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Tuesday, February 19, 2019

The Empty Brain | Data & Information - aeon

This post originally appeared on aeon.

Robert Epstein, senior research psychologist at the American Institute for Behavioral Research and Technology in California notes, No matter how hard they try, brain scientists and cognitive psychologists will never find a copy of Beethoven’s 5th Symphony in the brain – or copies of words, pictures, grammatical rules or any other kinds of environmental stimuli.

What’s in a brain?
Photo: Unsplash

The human brain isn’t really empty, of course. But it does not contain most of the things people think it does – not even simple things such as ‘memories’.

Our shoddy thinking about the brain has deep historical roots, but the invention of computers in the 1940s got us especially confused. For more than half a century now, psychologists, linguists, neuroscientists and other experts on human behaviour have been asserting that the human brain works like a computer.

To see how vacuous this idea is, consider the brains of babies. Thanks to evolution, human neonates, like the newborns of all other mammalian species, enter the world prepared to interact with it effectively. A baby’s vision is blurry, but it pays special attention to faces, and is quickly able to identify its mother’s...

But here is what we are not born with: information, data, rules, software, knowledge, lexicons, representations, algorithms, programs, models, memories, images, processors, subroutines, encoders, decoders, symbols, or buffers – design elements that allow digital computers to behave somewhat intelligently. Not only are we not born with such things, we also don’t develop them – ever...

In his book In Our Own Image (2015), the artificial intelligence expert George Zarkadakis describes six different metaphors people have employed over the past 2,000 years to try to explain human intelligence.
Read more... 

Source: aeon via Pocket. 

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Moving into Management: The Skills New Managers Are Learning | Leadership - LinkedIn Learning

Imagine you’ve just reached a major landmark in your career - you’ve been promoted from an individual contributor to a manager! according to Sophie (Wharton) Smith, Insight Analyst, Learning Solutions at LinkedIn.

Photo: The Learning Blog

This is a moment to celebrate, but it can also be a challenging transition. Research suggests that adjusting to a promotion can be a stressful life experience; however, it’s also the perfect time to learn.

So when new managers seek help, what types of skills are they looking to learn? We analyzed data from LinkedIn Learning to understand what courses this group is watching at higher rates than the average user. Of the 13,000 courses on our platform, which do first-time managers flock to when they’re starting their new role?

Two main insights emerged from our analysis: new managers are focused on thinking more strategically and learning to build stronger relationships.

Source: LinkedIn Learning (Blog) 

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Significant Endowment Inspires Rural Students ‘To Learn To Love The Flute’ | Colorado Mesa University - CBS Denver

Matt Kroschel, Mountain Newsroom Reporter explains, A woman on Colorado’s Western Slope wanted to make a difference in the lives of a very specific group of young musicians. In 2018, Dr. Ruth Maurer gifted Colorado Mesa University a significant endowment for the purposes of enhancing the flute in rural communities.

Dr. Ruth Maurer
(Photo: CBS)

Her act of kindness is already impacting young lives in rural western Colorado.

“I thought about this for a while. I decided I would like to give some money to CMU because they’ve been really nice to me at the music department. They make it feel like home,” she said.

Maurer is a Renaissance woman who is not only a mathematician with a Ph.D but also an artist and philanthropist who pioneered a pathway for young women.

“It’s just amazing. It’s amazing, because it just comes from nowhere. Very generous woman who loves what she does, very talented. When people want to give back like that it warms the heart,” CMU President Tim Foster said...

Using the newly established Ruth Maurer Flute Endowment, the music department will host an annual Flute Fest West, including a Western region flute competition for small, rural high school students.

“You want to put your money where you can do the most good on something that you really like. I really like the flute. I think by endowing this flute program in helping it grow, more people will learn to love the flute,” Maurer said.
Read more... 

Source: CBS Denver

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Latest prime number discovery mind-bogglingly enormous | Complete Colorado

We have a winner! In December, Patrick LaRoche of Ocala, Fla., discovered the largest prime number known to humanity, observes Barry Fagin, Senior Fellow in Technology Policy at the Independence Institute, free maret think tank in Denver, and a Professor of Computer Science.  

Geralt/Pixabay [Licensed under CC0 Creative Commons]

It’s got almost 25 million digits. Just writing it down would take you a couple of years. Provided you didn’t take a vacation.

A prime number is a number greater than 1 that is divisible only by 1 and itself. For example, 2, 3, 5, and 7 are primes. 6, 8, 9 and 10 are not. Primes have fascinated humans ever since we learned to count, because they are the fundamental building blocks of arithmetic. And yet, there is no known pattern to them.

They’re just out there, waiting to be found.

How many primes are there? Over two thousand years ago, the Greek mathematician Euclid proved they were infinite in number. That’s how long we’ve been studying these strange beasts of the counting world...

For the past few decades, the largest known primes have been what are known as Mersenne Primes. Marin Mersenne was a Catholic priest and theologian who lived in the 17th century. He was also a gifted scientist and mathematician. The primes that bear his name are of a special form that makes them easy to test quickly, even though at this point they’re now mind-bogglingly enormous.

The new champion is the 51st Mersenne Prime. It will bear Laroche’s name for all eternity. How big is it, you ask? 

Source: Complete Colorado

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For a Black Mathematician, What It’s Like to Be the ‘Only One’ | Science - The New York Times

Amy Harmon, national correspondent for The New York Times, covering the intersection of science and society reports, Fewer than 1 percent of doctorates in math are awarded to African-Americans. Edray Goins, who earned one of them, found the upper reaches of the math world a challenging place.

At the Baltimore conference, Dr. Goins delivered a keynote address titled “A Dream Deferred: 50 Years of Blacks in Mathematics.”
Photo: Jared Soares for The New York Times

It was not an overt incident of racism that prompted Edray Goins, an African-American mathematician in the prime of his career, to abandon his tenured position on the faculty of a major research university last year.

The hostilities he perceived were subtle, the signs of disrespect unspoken.

There was the time he was brushed aside by the leaders of his field when he approached with a math question at a conference. There were the reports from students in his department at Purdue University that a white professor had warned them not to work with him.

One of only perhaps a dozen black mathematicians among nearly 2,000 tenured faculty members in the nation’s top 50 math departments, Dr. Goins frequently asked himself whether he was right to factor race into the challenges he faced.

That question from a senior colleague on his area of expertise, directed to someone else?...

“Who do they make eye contact with?”
In an essay that has been widely shared over the last year, Dr. Goins sought to explain himself. He extolled the virtues of teaching undergraduates and vowed to continue his research. But he also gave voice to a lament about the loneliness of being black in a profession marked by extraordinary racial imbalance.

“I am an African-American male,” Dr. Goins wrote in a blog published by the American 

Mathematical Society. “I have been the only one in most of the universities I’ve been to — the only student or faculty in the mathematics department.”

“To say that I feel isolated,” he continued, “is an understatement.”
Experiences similar to Dr. Goins’s are reflected in recent studies by academic institutions on attrition among underrepresented minorities and women across many disciplines. 

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Sunday, February 17, 2019

Winner of the 2019 PROSE Award for Mathematics, from the Association of American Publishers | Book - Cambridge University Press

Be sure to check out the New edition of High-Dimensional Probability, An Introduction with Applications in Data Science by Roman Vershynin, University of California, Irvine. 

High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability, analysis, and geometry, it lends itself to applications in mathematics, statistics, theoretical computer science, signal processing, optimization, and more. It is the first to integrate theory, key tools, and modern applications of high-dimensional probability...

A broad range of illustrations is embedded throughout, including classical and modern results for covariance estimation, clustering, networks, semidefinite programming, coding, dimension reduction, matrix completion, machine learning, compressed sensing, and sparse regression.
  • Closes the gap between the standard probability curriculum and what mathematical data scientists need to know
  • Selects the core ideas and methods and presents them systematically with modern motivating applications to bring readers quickly up to speed
  • Features integrated exercises that invite readers to sharpen their skills and build practical intuition

Source: Cambridge University Press 

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The Voices of Black Mathematicians | Roots of Unity - Scientific American

Black History Month in the U.S. is a good time to celebrate these important people, observes Evelyn Lamb, Freelance math and science writer based in Salt Lake City, Utah.

Six of the mathematicians featured on the Mathematically Gifted and Black website: Raymond Johnson, Suzanne L. Weekes, Mohamed Omar, Talithia Williams, Scott Williams, and Kimberley Sellers
Photo: Raymond Johnson, Suzanne L. Weekes, Mohamed Omar, Talithia Williams, Scott Williams, and Kimberley Sellers

February is Black History Month in the United States, and as such it is an excellent time to learn about black history, yes, but also to listen to black people when they talk about their lives today. As this is a math blog, I am going to focus on black mathematicians, but I hope you’re taking advantage of other black history month observances, including this literary series from Very Smart Brothas and Chelsea Green’s Instagram series of black women composers and musicians.

Mathematically Gifted and Black is a good place to start learning about living black mathematicians. (To save you time, here’s a link to Nina Simone singing “Young, Gifted and Black,” which I get stuck in my head every time I see the name of that website.) Mathematically Gifted and Black was founded in 2017 and features a short Q&A with a black mathematician every day in February. For information on both historical and modern black mathematicians, see Scott Williams’ website Mathematicians of the African Diaspora. The American Mathematical Society blog inclusion/exclusion recently published a post about the impact that site has had on African American math students and mathematicians...

In that spirit (and with only a sliver of shameless self-promotion), I want to point to the My Favorite Theorem podcast episodes Kevin Knudson and I have recorded with black mathematicians. Click through for audio, show notes, and links to transcripts. Emille Davie Lawrence told us why she loves the surface classification theorem. Mohamed Omar told us how to count symmetries using a clever lemma. Candice Price told us about DNA topology and mathematical “tangles.” John Urschel told us about graph sparsifiers.  Chawne Kimber told us about the Hahn embedding theorem. Nira Chamberlain told us about the Lorenz system of equations. This year and last year, the Notices of the American Mathematical Society has devoted its February issue to Black History Month and the work of black mathematicians. Find this year's articles here through the end of February 2019 and last year's here (pdf).

Source: Scientific American

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Culturally Responsive Mathematics Teaching | Education Week

This white paper is provided by Curriculum Associates.

Check out mathematics expert Dr. Mark Ellis "Knowing and Valuing Every Learner: Culturally Responsive Mathematics Teaching (CRMT)".

Culturally responsive mathematics teaching (CRMT) is about inviting all students into mathematics as participants because their ways of thinking and reasoning are worth sharing. It’s about ensuring each and every learner not only has success with mathematics, but also comes to see mathematics as a tool to examine the world.

We know from decades of research that:
• Student success with mathematics is primarily due to opportunities to learn meaningful
mathematics—and not due to innate intelligence;
• effective mathematics teaching cultivates the mathematics abilities of all students;
• equitable access and support in learning mathematics includes attention to students’
reasoning and identities (Boaler & Staples, 2008; Gutiérrez, 2013; Kisker, et al., 2012; Malloy &
Malloy, 1998; NCTM, 2014; National Research Council, 2009; Razfar, Licón Khisty, & Chval, 2009).

Read more... 

Source: Education Week

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Saturday, February 16, 2019

Mathematicians report a way to optimize post-stroke therapy | Mathematics - Phys.Org

RUDN scientists have created a mathematical model describing changes in the properties of brain tissues after stroke, says Phys.Org

Photo: Natalia Deryugina/VSRao

The development will help clinicians to optimize post-stroke therapy by stimulating brain neurons and taking into account each patient's individual situation. The results of the study were published in Mathematical Biosciences.

Over 15 million people have strokes each year. A stroke is an acute blood circulation failure in the brain that kills neural cells. Patients who suffer a stroke often face partial or total speech loss, and find it difficult to move their limbs or the whole body. One rehabilitation method after a stroke is cerebral cortex stimulation with brain-implanted electrodes or magnetic impulses. The success of the therapy depends on many factors, including the area of the brain that is stimulated and the types of signals used. Currently, optimal therapy parameters are selected manually. RUDN mathematicians have created a theoretical model to base such selection on exact calculations.

"Our task was to develop a theoretical model describing how the speed of a nervous impact propagation (i.e. the excitation of the tissue) fades down due to post-stroke damage to the cerebral cortex. Moreover, we demonstrated that in certain cases electric stimulation of the brain may compensate for this process," said Vitaly Volpert, the author of the article, and the head of the laboratory of mathematical modeling in biomedicine at RUDN.

After a stroke, a so-called penumbra forms in the brain. It is an area where the blood supply is reduced compared to requirements for normal functioning, but which is still higher than the critical level after which an irreversible change occurs. Penumbra cells become less excitable and lose connection with other neurons, leading to changes in the shape and speed of the excitation wave. RUDN mathematicians calculated the conditions at which the speed of neural impulses may be restored to normal levels with the help of external stimulation.

The model is based on the continual nerve tissue theory.

Read more... 

Additional resources 
Mathematician calculates wave velocity for post-stroke therapy

A. Beuter et al. Modeling of post-stroke stimulation of cortical tissue, Mathematical Biosciences (2018). 
DOI: 10.1016/j.mbs.2018.08.014

Source: Phys.Org

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Monday, January 21, 2019

How one German city developed – and lost – generations of math geniuses | Science and Technology -

This article first appeared on The Conversation.

Anti-Semitism brought down one of the world's greatest centers for mathematical research, explains David Gunderman, PhD student in Applied Mathematics, University of Colorado.

Auditorium University of Göttingen, Germany
Photo: Daniel Schwen/Wikimeida Cmmmons [Licensed under CC BY 2.5]
There are two things that connect the names Gauss, Riemann, Hilbert and Noether. One is their outstanding breadth of contributions to the field of mathematics. The other is that each was a professor at the same university in Göttingen, Germany.

Although relatively unknown today, Göttingen, a small German university town, was for a time one of the most productive centers of mathematics in history.

Göttingen’s rise to mathematical primacy occurred over generations, but its fall took less than a decade when its stars were pushed abroad by the advent of National Socialism, the ideology of the Nazi Party. The university’s best minds left Germany in the early 1930s, transferring its substantial mathematical legacy to Princeton, New York University, and other British and American universities. By 1943, 16 former Göttingen faculty members were in the US.

The story of the rise and fall of mathematics in Göttingen has largely been forgotten, but names associated with the place still appear frequently in the world of mathematics. Its legacy survives today in other mathematical research powerhouses around the world...

Great mathematicians 
By the late 18th century, the university in Göttingen was a well-known center of scientific learning in Germany. Its enduring mathematical prowess, however, originated in Carl Friedrich Gauss. Often referred to as the prince of mathematics, his research at Göttingen between 1795 and 1855 spanned from algebra to magnetism to astronomy.

Gauss’s discoveries were groundbreaking, but the reputation that he started in Göttingen only grew as mathematicians from across Europe flocked to the town. Bernhard Riemann, the head of mathematics at Göttingen from 1859 to 1866, invented Riemannian geometry, which paved the way for Einstein’s future work on relativity. Felix Klein, the chair of mathematics from 1886 to 1913, was the first to describe the Klein bottle, a 3-dimensional object with just one side, similar to the Mobius strip...

The exodus 
Emmy Noether, who had been the first female professor of mathematics at Göttingen and was described by Einstein as the most important woman in the history of mathematics, left in 1933 to teach at Bryn Mawr College. Richard Courant left in 1933 to help found the top US applied mathematics institute at New York University. Hermann Wey, who had been appointed Hilbert’s successor as chair of mathematics in Göttingen,l moved to Princeton, where he helped to transform the Institute for Advanced Studies into a research powerhouse.


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