The mystique of mathematics: 5 beautiful math phenomena | Mathematics - Phys.org

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Sherry Landow, News & Content Producer at UNSW Sydney (the University of New South Wales) notes, Mathematics is visible everywhere in nature, even where we are not expecting it. 

Fractals - patterns that repeat themselves on smaller scales - can be seen frequently in nature, like in snowflakes.
Photo: Unsplash.

It can help explain the way galaxies spiral, a seashell curves, patterns replicate, and rivers bend. 

Even subjective emotions, like what we find beautiful, can have mathematic explanations.

"Maths is not only seen as beautiful—beauty is also mathematical," says Dr. Thomas Britz, a lecturer in UNSW Science's School of Mathematics & Statistics. "The two are intertwined."

Dr. Britz works in combinatorics, a field focused on complex counting and puzzle solving. While combinatorics sits within pure mathematics, Dr. Britz has always been drawn to the philosophical questions about mathematics. 

Here, Dr. Britz shares some of his favorite connections between maths and beauty.

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Source: Phys.org

Good data is a key component to AI innovation and machine learning | Technology - Federal News Network

When the Biden Administration launched an AI task force earlier this month to create a path to “democratize access to research tools to promote AI,” the goal of access was paramount by Peter Musurlian, producer at Federal News Network.

Photo: Tara Winstead from Pexels

“The task force consists of some of the top experts in academia and industry,” said Dinesh Manocha, a professor of computer science and electrical and computer engineering at the University of Maryland, on Federal Monthly Insights – Repurposing Manpower through Automation. “They recognize the importance and they’re pushing for more development in the field by making good data available. So data is a very key component of AI and machine learning-based methods.

Manocha said AI is as old as the field, pointing to “Founding Father” Alan Turing, whom he said laid the foundations in the 1950s.

“Machine learning is one sub-area in the broader field of AI,” said Manocha on Federal Drive with Tom Temin. “All the recent developments in AI, all the penetration in the real world, has primarily been driven by the excitement in last five to 10 years from machine learning.”...

Focusing on data and algorithms, AI and machine learning imitate the way humans learn. “So you know one of the grand challenges in AI is how can we emulate human-like intelligence, which is still a big open problem,” Manocha said. “There have been a lot of approaches pursued and proposed by a wonderful researchers the last 50 to 60 years.”

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Source: Federal News Network 

Successful PhD course on a differentiated Europe | Science - Mirage News

/University of Oslo Public Release. This material comes from the originating organization and may be of a point-in-time nature, edited for clarity, style and length. View in full here.

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In May 2021, ARENA organised a new PhD course, gathering doctoral students and leading scholars to discuss a differentiated Europe and its implications.

Photo: Colourbox

STV9431 – A differentiated Europe and its implications

• Level: PhD
• Credits: 10
• Open for students enrolled in international and Norwegian PhD programmes
• No participation fee
• Teaching: Spring 2021, 2022 and 2023

The PhD course STV9431 – A differentiated Europe and its implications took place online on 18-21 May 2021. The teaching was built on the topics and research of the ARENA-coordinated project EU Differentiation, Dominance and Democracy (EU3D).

John Erik Fossum, Professor and Jarle Trondal, Professor who led and organised the course, were particularly pleased with the many fruitful discussions and the contributions from all participants.

‘Despite being an online zoom event, we were happy to see lively debates among the participants and also some possibility to get to know each other,’ said Jarle Trondal...

Following the evaluation of the social sciences in Norway (SAMEVAL), ARENA has also been granted funds to organise the course in 2022 and 2023.

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Source: Mirage News 

Indian PhD enrolment up 60 per cent in five years | Gender - Times Higher Education

Joyce Lau, Hong Kong-based journalist summarize, Nationwide survey shows overall gains in capacity, enrolment and gender balance. 

Photo: iStock

Enrolment on PhDs has increased by 60 per cent in India over the past five years, according to new data.

Education minister Ramesh Pokhriyal Nishank called the rise, reported in the All India Survey on Higher Education, “heartening”. India plans to greatly boost innovation with a 500 billion rupee (£5 billion) National Research Foundation announced this year.

The survey, released this month, showed growth across almost all key higher education metrics, in line with the goals of the 2020 National Education Policy (NEP), which aims to double the size of the higher education sector over two decades..

However, the total number of male students still exceeds female students because of a gender imbalance in the country’s birth rates. Male students still dominate at the elite institutions of national importance.

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Source: Times Higher Education

Mathematical Modeling | Mathematics - Academic Minute

Mathematical models help with predicting the future, according to David Abrahamson, professor of mathematical sciences.

Photo: Academic Minute

In today's Academic Minute, part of Rhode Island College Week, David Abrahamson discusses this exciting part of mathematical study. A transcript of this podcast can be found here.

David Abrahamson, discusses this exciting part of mathematical study.

One of the most fascinating fields in applied mathematics is something called “mathematical  modeling.” In mathematical modeling, we try to create mathematical representations of real world processes. These representations can then be used to make predictions and, in particular,  to help with decision-making. Many phenomena are well-understood, and appropriate models  are in place: for example, the mathematical model for radioactive decay has been understood for  many decades, and important science like carbon dating is a result.

The challenge in mathematical modeling is how to deal with new situations. A model has to  satisfy multiple criteria.

Listen to the Audio

Source: Academic Minute 

What makes a good digital math tool? | Apps - eSchool News

As popularity and usage of digital tools rises, it's important to know what, exactly, makes a good digital math tool, says Laura Ascione, Editorial Director at eSchool Media. 

 

We recently spoke with Texthelp’s Chief Technology Officer, Ryan Graham, on the current state of edtech tools in math and the future of math education. As popularity and usage of digital tools rises, Graham shares his thoughts on what makes a good digital math tool.

During the COVID-19 disruption to education, the use of edtech tools surged. In fact, according, recent research, downloads of education apps in the U.S. increased by 130 percent. 

Within this surge, math saw the biggest jump in edtech tool usage. Math has historically been board-based in the classroom and paper-based at home. And while students had used digital tools like math games and at-home practice apps, these were strictly supplemental. Over this last year, however, as a result of COVID-19, teachers and students have had to adapt to using digital math-related tools, some for the first time. 

Since March of 2020, the usage of Texthelp’s own STEM application, EquatIO, has risen by more than 150 percent. 

We recently spoke with Texthelp’s Chief Technology Officer, Ryan Graham, on the current state of edtech tools in math and the future of math education. As popularity and usage of digital tools rises, Graham shares his thoughts on what makes a good digital math tool.

Read more... 

Source: eSchool News  

The Epiphanies of Mathematics | Mathematics -Medium

I was 15 in 2015, and all I wanted to be was a physicist, writes Sparsh Joshi, A fan of Pop-Culture, Science, Philosophy & Politics, published in Cantor’s Paradise. 

Photo: Greg Bernhardt

Greg Bernhardt

Source https://www.physicsforums.com/insights/author/Greg-Bernhardt/

Greg Bernhardt

Source https://www.physicsforums.com/insights/author/Greg-Bernhardt/

Greg Bernhardt

Source https://www.physicsforums.com/insights/author/Greg-Bernhardt/

Greg Bernhardt

Source https://www.physicsforums.com/insights/author/Greg-Bernhardt/

Greg Bernhardt

Source https://www.physicsforums.com/threads/beautiful-math-and-physics-blackboards.704819/#post-4467943

Greg Bernhardt

Source https://www.physicsforums.com/threads/beautiful-math-and-physics-blackboards.704819/#post-4467943

Greg Bernhardt

Source https://www.physicsforums.com/threads/beautiful-math-and-physics-blackboards.704819/#post-4467943

Greg Bernhardt

Source https://www.physicsforums.com/threads/beautiful-math-and-physics-blackboards.704819/#post-4467943

I had been on a learning spree of the keywords for years — from the standard model of particle physics to learning about the ergospheres of black holes.

I was reading some simple papers and their introduction — blogs, videos, podcasts. I was learning about things like quark-gluon plasma, quantum entanglement, and whatnot. All that seemed weird and wonderful, I had my eye on it.

It was my dream to solve the Hawking Information Paradox and AMPS paradox, both a blend of quantum mechanics and black holes. I remember reading something new in this area and immediately coming up with ideas that I thought were “revolutionary” or “the missing piece” to these problems. I would write doc files with catchy names like “Solving AMPS Paradox using Tensor Networks” or “Creating Chameleon-Electron pairs to Simulate Hawking Entanglement Pairs” with nothing but gibberish inside...

Alas, if I had to pick a subject I was the worst at, it was mathematics...

Becoming Better: How getting better at Math has nothing to do with Math

TIMMS, a series of international assessment exams, is taken all over the world to know the aptitude of people in the universe of mathematics and science. It's a tedious, hard and long exam — 120 questions of hard math problems for 4th and 8th graders of the world just to know more about the way their countries produce math and science-literate citizens. It is a tiring process, especially for kids so small. Naturally, a student would want to leave some blanks. And they do — some even leave as many as 15–20 questions. Yes, some leave one-sixth of the paper empty. Either because they don't know how to solve the question or are too tired of not knowing what to do...

In hindsight, maybe that was what had happened the evening a day before my exams, but maybe the difference was that it was all forced. I was forced to study my books, my worksheets. I was forced by my peer pressure to go beyond my laziness, to pursue each problem with persistent efforts and to see what happened and how it happened. I was pulled by my circumstances to get better, and that made all the difference.

That day changed my life forever — I have grown so much more. From the equations of Euclid to the Reimann Hypothesis, I have unlocked the beauty of nature.

Read more... 

Source: Medium

The foundations of computer science | Book Announcement - EurekAlert

Two books by Ömer Eğecioğlu invite students to explore the fascinating world of combinatorics by University of California - Santa Barbara.

Photo: Ömer Eğecioğlu

At first pass, it may seem odd for a computer science professor to pen a book about mathematical topics. But a chat with  quickly dispels the notion that the fields are that different, at least from his point of view. The two titles, "Lessons in Enumerative Combinatorics" (2021) and "Lectures in Algebraic Combinatorics" (2020) offer an insightful introduction to the branch of mathematics that gives rise to theoretical computer science.

Ömer Eğecioğlu co-authored the works with his own Ph.D. advisor, Adriano Garsia, emeritus professor of mathematics at UC San Diego. He put together most of "Lessons" from his own teaching materials, while "Lectures" traces its origins to over six decades of Garsia's research and unique perspective. "I was more of a collaborator on the 'Lectures' book," Ömer Eğecioğlu said.

A combinatorial structure is a visual representation of some mathematical construct which often reveals aspects not readily apparent in the original formulation. The methods for counting these structures form the discipline known as enumerative combinatorics.

Among its many other applications, combinatorics opens up the basic theory of computability itself. The mathematics of counting, combinations and ordering eventually leads to symbolic representations, algorithmic thinking and finally, the Turing machine model...

Ömer Eğecioğlu hopes that the two books make combinatorics accessible to people just beginning to learn about the subject, whether they're actually pursuing an advanced degree or simply interested in the topic. And he hopes that these books can help students see the connections between topics in computer science and mathematics that they may otherwise have overlooked.

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Source: EurekAlert 

Creative distortions: the mathematical art of M.C. Escher | Music & art - Cyprus Mail

In this video, Professor Ian Stewart of Warwick University explores the mathematical influences in the works of Dutch artist M. C. Escher by CM Guest Columnist.

Photo: Screenshot of 5imone5's video.

“If you wander around university mathematics departments, you will find Escher pictures all over the place. You’ll even find them in the textbooks, because they really do talk to mathematicians,” says Stewart.

“And from today’s perspective, I think mathematicians understand much more clearly what it was Escher was trying to do – to the extent we can actually write down formulas for some of the things that he does, and we can investigate what mathematical ideas lie behind them.”...

For this reason, even though neglected by the art world until fairly late in his career – even in his native Netherlands – Escher’s creations became well-known among scientists and mathematicians, as well as in pop culture, in particular after having been featured in the 1966 ‘Scientific American’.

“Mathematicians know their subject’s beautiful; Escher shows us that it’s beautiful,” says the Warwick University academic...

View the original video here.

Read more... 

Source: Cyprus Mail 

Now MATH is racist | Daily Mail

Now MATH is racist: Educators condemn $1M 'Dismantling Racism in Mathematics' program funded by Bill Gates which tells teachers NOT to push students to find the correct answer because it promotes white supremacy

• Educators around the US have come out to condemn the 'Dismantling Racism in Mathematics' program
• It centers around a workbook which asserts that asking students to find the correct answer for math problems is inherently harmful for minorities
• So far, the workbook is being used by school districts in Georgia, Ohio, California and Oregon
• Critics say to it actually reinforces negative stereotypes and drives wedges between students according to their race
• 'The workbook's ultimate message is clear: Black kids are bad at math, so why don't we just excuse them from really learning it,' one critic said 
• The program was funded through a $1million grant from The Bill and Melinda Gates Foundation
• It's part of a larger push nationwide to teach students about critical race theory
  

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Educators around the country have come out to condemn a 'Dismantling Racism in Mathematics' program which tells teachers not to push students to find the correct answers to math problems because doing so promotes white supremacy by Brian Stieglitz For Dailymail.Com.

The pictured workbook has drawn criticism from educators for claiming that it's racist to expect students to get the right answer to a math problem

The program is centered around a workbook for teachers entitled 'A Pathway to Equitable Math Instruction' which asserts that America's education system – even mathematics instruction – reinforces the dominant power structures of white colonizers. 

Grading students, asking them to show their work, requiring participation and even pushing them to get the right answer are depicted in the workbook as harmful to minorities.  

The workbook was created by Oakland, California-based advocacy group The Education Trust-West under its 'Dismantling Racism in Mathematics Instruction' initiative, which is funded through a $1million grant from The Bill and Melinda Gates Foundation...

'The concept of mathematics being purely objective is unequivocally false,' reads the manual. 'Upholding the idea that there are always right and wrong answers perpetuates "objectivity." '

Instead, it encourages teachers to have more than one answer for math problems, refrain from calling on students to answer problems for the class, relate math to minority students' experiences and provide examples of how math is used by political revolutionaries.

Read more... 

Source: Daily Mail