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Wednesday, June 30, 2021

Mathematicians welcome computer-assisted proof in ‘grand unification’ theory | Mathematics and Computing - Nature.com

Davide Castelvecchi, Senior Reporter - Physical Sciences notes, Proof-assistant software handles an abstract concept at the cutting edge of research, revealing a bigger role for software in mathematics.

Efforts to verify a complex mathematical proof using computers have been successful
Photo: Fadel Senna/AFP via Getty

Peter Scholze wants to rebuild much of modern mathematics, starting from one of its cornerstones. Now, he has received validation for a proof at the heart of his quest from an unlikely source: a computer.

Although most mathematicians doubt that machines will replace the creative aspects of their profession any time soon, some acknowledge that technology will have an increasingly important role in their research — and this particular feat could be a turning point towards its acceptance.

Scholze, a number theorist, set forth the ambitious plan — which he co-created with his collaborator Dustin Clausen from the University of Copenhagen — in a series of lectures in 2019 at the University of Bonn, Germany, where he is based. The two researchers dubbed it ‘condensed mathematics’, and they say it promises to bring new insights and connections between fields ranging from geometry to number theory.

Other researchers are paying attention: Scholze is considered one of mathematics’ brightest stars and has a track record of introducing revolutionary concepts...

Many researchers say that mathematicians are unlikely to be replaced by machines any time soon. Proof assistants can’t read a maths textbook, they need continuous input from humans, and they can’t decide whether a mathematical statement is interesting or profound — only whether it is correct, Buzzard says. Still, computers might soon be able to point out consequences of the known facts that mathematicians had failed to notice, he adds.

Read more... 

Additional resources

Nature 595, 18-19 (2021)

doi: https://doi.org/10.1038/d41586-021-01627-2

Source: Nature.com

Will AI replace mathematicians? | Mathematics - Big Think

  • Most everyone fears that they will be replaced by robots or AI someday.
  • A field like mathematics, which is governed solely by rules that computers thrive on, seems to be ripe for a robot revolution.
  • AI may not replace mathematicians but will instead help us ask better questions.
The following is an excerpt adapted from the book Shape. It is reprinted with permission of the author.

Dr. Jordan Ellenberg, professor of mathematics at the University of Wisconsin observes, Will machines replace us? 

Photo: Patrick Lux via Getty Images

Since the origin of artificial intelligence (AI), people have worried that computers eventually (or even imminently!) will surpass the human cognitive capacity in every respect.

Artificial intelligence pioneer Oliver Selfridge, in a television interview from the early 1960s, said, "I am convinced that machines can and will think in our lifetime" — though with the proviso, "I don't think my daughter will ever marry a computer." (Apparently, there is no technical advance so abstract that people can't feel sexual anxiety about it.)

AI Anxiety

Let's make the relevant question more personal: will machines replace me? I'm a mathematician; my profession is often seen from the outside as a very complicated but ultimately purely mechanical game played with fixed rules, like checkers, chess, or Go. These are activities in which machines have already demonstrated superhuman ability.

But for me, math is different: it is a creative pursuit that calls on our intuition as much as our ability to compute...

Some people imagine a world where computers give us all the answers. I dream bigger. I want them to ask good questions.

Read more... 

Source: Big Think   

Mission to diversify mathematics pushes professor to leave top spot | Education - Spectrum News 1

What You Need To Know

  • Dr. Edray Goins, a professor of mathematics at Pomona College, was recently awarded more than $120,000 in grant money

  • The money is for an undergraduate summer research program that prioritizes students of color

  • Nationally, the number of Black students majoring in math is dropping

  • By leaving his tenured position at a top research university, Goins has been able to grow this summer program and devote more time to undergraduates of color

A professor took a calculated professional gamble, and it’s paying off, says Parker Collins, Multimedia Journalist at Spectrum News 1. 

Photo: Spectrum News 1

Dr. Edray Goins, a professor of mathematics at Pomona College, was recently awarded more than $120,000 in grant money from the National Security Agency to run an eight-week summer program in mathematics. He received hundreds of applicants so he took special care to select a diverse group of students, especially because the number of Black students majoring in math is dropping nationally.

Goins has devoted his life to math research and teaching — a path that surprised even him...

By leaving, Goins has been able to grow this summer program, devote more time to undergraduates of color and see more diversity within his department. There have been breakthroughs.

Read more... 

Source: Spectrum News 1  

How Aristotle Created the Computer | Technology - The Atlantic

Chris Dixon, general partner at Andreessen Horowitz writes,The philosophers he influenced set the stage for the technological revolution that remade our world.

Photo: Wikimedia / donatas1205 / Billion Photos / vgeny Karandaev / The Atlantic
THE HISTORY Of computers is often told as a history of objects, from the abacus to the Babbage engine up through the code-breaking machines of World War II. In fact, it is better understood as a history of ideas, mainly ideas that emerged from mathematical logic, an obscure and cult-like discipline that first developed in the 19th century. Mathematical logic was pioneered by philosopher-mathematicians, most notably George Boole and Gottlob Frege, who were themselves inspired by Leibniz’s dream of a universal “concept language,” and the ancient logical system of Aristotle.

Mathematical logic was initially considered a hopelessly abstract subject with no conceivable applications. As one computer scientist commented: “If, in 1901, a talented and sympathetic outsider had been called upon to survey the sciences and name the branch which would be least fruitful in [the] century ahead, his choice might well have settled upon mathematical logic.” And yet, it would provide the foundation for a field that would have more impact on the modern world than any other.

The evolution of computer science from mathematical logic culminated in the 1930s, with two landmark papers: Claude Shannon’s “A Symbolic Analysis of Switching and Relay Circuits,” and Alan Turing’s “On Computable Numbers, With an Application to the Entscheidungsproblem.” In the history of computer science, Shannon and Turing are towering figures, but the importance of the philosophers and logicians who preceded them is frequently overlooked...

Today, Boole’s name is well known to computer scientists (many programming languages have a basic data type called a Boolean), but in 1938 he was rarely read outside of philosophy departments. Shannon himself encountered Boole’s work in an undergraduate philosophy class. “It just happened that no one else was familiar with both fields at the same time,” he commented later.

Boole is often described as a mathematician, but he saw himself as a philosopher, following in the footsteps of Aristotle. The Laws of Thought begins with a description of his goals, to investigate the fundamental laws of the operation of the human mind:

The design of the following treatise is to investigate the fundamental laws of those operations of the mind by which reasoning is performed; to give expression to them in the symbolical language of a Calculus, and upon this foundation to establish the science of Logic ... and, finally, to collect ... some probable intimations concerning the nature and constitution of the human mind...

Today’s most promising machine learning techniques use neural networks, which were first invented in 1940s by Warren McCulloch and Walter Pitts, whose idea was to develop a calculus for neurons that could, like Boolean logic, be used to construct computer circuits. Neural networks remained esoteric until decades later when they were combined with statistical techniques, which allowed them to improve as they were fed more data. Recently, as computers have become increasingly adept at handling large data sets, these techniques have produced remarkable results. Programming in the future will likely mean exposing neural networks to the world and letting them learn.

Read more... 

Source: The Atlantic  

National Statistics Day 2021 Today: Significance, Theme And Courses In Statistics | Education - Republic World

National Statistics Day 2021 is being celebrated by Government today. Check theme, significance, and awards in Stats. Also, know about courses in Statistics by Ruchika Kumari, Author at Republic World.

Photo: Unsplash

National Statistics Day 2021: The nation is celebrating 'Statistics Day' today. The Indian Government has been celebrating Statistics Day every year on June 29. The celebration aims to popularise the use of Statistics in everyday life and sensitize the public as to how Statistics helps in shaping and framing policies. Read to know the significance of statistics and also courses available in statistics in India. 

National Statistics Day 2021 theme

Every year, one particular theme of current national importance is chosen. It is being done for focused discussions towards improvements in statistical systems of the area and filling the data gaps. The theme of Statistics Day, 2021 is Sustainable Development Goal (SDG)- 2 (End Hunger, Achieve Food Security and Improved Nutrition and Promote Sustainable Agriculture).

National Statistics Day significance

Statistics Day is one of the special days that is celebrated at the National level. It is celebrated on the birth anniversary of Late Prof. PC Mahalanobis. The day is celebrated to honor the invaluable contribution in establishing the National Statistical System...

Importance of Statistics

Statistics help in forming economic plans and policies. It presents facts in a precise and definitive form. Statistics plays a vital role in the health field and helps conduct social surveys. It is also an essential part of Mathematics...

Some Colleges offering Statistics course in India
  • Indian Statistical Institute, Bangalore
  • Indian Statistical Institute, Delhi
  • Indian Statistical Institute, Kolkata
  • Indian Statistical Institute, Vadodara
  • CR Rao Institute of Advanced Statistics, Hyderabad

Read more...

Source: Republic World

Sunday, June 27, 2021

What We Are Reading Today: Do Not Erase: Mathematicians and Their Chalkboards | Book - Arab News

 “A mathematician, like a painter or poet, is a maker of patterns,” wrote the British mathematician G. H. Hardy. In Do Not Erase, photographer Jessica Wynne presents remarkable examples of this idea through images of mathematicians’ chalkboards. 

Photo/Supplied

While other fields have replaced chalkboards with whiteboards and digital presentations, mathematicians remain loyal to chalk for puzzling out their ideas and communicating their research. Wynne offers more than 100 stunning photographs of these chalkboards, gathered from a diverse group of mathematicians around the world. The photographs are accompanied by essays from each mathematician, reflecting on their work and processes. Together, pictures and words provide an illuminating meditation on the unique relationships among mathematics, art, and creativity.

The mathematicians featured in this collection comprise exciting new voices alongside established figures, including Sun-Yung Alice Chang, Alain Connes, Misha Gromov, Andre Neves, Kasso Okoudjou, Peter Shor, Christina Sormani, Terence Tao, Claire Voisin, and many others...

Do Not Erase is a testament to the myriad ways that mathematicians use their chalkboards to reveal the conceptual and visual beauty of their discipline—shapes, figures, formulas, and conjectures created through imagination, argument, and speculation.

Read more... 

Additional resources

 Do Not Erase:
Mathematicians and Their Chalkboards 
 
Source:  Arab News

The joy of second hand books | Culture - Spectator.co.uk

There are few aesthetic and literary pleasures that compare to browsing in a second-hand bookshop by Alexander Larman, The Spectator columnists & writers.

Photo: Spectator.co.uk

While it is more or less a given what books will be found in a new bookshop, one of the chief joys of going second hand is that it’s entirely unpredictable what you'll emerge with. Sometimes, the browser will leave empty-handed, but more often than not – and I speak from personal experience here – ‘a quick look’ will turn into the purchase of a dozen interesting volumes and a solid half an hour’s perusal.

Yet the industry, once so much part of every town and city, has been existentially threatened by the growth of the charity bookshop trade over the past two decades, not least the Oxfam bookshops. I would not seek to denigrate either these excellent shops – the Oxfam on St Giles in Oxford remains one of my favourite places to browse – or the intention behind them, but the advantages they face (free stock, volunteer staff, tax breaks from the government) means that many second-hand bookshop proprietors, their reluctant rivals, have either shut their bricks and mortar shops, or retired altogether...

Outstanding second-hand bookshops in the United Kingdom:

Read more... 

Source: Spectator.co.uk 

The Kingdom of Books | Culture - Oxford Student

Poppy Atkinson Gibson, Student at University of Oxford writes, Some places are just special, stamped with a cosmic seal of approval which is felt by anyone who visits: Hay-on-Wye is one of those places. 

Crowded stacks of second hand books

Located in Powys on the border between England and Wales, Hay, or Y-Gelli Gandryll (‘the shattered grove’) as it is known in Welsh, is a bustling market town full of quirks. Mostly, however, it is full of books. With over twenty secondhand bookshops, Hay is the must-go-to destination for any avowed bibliophile.

With so many shops to choose from, it can be difficult to know where to start. Hay-on-Wye Booksellers caters to every taste, stocking books on all manner of subjects, from botany to impressionism. Must-see sites include Cinema Books, a redundant cinema converted into a bookshop in 1965, is likely to please everyone, containing roughly 200,000 volumes. A special favourite with visitors and locals alike is Murder and Mayhem, which, as the name implies, exclusively sells murder mysteries, crime ,and horror stories. Meanwhile, Rose’s Books on Hay’s very own Broad Street specializes in the trade of rare and out-of-print illustrated children’s books. At the centre of the town stands Hay Castle, beaming down upon the book-laden shoppers of Castle Street. Every kingdom needs a castle after all...

Not only is Hay home to hundreds of thousands of books, but every year since 1988, the town has thrown open its doors to visitors during its annual literary festival, aptly named Hay Festival.

Read more... 

Source: Oxford Student  

Book lover from Okehampton leaves extraordinary antiquarian collection to Tavistock Oxfam | Local People - Tavistock Times Gazette

A TAVISTOCK bookshop has been left an extraordinary donation of 2,300 antiquarian titles, in the will of a regular customer by Alison Stephenson, Editor at Tavistock Times Gazette.

Photo: Tavistock Times Gazette

Andres Nurmela’s book collection, which includes hundreds of many valuable and beautifully bound items, is set to raise thousands of pounds for the charity Oxfam.

Manager of the Oxfam Books and Music Shop Val Sharpe said this week they owned Andres ‘a huge, huge thank you’

Andres kept the promise he made to Val before he died and left all his books to the place where he spent many enjoyable hours over the last 10 years...

‘There are a number of the books (added to and changed weekly) in the Collectables area in the shop, ongoing, for a long time yet. We are looking forward to doing lots of research, learning a lot and enjoying the whole process. We owe Andres a huge, huge thank you.’

Read more... 

Source: Tavistock Times Gazette   

Stunning 125-year-old book on display at Wightwick Manor | Attractions - expressandstar.com

One of the 'most important' books ever printed is on display at Wolverhampton's Wightwick Manor – to commemorate International Kelmscott Press Day on June 26, inform Dayna Farrington, Deputy chief reporter at the Express & Star.

The 125-year old copy of The Works of Geoffrey Chaucer

The Works of Geoffrey Chaucer, printed by William Morris' Kelmscott Press 125 years ago this week, set a new standard for book design at the end of the 19th century, which its number of illustrations and rich decorative borders.

Masters of the arts and crafts movement were involved in its conception – William Morris designed the title page, borders, initial letters and ornaments and Edward Burne-Jones created the woodcut illustrations.

Considered the greatest work of the Kelmscott Press, the Kelmscott Chaucer was a culmination of William Morris's vision for the ideal, finely crafted book.

In founding the Kelmscott Press, Morris sought to revive the art of hand-printing, derived from exemplars of medieval manuscripts and early printed books...

Visitors will be able to see the Kelmscott Chaucer and the other Kelmscott Press memorabilia on display at Wightwick Manor until November. Tickets need to be pre-booked by visiting nationaltrust.org.uk/wightwickmanor

Read more... 

Source: expressandstar.com

Saturday, June 26, 2021

How to Use Discussion Forums to Begin, Center, and Produce Student Writing | Online Course Design and Preparation - Faculty Focus

Crystal Edmonds, retired college educator recommends, Discussion forums are a foundation of online courses because they serve as a hub for student discussion of a subject. 

Photo: Faculty Focus

However, many online courses have become oversaturated with discussion forums that often serve as attendance assignments or ask obscure questions that really do not add to the purpose or content of the class. For my English composition course, specifically Freshman Composition II, the forum serves as a virtual location for students to discuss and center their ideas on a specific reading before moving to a major writing assignment.

The forum accomplishes three purposes: to engage them in conversation, to assess their comprehension of the text, and to serve as the first scaffolding task that leads to a major written task...

Refining the forum

Some experts have discouraged faculty from beginning a forum with questions saying that it is outdated, or students are bored by the structure because it is overused; however, in an asynchronous online English class, such forums reinforce the idea that writing is not an individual activity; it may be a community endeavor. Students should be able to generate ideas and shape those ideas with the help of classmates. Students should be able to express their ideas and be prepared to defend those ideas—both are done through conversation.

However, I do acknowledge that other forms of technology may foster the same types of conversations. Using Voice Thread, for example, allows students to view an image and vocalize their responses instead of reading them.

Read more... 

Source: Faculty Focus  

The Time Has Come: Include Research and Education in the Broadband Investment | From the President - EDUCAUSE Review

EDUCAUSE is working with representatives from across the research and education network (REN) community to highlight the importance of closing the institutional digital divide.


EDUCAUSE has consistently pressed for funding both to ensure that higher education students can overcome digital divides and to strengthen the networks that support research and education, as John O'Brien, President & CEO at EDUCAUSE reports.

Photo: EDUCAUSE Review
As Congress and the Biden administration negotiate a major federal investment in broadband, we at EDUCAUSE are happy to work with our sister organizations to elevate the voice of higher education in the debate. I am particularly encouraged by our recent collaboration, led by Internet2 and The Quilt, with representatives from across the research and education network (REN) community. Through that process, we have come together to highlight the importance of closing the institutional digital divide, which is essential to achieving vital national objectives.

Shortly before Memorial Day this year, our working group released The Minds We Need: Research and Education Infrastructure Inclusion, Innovation, and Competitiveness.  This report calls for a nearly $5 billion investment in REN infrastructure as a key element of addressing the broadband, research, and education goals of the United States. Together, we argue that this injection of funding into state and regional RENs and the country's research and education network backbone, Internet2, will make it possible to connect every college and university—including every community college, historically black college and university (HBCU), minority-serving institution (MSI), tribal college and university (TCU), and college and university-related research facility—to advanced, research-quality broadband.

Furthermore, the proposed funding will enable these critical connections while also expanding the capacity and capabilities of the networks for all of the institutions that rely on them...

Creating this rising tide of connectivity to lift all of higher education's boats will, in turn, allow institutions of all types across the country to incorporate bandwidth-intensive, multimedia knowledge resources into their courses and programs, enriching and extending the quality and effectiveness of the learning opportunities they make available. It will also open the door for many more institutions and students to participate in research projects and activities, which again will generate new, more advanced learning opportunities while strengthening academic research.  

Read more...

Source: EDUCAUSE Review

Study shows strong links between music and math, reading achievement | K-12 Education - Science Daily

Summary:
A music educator thought that if he could just control his study for the myriad factors that might have influenced previous ones - race, income, education, etc. -- he could disprove the notion of a link between students' musical and mathematical achievement. Nope. His new study showed statistically significant associations between the two at both the individual and the school-district levels.


Music educator Martin J. Bergee thought that if he could just control his study for the myriad factors that might have influenced previous ones -- race, income, education, etc. -- he could disprove the notion of a link between students' musical and mathematical achievement by Science Daily

Educational achievement in music is strongly linked to the same in reading and math in a new study by a KU researcher.
Photo: iStock

Nope. His new study,"Multilevel Models of the Relationship Between Music Achievement and Reading and Math Achievement," published in the Journal of Research in Music Education, showed statistically significant associations between the two at both the individual and the school-district levels. That the study of more than 1,000 mainly middle-school-aged students showed no such association at the classroom or school levels only shows how rigorously it was conceived by Bergee, a professor in the University of Kansas School of Music, and his co-author and Ph.D. student, currently a visiting professor of music education at the University of Washington, Kevin M. Weingarten.

The study has implications for school-board members considering budgets that impact music programs. It adds to the body of scientific research showing linkages between music and math/reading. And in his conclusion, Bergee even suggests some specific reasons for why that might be...

In a recent interview, Bergee said, "Based on the findings, the point we tried to make is that there might be, and probably are, general learning processes that underlie all academic achievement, no matter what the area is. Music achievement, math achievement, reading achievement -- there are probably more generalized processes of the mind that are brought to bear on any of those areas.

Read more... 

Additional resources

Journal Reference:

  1. Martin J. Bergee, Kevin M. Weingarten. Multilevel Models of the Relationship Between Music Achievement and Reading and Math Achievement. Journal of Research in Music Education, 2020; 002242942094143 DOI: 10.1177/0022429420941432

Source: Science Daily

The Two Forms of Mathematical Beauty | Mathematics - Quanta Magazine

Mathematicians typically appreciate either generic or exceptional beauty in their work, but one type is more useful in describing the universe, argues Professor Robbert Dijkgraaf, University Professor at the UvA since 1 January 2005

Photo: James O’Brien for Quanta Magazine

A time-honored practice in mathematical circles is to divide the field in two. There’s the traditional “applied versus pure” argument, which mirrors the experimental-theoretical divide of other disciplines — the tension between advancing knowledge toward a specific end and doing it for its own sake. Or we can bisect mathematics in the same way that our brain is split, with an algebraic “left hemisphere” that thinks in logical sequences and a geometric “right hemisphere” that has a more visual approach. But the field also breaks down according to a more subtle distinction: one’s preference between two flavors of mathematical beauty.

It’s tough for nonexperts to see mathematics as beautiful in the first place. Beauty is in the eye of the beholder, sure, but it’s also hard to see when the work of art is hidden in darkness, obscured by an impenetrable cloud of symbols and jargon. Trying to appreciate mathematics without understanding its inner workings is like reading a description of Beethoven’s Fifth Symphony instead of hearing it.

Yet mathematicians have no qualms about earnestly describing their equations and proofs as beautiful...

But the real world is very different from the idealized landscape of mathematics. Most sciences are tethered to the universe that describes the real world — but that’s just one out of an infinity of mathematical possibilities. As Jean-Pierre Serre reportedly quipped to his mathematician colleague Raoul Bott, “While the other sciences search for the rules that God has chosen for this Universe, we mathematicians search for the rules that even God has to obey.”

Read more... 

Source: Quanta Magazine   

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

Follow on Twitter as @spacebarge
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.

Read more...

Source: Phys.org

Friday, June 25, 2021

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.”

Read more... 

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.


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.

Read more... 

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.

Read more... 

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  

Thursday, June 24, 2021

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.

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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

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.

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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

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.

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Source: Daily Mail