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Monday, January 21, 2019

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

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.
Read more...

Source: Scroll.in


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Friday, January 18, 2019

Any Rubik's Cube can be solved in 20 moves, but it took over 30 years for anyone to figure that out | Strategy - INSIDER

  • The Rubik's Cube is an iconic puzzle toy.
  • But it is mathematically complicated — there are 43 quintillion possible configurations of the Cube.
  • Over 30 years after the Cube was invented, a group of mathematicians showed, using a bank of supercomputers at Google, that any cube could be solved in at most 20 moves.

The Rubik's Cube is a classic puzzle toy invented in 1974 by Hungarian architecture and design professor Erno Rubik, notes Andy Kiersz, senior quant reporter at Business Insider.

Competitors solve Rubik's cubes as they prepare for the world's largest Rubik's Cube championship in Aubervilliers, near Paris, France, July 15, 2017.
Photo: REUTERS/Stephane Mahe
The toy consists of a cube made up of 27 smaller cubes arranged in a 3x3x3 grid with colored stickers on the outer faces of the smaller cubes. A cube starts out in its "solved" configuration with the smaller faces each of the six sides sharing the same color. Each of the six faces of the cube can be rotated freely, moving the smaller cubes around.

The goal of a Rubik's Cube puzzle is to start with some randomized and shuffled messy configuration of the cube and, by rotating the faces, get back to the original solved pattern with each side being a single color.

Actually solving the puzzle is notoriously tricky. It took Erno Rubik himself about a month after inventing the cube to be able to solve it. 

Since then, several methods and techniques have been developed for solving a Rubik's Cube, like this basic strategy laid out on the official Rubik's Cube site. Practiced cube-solvers can complete the puzzle in a matter of seconds, with the current world-record holder solving a cube in 3.47 seconds.

Puzzles like the Rubik's Cube are the kind of thing that fascinate mathematicians. The toy's geometrical nature lends itself nicely to mathematical analysis...

As Erno Rubik put it in a recent interview with Business Insider, this question is "connected with the mathematical problems of the cube." 

Source: INSIDER


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Best online e-learning courses for female entrepreneurs | Technology - JBKlutse

JBKlutse.com says, There are thousands of e-learning courses to choose from, so it can be challenging to make the right choice and pick the one that will truly help you achieve your goals. 

Photo: JBKlutse

Having said that, if you’re looking for an online course designed for female entrepreneurs, you’ll find that it’s much easier to choose, as there aren’t so many such courses. Of course, there’s no reason not to enrol in any other course that’s not specifically aimed at women, because you can certainly learn a lot of useful stuff that can help you build a successful career. Nevertheless, we’ve created a short list of e-learning courses that are aimed at female entrepreneurs. Read on to check them out.
Read more... 

Source: JBKlutse


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E-learning course | College Notes - The Tribune

Ludhiana: Khalsa College for Women, Civil Lines, has been selected by SWAYAM-NPTEL to host a local chapter in the institution.  The National Programme on Technology Enhancement Learning (NPTEL), a project funded by the Ministry of Human Resource Development (MHRD), provides e-learning through online web and video courses in engineering, Sciences, technology, management and humanities. 
 

Photo: FreeDigitalPhotos.net

This is a joint initiative by a number of IITs and IISc Bangalore and other selected premier institutions, which act as associated partner institutions.  Dr Monita Dhiman, Assistant Professor Zoology, has been nominated as the Single Point of Contact (SPOC) from the college.  The main objective of the NPTEL is to facilitate students of various institutions through easier competitive means, which will aid in improving the Indian industry in the global market. SWAYAM-NPTEL is playing a vital role for enhancement of knowledge of both teachers and students. 

Placement drive  
The training and placement cell of Guru Nanak Khalsa College for Women, Gujarkhan Campus, Model Town, organised a placement drive in collaboration with CONCENTRIX...

Career counselling for students

The career coaching cell of Khalsa College for Women, Civil Lines, organised a seminar on ‘Career Guidance And Enhancement Of Employability Skills’. The seminar provided the opportunity to the students to learn and pursue various careers after graduation. 
Read more...

Source:The Tribune


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Williams College students help Pownal 5th-graders learn coding | Berkshire Eagle

Computers know what to do — only if you tell them precisely what you want, summarizes Patricia LeBoeuf, Reporter at Bennington Banner.

Students in Taylor Robinson's fifth-grade class learn coding during the hour of code on Tuesday morning at Pownal Elementary School. 
Photo: Holly Pelczynski - The Bennington Banner
Students at Pownal Elementary School learned that lesson from Williams College students in a workshop Tuesday, part of a brand-new effort from the college to teach fifth-graders about coding.

"Have you guys ever baked cookies with your parents, or followed a recipe?" asked Francesca Hellerman, a Williams College student, of the students in Taylor Robertson's fifth-grade glass. Many hands went up.

"That's a lot like coding," she said.

Hellerman, along with another Williams student, Suzanna Penikis, conducted the workshops as part of a winter session course at the college, Hour of Code. The workshops run Tuesday and Thursday for an hour each at Pownal Elementary in Robertson and Traci Cristofolini's fifth-grade classrooms; they're also bringing the workshop to students in North Adams and Williamstown this month.

Students went through the coding exercises at their own pace, telling the program to do things like print words and make emojis — happy and otherwise...

Recipes for computers
An hour isn't a lot of time to actually teach computer science, he said. The workshops are intended to expose kids to the idea of coding, he said.

Students are given "a bunch of little recipes" to follow — basic coding.

"They're sort of drawing things on the screen," Barowy said. "We also have an extensive set of emojis."

Coding itself can be thought of like writing down a recipe for a computer to follow, he said.

And that's the challenge. 
Read more...

Source: Berkshire Eagle


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Cleveland's New Musical Instrument Donation Drive Kicks Off MLK Day | Arts - Cleveland Scene

Thanks to expert tidier Marie Kondo's new Netflix series, people everywhere are purging their homes of unused and unneeded things this new year. 

Photo: via Wikimedia Commons
And in Cleveland, there's a new way to donate your dust-collecting musical instruments (think: that trumpet or violin you haven't touched since high school).
 

Starting Monday, five non-profit/public groups, including Arts Cleveland, the Center for Arts-Inspired Learning, Cleveland City Council, Cleveland Metropolitan School District and the Cleveland Orchestra, have come together for a city-wide instrument drive for kids called Play It Forward. This year, all gently used instruments will go to children involved with rec center music programs in the Glenville neighborhood, but expansions are planned for the future.
Read more...  


Source: Cleveland Scene


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The idea that successful people can teach their secrets isn’t new. Now MasterClass is selling it for $180 | The Goods - Vox.com

Can a video of Serena Williams teach you tennis? Probably not.

Photo: Sarah Lawrence for Vox

After surviving for five months in space, astronaut Chris Hadfield has a new, tougher challenge: teaching me, a grown man whose only qualifications are narrowly passing 10th-grade science and usually keeping motion sickness at bay when commuting, to be a space explorer.

“It will be a great moment of introspection for humanity if you’re the person who finds that one little fossilized flower on Mars,” he says over rousing music. He points at the viewer when he says “you.” That viewer, not the first or even the millionth, is me as I watch the trailer for his MasterClass.

MasterClass burst onto the scene in 2015 with more star power than Love, Actually. Its pitch was simple: Famous people teach you about the thing that made them famous. For $90, you’d get access to the instructional videos and workbooks that made up each course. Students could also interact with one another and maybe their star instructor. Serena Williams reportedly invited one of her students to play tennis. James Patterson published a novel with one of his pupils.

2015 was a heady time for online learning. It was only a few years after the New York Times announced the “Year of the MOOC (massive open online course).” Universities had started putting lectures by their star instructors online. In 2013, the video e-learning platforms CreativeLive and Coursera completed Series B rounds of $21.5 million and $63 million, respectively. MasterClass appeared to synthesize all these developments, with the addition of copious stardust.

While much of e-learning matured into mundanity, MasterClass has doubled down on celebrity glitz. It now focuses on selling annual, all-access subscriptions...

Every MasterClass follows the same formula. Bathed in soft light, the instructor delivers 15 to 30 brief lectures. If the instructor does something inherently visual for a living, like cooking or sports, those lessons include demonstrations. The writers just talk. Each lesson comes with a PDF workbook containing a summary and links to further reading. Students can record questions for instructors, who periodically post video replies during “office hours.” The formula extends all the way to course titles: Person Teaches Skill. Deadmau5 Teaches Electronic Music Production. Frank Gehry Teaches Design and Architecture. James Suckling Teaches Wine Appreciation. Teaches.
Read more...  

Source: Vox.com


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Thursday, January 17, 2019

Do YOU suffer from 'statistics anxiety'? Researchers say stress from math is real (and reveal how to beat it) | Science - Daily Mail

  • Approximately 80 percent of college students suffer from 'statistics anxiety'
  • University of Kansas researchers sought to quantify what factors add to this fear
  • Students were asked how they feel about their ability to do math, fear of statistics teachers, test and class anxiety and if they feared asking for help

Many people find math frustrating, as Daily Mail reports.  

Many people find math frustrating. But for some, it can turn into 'statistics anxiety,' a fear of doing math problems that can be debilitating or even stand in the way of graduation
Photo: Ollyy - Shutterstock

But for some, it can actually turn into 'statistics anxiety,' a fear of doing math or statistics problems that can be debilitating or even stand in the way of graduation. 

A new study from the University of Kansas discovered which factors can contribute to statistics anxiety and how it can be dealt with. 

Previous studies have shown that some 80 percent of college students suffer from statistics anxiety, the University of Kansas explained.  

'We teach a statistics class in the psychology department and see many students put it off until senior year because they're scared of this class,' Michael Vitevitch, professor and chair of psychology at the University of Kansas, said in a statement...

They used a technique called network science, which 'puts the most important contributors or symptoms of statistical anxiety at the center of a visual diagram of connecting nodes.'

'With statistics anxiety, it's not just that you have symptoms, it's how long you have them and which ones are more important?,' Vitevitch explained. 
Read more...

Source: Daily Mail


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Science as a social practice | MIT News

PhD student Marion Boulicault believes in an interdisciplinary path forward for science, feminism, and philosophy, says

Marion Boulicault
Photo: Joseph Lee

Marion Boulicault hates making decisions. “I want to do everything,” she says, “and one of the effects of making a choice is that other choices are closed off.” Alternately drawn to work in environmental science, public policy, and philosophy, she has always felt compelled to bring her interests together.

So when she first began her doctorate in philosophy at MIT, Boulicault assumed that choosing such an abstract field meant letting go of the pragmatic, on-the-ground impact of a career in public service... 

Working at the interface of philosophy and science
Through her HASTS interdisciplinary coursework, Boulicault first encountered a field that intrigued her: the feminist philosophy of science. She was struck that problems of gender in science go far beyond equal representation. “The notion of ‘bias’ can’t be understood only at an individual level — it’s also social, cultural, and structural. Although science is often idealized as value-free and purely ‘objective,’ it’s a practice done by people and institutions,” she says. “Science is inherently social.”...

Bringing a humanities perspective to science
Boulicault has managed to merge her dual passions for conceptual thinking and public service as a founding member of the Harvard GenderSci Lab, which generates feminist critiques, methods, and concepts for scientific research on sex and gender.  

At times, operating within a truly interdisciplinary framework is difficult — the GenderSci Lab consists of biologists, psychologists, philosophers, and historians — but she has found others with similar interests and has created her own interdisciplinary space.
Read more... 

Source: MIT News 


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Maths discoveries by amateurs and distractions by cranks | Opinion & Analysis - The Irish Times

The fact that certain problems are impossible to solve does not deter enthusiasts, writes Peter Lynch, emeritus professor at UCD school of mathematics and statistics, blogs at thatsmaths.com

Srinivasa Ramanujan, one of the most brilliant mathematicians of the last century, wrote unsolicited letters to three leading mathematicians at Cambridge
Photo: The Irish Times 
Do amateurs ever solve outstanding mathematical problems? Professional mathematicians are aware that almost every new idea they have about a mathematical problem has already occurred to others. Any really new idea must have some feature that explains why no one has thought of it before.

It is both difficult and rare to come up with a truly original idea. Such insights almost invariably result from an extended period of intensive work. If one mathematician thinks of something original, why would others not have done the same? Yet, there are those who convince themselves, without justification, that they have done what no one else could do.

Pseudomaths
Pseudomathematics is an activity that fails to observe the rigorous standards of formal mathematical practice and proof. Pseudomathematicians who persist in this activity become cranks. Most professional mathematicians have received communications that contain “proofs” of long-open problems. Often, these claim solutions of problems that have been proven mathematically to be impossible to solve...

The British mathematician and logician Augustus De Morgan wrote a book, A Budget of Paradoxes, in which he introduced the term pseudomath. As an example of a pseudomath, De Morgan mentioned one James Smith who claimed persistently to have proved that pi is equal to three and one eighth. De Morgan wrote that Smith “is beyond doubt the ablest head at unreasoning, and the greatest hand at writing it.”

In the past, many European scientific academies were bombarded by circle-squarers, angle-trisectors and cube-duplicators demanding immediate recognition of their mathematical achievements.

Source: The Irish Times


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