27,000 or so math graduates being produced each year—and not all math degree holders go into math fields. Shortages will also arise in several other areas, since math is a gateway to many STEM fields.

For all of these reasons and more, as a mathematician who thinks deeply about the importance of math and what it means to our world—and even to our existence as human beings—I believe this year, and probably for the foreseeable future, educators, policymakers and employers need to take Mathematics and Statistics Awareness Month more seriously than ever before.

Struggles with mastery

Subpar math achievement has been endemic in the U.S. for a long time.

Data from the National Assessment of Educational Progress shows that no more than 26% of 12th graders have been rated proficient in math since 2005.

The pandemic disproportionately affected racially and economically disadvantaged groups. During the lockdown, these groups had less access to the internet and quiet studying spaces than their peers. So securing Wi-Fi and places to study are key parts of the battle to improve math learning.

Some people believe math teaching techniques need to be revamped, as they were through the Common Core, a new set of educational standards that stressed alternative ways to solve math problems. Others want a return to more traditional methods. Advocates also argue there is a need for colleges to produce better-prepared teachers.

Other observers believe the problem lies with the “fixed mindset” many students have—where failure leads to the conviction that they can’t do math—and say the solution is to foster a “growth” mindset—by which failure spurs students to try harder.

Although all these factors are relevant, none address what in my opinion is a root cause of math underachievement: our nation’s ambivalent relationship with mathematics.

Low visibility

Many observers worry about how U.S. children fare in international rankings, even though math anxiety makes many adults in the U.S. steer clear of the subject themselves.

Mathematics is not like art or music, which people regularly enjoy all over the country by visiting museums or attending concerts. It’s true that there is a National Museum of Mathematics in New York, and some science centers in the U.S. devote exhibit space to mathematics, but these can be geographically inaccessible for many.

A 2020 study on media portrayals of math found an overall “invisibility of mathematics” in popular culture. Other findings were that math is presented as being irrelevant to the real world and of little interest to most people, while mathematicians are stereotyped to be singular geniuses or socially inept nerds, and white and male.

Math is tough and typically takes much discipline and perseverance to succeed in. It also calls for a cumulative learning approach—you need to master lessons at each level because you’re going to need them later.

While research in neuroscience shows almost everyone’s brain is equipped to take up the challenge, many students balk at putting in the effort when they don’t score well on tests. The myth that math is just about procedures and memorization can make it easier for students to give up. So can negative opinions about math ability conveyed by peers and parents, such as declarations of not being “a math person.”

A positive experience

Here’s the good news. A 2017 Pew poll found that despite the bad rap the subject gets, 58% of U.S. adults enjoyed their school math classes. It’s members of this legion who would make excellent recruits to help promote April’s math awareness. The initial charge is simple: Think of something you liked about math—a topic, a puzzle, a fun fact—and go over it with someone. It could be a child, a student, or just one of the many adults who have left school with a negative view of math.

Can something that sounds so simplistic make a difference? Based on my years of experience as a mathematician, I believe it can—if nothing else, for the person you talk to. The goal is to stimulate curiosity and convey that mathematics is much more about exhilarating ideas that inform our universe than it is about the school homework-type calculations so many dread.

Raising math awareness is a first step toward making sure people possess the basic math skills required not only for employment, but also to understand math-related issues—such as gerrymandering or climate change—well enough to be an informed and participating citizen. However, it’s not something that can be done in one month.

Given the decline in both math scores and the percentage of students studying math, it may take many years before America realizes the stronger relationship with math that President Reagan’s proclamation called for during the first National Math Awareness Week in 1986.

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to Manil Suri, The Conversation

Studies by applied mathematicians at the University of Surrey are helping to identify ways of reducing how much liquids slosh around inside tanks.

Baffles slow down the movement of fluid by diverting its flow. The research found that two or three porous baffles dividing a tank calms sloshing better than a single separator, but the returns diminish as more baffles are added. The paper is published in the Journal of Engineering Mathematics.

The findings and improved understanding into how external movement impacts the way liquids slosh could help mathematicians and engineers design better tankers to transport liquids on land or at sea.

The findings could also be used in tuned liquid dampers, which reduce the sway of skyscrapers in earthquakes and high winds.

Dr. Matthew Turner, a mathematician at the University of Surrey and expert in fluid dynamics who conducted the research using mathematical modeling, said, “Sloshing liquids can impact safety and efficiency. For example, if a tanker transporting liquids via road stopped suddenly, extreme movement of liquid inside the tanker could move the vehicle forwards, and unstable fuel loads in a space rocket could be catastrophic. Porous baffles inserted within a tank can help stabilize loads and reduce sloshing. Our research helps clarify how many it’s worth using.”

Jane Nicholson, EPSRC’s director of research base, said, “This fundamental research demonstrates the potential impact of math research, as a result of our mathematical sciences small grants investment. It is motivated by real-world applications to ensure the safer and more efficient transportation of liquids and will bring new solutions in a wide range of sectors.”

Next Dr. Turner wants to investigate whether actively varying how porous the baffles are could offer further benefits, “A mechanism which controls the rate of flow through the baffle could help us optimize designs. It could also be helpful when designing wave energy converters.”

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article to be given UK Research and Innovation