The Future of Computer Science

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The original article can be found at http://blogs.siam.org/the-future-of-computer-science/

The Future of Computer Science

John Hopcroft (Cornell University) writes:

The information age is causing  fundamental changes to all aspects of our lives and I believe that those individuals, organizations, and nations who position themselves for the future will benefit enormously.  In particular, there are major opportunities right now for those who are starting their careers in computer science research.

My professional career started in 1964 when I graduated from Stanford in electrical engineering. I was hired as an assistant professor at Princeton in an electrical engineering department.  There were no computer science departments.  Fortunately for me, Ed McCluskey asked me to teach a course in computer science.  There were no books so I had to ask what is the content of such a course.  He gave me four papers and told me if I covered them it would be fine.  What I did not realize is that teaching that course made me one of the world’s first computer scientists.  Whenever someone was looking for a senior computer scientist I was probably on the short list.  That is probably why in 1992, President George H.W. Bush appointed me to the National Science Board which oversees the National Science Foundation.  Imagine if I had been in high energy particle physics.  I would still be waiting today for the senior faculty ahead of me to retire so I could have some good opportunities.  When I tell this story to students today they respond by saying I was lucky to have started my career in 1964 when computer science was just beginning.  The message I am giving is that those starting today are starting at a time of fundamental change and if they position themselves for the future they will have great careers.

In the past 30 years computer science was concerned with making computers useful: developing programming languages, compilers, operating systems, databases and so on.  Today it is focused on how computers are being used.  We need to develop the science base to support the new directions and of course update curriculums so that our students are trained in the relevant aspects. Continue reading

The Math Behind Disney

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This article is from http://www.ksl.com/?sid=27742483&nid=1017&title=have-you-seen-this-the-math-behind-disney-animation&fm=home_page&s_cid=featured-5

Have You Seen This? The math behind Disney animation
By Josh FurlongNovember

SALT LAKE CITY — Disney’s newest animation creation “Frozen” hits theaters on Thanksgiving, and it looks to be a cute story.

The animation involves a lot of snow — hence the name frozen. I assumed — wrongly — Disney animators just drew up some cool scenes and put together a cool story, but apparently it takes a lot more logic and math than I was expecting.

Disney Animation released a YouTube video describing the different properties of snow and how they use algorithms to replicate said properties in animation — stay with me.

If you can get past the math — just assume they know what they’re talking about — the visuals are actually pretty cool and it’s interesting to see the actual math behind the animation. It makes Photoshop seem so amateur.

So the next time you’re watching your favorite animated movie from Disney, remember there is more math that goes into it than just brilliant animators — it just means they’re more than artists.

My next question: Can Buzz Lightyear actually fly?

How Google Converted Language Translation Into a Problem of Vector Space Mathematics

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This article is from http://www.technologyreview.com/view/519581/how-google-converted-language-translation-into-a-problem-of-vector-space-mathematics/

To translate one language into another, find the linear transformation that maps one to the other. Simple, say a team of Google engineers
Computer science is changing the nature of the translation of words and sentences from one language to another. Anybody who has tried BabelFish or Google Translate will know that they provide useful translation services but ones that are far from perfect.The basic idea is to compare a corpus of words in one language with the same corpus of words translated into another. Words and phrases that share similar statistical properties are considered equivalent.

 

The problem, of course, is that the initial translations rely on dictionaries that have to be compiled by human experts and this takes significant time and effort.

Now Tomas Mikolov and a couple of pals at Google in Mountain View have developed a technique that automatically generates dictionaries and phrase tables that convert one language into another.

The new technique does not rely on versions of the same document in different languages. Instead, it uses data mining techniques to model the structure of a single language and then compares this to the structure of another language.

“This method makes little assumption about the languages, so it can be used to extend and refine dictionaries and translation tables for any language pairs,” they say.

The new approach is relatively straightforward. It relies on the notion that every language must describe a similar set of ideas, so the words that do this must also be similar. For example, most languages will have words for common animals such as cat, dog, cow and so on. And these words are probably used in the same way in sentences such as “a cat is an animal that is smaller than a dog.”

The same is true of numbers. The image above shows the vector representations of the numbers one to five in English and Spanish and demonstrates how similar they are.

This is an important clue. The new trick is to represent an entire language using the relationship between its words. The set of all the relationships, the so-called “language space”, can be thought of as a set of vectors that each point from one word to another. And in recent years, linguists have discovered that it is possible to handle these vectors mathematically. For example, the operation ‘king’ – ‘man’ + ‘woman’ results in a vector that is similar to ‘queen’.

It turns out that different languages share many similarities in this vector space. That means the process of converting one language into another is equivalent to finding the transformation that converts one vector space into the other.

This turns the problem of translation from one of linguistics into one of mathematics. So the problem for the Google team is to find a way of accurately mapping one vector space onto the other. For this they use a small bilingual dictionary compiled by human experts–comparing same corpus of words in two different languages gives them a ready-made linear transformation that does the trick.

Having identified this mapping, it is then a simple matter to apply it to the bigger language spaces. Mikolov and co say it works remarkably well. “Despite its simplicity, our method is surprisingly effective: we can achieve almost 90% precision@5 for translation of words between English and Spanish,” they say.

The method can be used to extend and refine existing dictionaries, and even to spot mistakes in them. Indeed, the Google team do exactly that with an English-Czech dictionary, finding numerous mistakes.

Finally, the team point out that since the technique makes few assumptions about the languages themselves, it can be used on argots that are entirely unrelated. So while Spanish and English have a common Indo-European history, Mikolov and co show that the new technique also works just as well for pairs of languages that are less closely related, such as English and Vietnamese.

That’s a useful step forward for the future of multilingual communication. But the team says this is just the beginning. “Clearly, there is still much to be explored,” they conclude.

Ref: arxiv.org/abs/1309.4168: Exploiting Similarities among Languages for Machine Translation

 

 

Aren’t You Glad You Majored in Math?

Math-challenged Americans more likely to end up in foreclosure

 

Bob Sullivan, Columnist, NBC News

June 24, 2013 at 2:58 PM ET

 

Americans who have trouble dividing 300 by 2 are much more likely to end up in foreclosure than consumers with average math skills, a new study has found. The research is among the first to directly link mortgage trouble and financial literacy, according to its authors.

The study also found that math skills were a better predictor of foreclosure than type of mortgage, a result that takes blame away from so-called “risky” mortgages, such-as interest-only loans or adjustable rate mortgages.

“There are two big takeaways. First, that numerical ability heavily correlates to mortgage default, even controlling for a lot of other things,” said Stephan Meier, one of the report’s authors. He is a behavioral economics expert and professor at Columbia Business School. “Second, defaults were not driven by the mortgage choices people make.  Their mistakes come somewhere else.”

The results, “Numerical Ability Predicts Mortgage Default,” were published Monday in the Proceedings of the National Academy of Sciences.

Meier and co-authors Kris Gerari and Lorenz Goette examined actual mortgage payment streams obtained from the Federal Reserve, and then contacted mortgage holders to assess their math skills.  Each was asked a series of five questions (see them below) and then assigned into four “buckets.”  Four of those questions test the ability to perform simple division or calculate percentages, like this: “A shop is selling all items at half price. Before the sale, a sofa costs $300.How much will it cost in the sale?”

Roughly 1 in 7 test-takers couldn’t answer even two such questions correctly, and landed in the lowest bucket.  That group was four times more likely to be in foreclosure than consumers who landed in the top bucket by answering all five questions correctly.

The fifth question tested ability to compute compound interest. Only 1 in 8 test-takers scored in this highest group, and of those, only 5 percent were in foreclosure.

The researchers went to great pains to control for numerous outside factors, such as income, overall education level, IQ, and type of mortgage, Meier said.  Math skills had the most pronounced effect on likelihood that consumers would run into trouble. For example, homeowners with no college degree but high math skills performed better than college graduates with poor math skills, he said.

“This is very specific to numerical ability,” Meier said.

The study does not offer additional insight into why math skills can predict mortgage trouble. Other studies have shown that those with poor math skills save less for the future, so that might suggest the group is “more vulnerable to income shocks,” Meier said.  Or they might make less informed choices about credit cards or insurance.

But math skills turned out to be a much better predictor of default than type of mortgage, he said.

“Even if you gave this group a plain vanilla, 30-year fixed mortgage, this group would still have difficulties,” Meier said. “I’m not saying (exotic) mortgages are good…the results suggest the problems are outside the mortgage.”

Americans’ trouble with math is well-documented. U.S. students’ math skills frequently grade among the poorest in the developed world (in one recent study, the U.S. ranked 31st).

Meanwhile, the most recent U.S. Department of Education’s National Assessment of Adult Literacy showed that consumers are terrible at solving real-world math problems, such as calculating tips or comparing prices in grocery stores.  For example, only 42 percent of U.S. adults could pick out two items on a restaurant menu, add them and calculate a tip. In a result that neatly parallels Meier’s study, only 13 percent were deemed “proficient,” and only 1 in 5 could calculate mortgage interest.

But the Department of Education results are more than 10 years old, showing little progress has been made in shoring up Americans’ basic math skills

The phenomenon was identified even longer ago, in 1988, by mathematician John Allen Paulos in a book called “Innumercy” — the author’s invented term for mathematical illiteracy.In the book, Paulos argues that being a math dummy in America is not frowned upon, like illiteracy — in fact, it can be socially desirable. People often joke about their inability to balance a checkbook, he said, to the delight of friends.

“The same people who cringe when words such as imply and infer are confused react without of trace of embarrassment to even the most egregious of numerical (errors),” Paulos wrote. He goes on to poke fun at a linguistically nit-picking acquaintance who heard a weathercaster pronounces a 50 percent chance of rain on Saturday and on Sunday and concluded that there must be a “100 percent chance of rain that weekend.”

While the problem may be clear, the solution is not.  There are already numerous financial literacy programs run by schools, non-profit organizations, and even banks. Research has shown these have so far been ineffective.  It’s unclear, for example, whether consumers should be taught about mortgages during high school math class or later in life, when they are about to take out a mortgage.

Meier’s research offers a hint however. His test questions don’t really invoke finance skills, but rather general math concepts, such as division.  Such concepts are key to good financial decision-making, but seem like black magic to the uninitiated.  It might help to stress the high-level math concepts in schools, Meier said.

“One policy implication could be if we increase numerical ability people might make better decisions … that might deal with the problem,” he said.

TAKE THE MATH SKILLS TEST:

1. In a sale, a shop is selling all items at half price. Before the sale, a sofa costs $300. How much will it cost in the sale?

2. If the chance of getting a disease is 10 per cent, how many people out of 1,000 would be expected to get the disease?

3. A second-hand car dealer is selling a car for $6,000. This is two-thirds of what it cost new. How much did the car cost new?

4. If 5 people all have the winning numbers in the lottery and the prize is $2 million, how much will each of them get?

5. Let’s say you have $200 in a savings account. The account earns 10 percent interest per year. How much will you have in the account at the end of two years?

Answers: 1) $150 2) 100 3) $9,000 4) $400,000 5) $242 (compounded annually)

 

 

http://www.nbcnews.com/technology/math-challenged-americans-more-likely-end-foreclosure-6C10429260?franchiseSlug=technolog

Student Test Scores Show That ‘Grit’ Is More Important Than IQ

 

What’s the best predictor of success? IQ, talent, luck?

Angela Lee Duckworth

Nope. It’s ‘grit,’ more than anything else.

Through her research at the University of Pennsylvania — and firsthand experience teaching in New York City’s public schools —psychologist Angela Duckworth has found that the ability to withstand stress and move past failures to achieve a goal is the best indicator of future success.

“What struck me was that IQ was not the only difference between my best and my worst students,” she shared in her recent TED talk. “Some of my strongest performers did not have stratospheric IQ scores. Some of my smartest kids weren’t doing so well.”

After teaching in New York City, Duckworth went to graduate school to become a psychologist, where she studied what types of people were successful at West Point Military Academy, the National Spelling Bee, in classrooms, and beyond. Again, she said, “it wasn’t social intelligence. It wasn’t good looks, physical health, and it wasn’t IQ. It was grit.”

She began by studying grit in the Chicago public schools. “I asked thousands of high school juniors to take grit questionnaires, and then waited around more than a year to see who would graduate,” she said. “Turns out that grittier kids were significantly more likely to graduate, even when I matched them on every characteristic I could measure, things like family income, standardized achievement test scores, even how safe kids felt when they were at school.”

In a paper, “Self-Discipline Outdoes IQ In Predicting Academic Performance Of Adolescents,” Duckworth and colleague Martin Seligman tested 164 eighth graders “recruited from a socioeconomically and ethnically diverse magnet public school” in the Northeast for self-discipline and IQ. They measured the students in the fall and spring through self-assessment, a behavioral delay-of-gratification task, and a survey of study and lifestyle habits, along with a group IQ test. They found that “self-discipline predicted academic performance more robustly than did IQ. Self-discipline also predicted which students would improve their grades over the course of the school year, whereas IQ did not.”

This chart shows their findings about self-discipline vs IQ:

 

IQ measurement

 

But why do some people have grit and others don’t? That’s where science needs to fill in the gaps.

“What I do know is that talent doesn’t make you gritty,” Duckworth said in her TED talk. “Our data show very clearly that there are many talented individuals who simply do not follow through on their commitments. In fact, in our data, grit is usually unrelated or even inversely related to measures of talent.”

One way to instill it, she says, it to help people understand that learning and ability isn’t fixed. And that there’s life after failure.

Welcome to ACME

Welcome to the official website for Brigham Young University’s Applied and Computational Math Emphasis. Here you will find all the information you need to know about what this program is about and how it can help you further your education and your career. If you have questions not answered by this website you can contact us using the information under the “Contact” tab.