Think it doesn’t matter where you study engineering or computer science since all STEM majors make big bucks?

You may have gotten at impression from recent studies and advice suggesting that techies do well no matter where they attend college.

Eric Eide and Mike Hilmer, economics professors at Brigham Young University and San Diego State University, respectively, reported in a June 2015 paper that, for STEM majors, the prestige of a school doesn’t play a significant role in boosting salary. “It largely doesn’t matter whether students go to a prestigious, expensive school or a low-priced one—expected earnings turn out the same,” they concluded in a *Wall Street Journal* article in January.

However, a MONEY analysis of the earnings of students who majored in science, technology, engineering, and math found there is actually a wide variation and that some colleges are more likely to produce dropouts or debt-laden graduates than Silicon Valley success stories.

According to PayScale.com data, the average salary of recent graduates (defined as those who graduated within the last five years) who majored in science, technology, engineering, or math is more than $51,000. However, there were more than 40 schools on its list where graduates earned an average salary below $40,000.

“Where you go matters a lot less than people think…[but] it does matter,” says Anthony Carnevale, director of Georgetown University’s Center on Education and the Workforce. “If you’re going to study STEM, schools like MIT or Carnegie Mellon University—those are the places you want to go because they have higher graduation rates, and more money is spent on you, and you have more access to graduate schools.”

Indeed, the numbers show that, even if you’re a STEM major, the decision about which college to attend could be crucial not only in terms of your future earnings but in the amount of debt you’ll carry after you graduate—and even your likelihood of graduating at all.

Despite all the hype these days, STEM graduates aren’t necessarily guaranteed a high early-career salary. STEM alumni of Alverno College in Milwaukee report making an annual salary of just $34,600. That’s almost $2,000 less than the national average early-career earnings of dance majors. Similarly, STEM graduates at Oklahoma Panhandle State University earn just $40,300 within five years after graduation—about $10,000 below the national median for STEM majors.

What’s more, the glowing statistics about STEM earnings are inflated because they look only at graduates. But at many schools, most freshmen flunk out. For instance, graduates of Bloomfield College, a four-year private liberal arts school in New Jersey, report making an average of $69,300 within five years of graduation. But only 32% of the college’s students will graduate within six years.

“If you start by looking at graduates, you’ve already missed so much about what happens to students after they enroll,” says Jordan Matsudaira, a professor of policy analysis and management at Cornell University.

Even the authors of the much-cited study mentioned above caution that there are a number of factors—such as different majors’ earning potential, job and internship placement rates, and opportunities for research with professors—that should be considered along with a school’s reputation.

“Our advice would be to gather as much of that kind of information as possible,” Hilmer says.

One useful rule of thumb is that the amount that you take out in student loans should not exceed your first-year salary, says Mark Schneider, a vice president and institute fellow at the American Institutes for Research and a consultant on MONEY’s college rankings.

Schneider also suggests you automatically cross schools off your list that have a graduation rate below 30%. “Every student believes they’re going to beat the odds,” he says. But the reality is, most don’t.

Here, based on MONEY’s analysis, are schools with have some of the lowest starting salaries, subpar graduation rates, and higher-than-average loans taken out by students:

College | Early Career Median Salary for STEM Graduates | Overall 6-Year Graduation Rate | Average Loan Taken Out Each Year by Students Who Borrow | Percent of Students Who Take Out Federal Loans |
---|---|---|---|---|

Texas Woman’s University | $38,000 | 44% | $7,199 | 56% |

Auburn University at Montgomery | $38,800 | 22% | $7,159 | 58% |

Valdosta State University | $38,400 | 39% | $6,398 | 65% |

Hawaii Pacific University | $38,700 | 42% | $9,662 | 45% |

SUNY College of Agriculture and Technology at Cobleskill | $34,500 | 36% | $6,421 | 68% |

Concord University | $35,000 | 34% | $6,395 | 72% |

Nova Southeastern University | $37,400 | 46% | $9,516 | 58% |

Southern Wesleyan University | $36,100 | 49% | $8,135 | 70% |

William Penn University | $37,300 | 35% | $7,651 | 78% |

Northland College | $33,300 | 46% | $7,648 | 80% |

University of Dubuque | $36,400 | 48% | $7,863 | 83% |

Alverno College | $34,600 | 36% | $7,546 | 87% |

Virginia Union University | $33,400 | 36% | $7,972 | 87% |

SOURCES: PayScale.com, U.S. Department of Education

Still, the news isn’t all bad for techies: Here’s a list of 25 great non-elite colleges where STEM graduates soar.

]]>British professor Sir Andrew Wiles was awarded mathematics’ most prestigious prize this week, for providing the proof to a theorem that had stymied everyone in the field for over 350 years.

Wiles was bestowed this year’s $700,000 Abel Prize for his proof of Fermat’s Last Theorem. Formulated by French mathematician Pierre de Fermat in 1637, it had long been the math world’s most famous — and confounding — of theorems when Wiles proved it in 1994 after years of research.

In its announcement, the Norwegian Academy of Science and Letters, which awards the prize, said, “Andrew J. Wiles is one of very few mathematicians — if not the only one — whose proof of a theorem has made international headline news.” The academy also recounted his first encounter with the problem as a 10-year-old boy in Cambridge, where he found a book on Fermat’s Last Theorem at his local library and, as he said, “knew from that moment that I would never let it go.”

In 1996, the New York *Times* stated the theorem in the following way:

“Everybody knew that it is possible to break down a squared number into two squared components, as in 5 squared equals 3 squared plus 4 squared (or, 25 = 9 + 16). What Fermat saw was that it was impossible to do that with any number raised to a greater power than 2. Put differently, the formula xn + yn = zn has no whole number solution when n is greater than 2.”

Wiles laid the groundwork for his monumental breakthrough over several years during a teaching tenure at Princeton University in the 1980s. He was knighted in 2000, six years after proving the theorem turned him into a global icon.

“Fermat’s equation was my passion from an early age, and solving it gave me an overwhelming sense of fulfilment,” the 62-year-old mathematician told Oxford University — where he is currently a research professor — on Tuesday, after learning he would receive the Abel Prize.

“It has always been my hope that my solution of this age-old problem would inspire many young people to take up mathematics and to work on the many challenges of this beautiful and fascinating subject,” he added.

]]>The number represented by pi (π) is used in calculations whenever something round (or nearly so) is involved, such as for circles, spheres, cylinders, cones and ellipses. Its value is necessary to compute many important quantities about these shapes, such as understanding the relationship between a circle’s radius and its circumference and area (circumference=2πr; area=πr^{2}).

Pi also appears in the calculations to determine the area of an ellipse and in finding the radius, surface area and volume of a sphere.

Our world contains many round and near-round objects; finding the exact value of pi helps us build, manufacture and work with them more accurately.

Historically, people had only very coarse estimations of pi (such as 3, or 3.12, or 3.16), and while they knew these were estimates, they had no idea how far off they might be.

The search for the accurate value of pi led not only to more accuracy, but also to the development of new concepts and techniques, such as limits and iterative algorithms, which then became fundamental to new areas of mathematics.

**Finding the actual value of pi**

Between 3,000 and 4,000 years ago, people used trial-and-error approximations of pi, without doing any math or considering potential errors. The earliest written approximations of pi are 3.125 in Babylon (1900-1600 B.C.) and 3.1605 in ancient Egypt (1650 B.C.). Both approximations start with 3.1 – pretty close to the actual value, but still relatively far off.

The first rigorous approach to finding the true value of pi was based on geometrical approximations. Around 250 B.C., the Greek mathematician Archimedes drew polygons both around the outside and within the interior of circles. Measuring the perimeters of those gave upper and lower bounds of the range containing pi. He started with hexagons; by using polygons with more and more sides, he ultimately calculated three accurate digits of pi: 3.14. Around A.D. 150, Greek-Roman scientist Ptolemy used this method to calculate a value of 3.1416.

Independently, around A.D. 265, Chinese mathematician Liu Hui created a another simple polygon-based iterative algorithm. He proposed a very fast and efficient approximation method, which gave four accurate digits. Later, around A.D. 480, Zu Chongzhi adopted Liu Hui’s method and achieved seven digits of accuracy. This record held for another 800 years.

In 1630, Austrian astronomer Christoph Grienberger arrived at 38 digits, which is the most accurate approximation manually achieved using polygonal algorithms.

**Moving beyond polygons**

The development of infinite series techniques in the 16th and 17th centuries greatly enhanced people’s ability to approximate pi more efficiently. An infinite series is the sum (or much less commonly, product) of the terms of an infinite sequence, such as ½, ¼, 1/8, 1/16, … 1/(2^{n}). The first written description of an infinite series that could be used to compute pi was laid out in Sanskrit verse by Indian astronomer Nilakantha Somayaji around 1500 A.D., the proof of which was presented around 1530 A.D.

In 1665, English mathematician and physicist Isaac Newton used infinite series to compute pi to 15 digits using calculus he and German mathematician Gottfried Wilhelm Leibniz discovered. After that, the record kept being broken. It reached 71 digits in 1699, 100 digits in 1706, and 620 digits in 1956 – the best approximation achieved without the aid of a calculator or computer.

In tandem with these calculations, mathematicians were researching other characteristics of pi. Swiss mathematician Johann Heinrich Lambert (1728-1777) first proved that pi is an irrational number – it has an infinite number of digits that never enter a repeating pattern. In 1882, German mathematician Ferdinand von Lindemann proved that pi cannot be expressed in a rational algebraic equation (such as pi²=10 or 9pi^{4} – 240pi^{2} + 1492 = 0).

**Toward even more digits of pi**

Bursts of calculations of even more digits of pi followed the adoption of iterative algorithms, which repeatedly build an updated value by using a calculation performed on the previous value. A simple example of an iterative algorithm allows you to approximate the square root of 2 as follows, using the formula (x+2/x)/2:

- (2+2/2)/2 = 1.5
- (
**1.5**+2/**1.5**)/2 = 1.4167 - (
**1.4167**+2/**1.4167**)/2 = 1.4142, which is a very close approximation already.

Advances toward more digits of pi came with the use of a Machin-like algorithm (a generalization of English mathematician John Machin’s formula developed in 1706) and the Gauss-Legendre algorithm (late 18th century) in electronic computers (invented mid-20th century). In 1946, ENIAC, the first electronic general-purpose computer, calculated 2,037 digits of pi in 70 hours. The most recent calculation found more than 13 trillion digits of pi in 208 days!

It has been widely accepted that for most numerical calculations involving pi, a dozen digits provides sufficient precision. According to mathematicians Jörg Arndt and Christoph Haenel, 39 digits are sufficient to perform most cosmological calculations, because that’s the accuracy necessary to calculate the circumference of the observable universe to within one atom’s diameter. Thereafter, more digits of pi are not of practical use in calculations; rather, today’s pursuit of more digits of pi is about testing supercomputers and numerical analysis algorithms.

**Calculating pi by yourself**

There are also fun and simple methods for estimating the value of pi. One of the best-known is a method called “Monte Carlo.”

The method is fairly simple. To try it at home, draw a circle and a square around it (as at left) on a piece of paper. Imagine the square’s sides are of length 2, so its area is 4; the circle’s diameter is therefore 2, and its area is pi. The ratio between their areas is pi/4, or about 0.7854.

Now pick up a pen, close your eyes and put dots on the paper at random. If you do this enough times, and your efforts are truly random, eventually the percentage of times your dot landed inside the square will approach 78.54% – or 0.7854.

Now you’ve joined the ranks of mathematicians who have calculated pi through the ages.

*This article originally appeared on The Conversation*

The Breakthrough Prize organization gave a total of $22 million in award money on Sunday to scientists, mathematicians, and researchers who have made “fundamental discoveries about the universe, life, and the mind,” the organization said in a statement.

“This year’s laureates have all opened up ways of understanding ourselves,” said biologist Anne Wojcicki, who sits on the organization’s board and who established the awards in 2012 with, among others, her ex-husband, Google co-founder Sergey Brin.

“In the life sciences, they have pushed forward new ideas about Alzheimer’s, cholesterol, neurological imaging and the origins of our species. And for that we celebrate them.”

One mathematician, five life scientists, and seven leaders of five physics experiments (along with 1,370 individuals who aided those experiments) received accolades at an awards ceremony at NASA’s Ames Research Center in Mountain View, Ca., hosted by comedian Seth MacFarlane.

Among the recipients were Svante Pääbo, a Swedish biologist who has spearheaded the sequencing of ancient DNA and genomes, and 18-year-old Ryan Chester, who won the inaugural Breakthrough Junior Challenge with his video explaining Einstein’s theory of special relativity.

Chester will take home $250,000 in scholarship money; his teacher, Richard Nestoff, gets $50,000 and his high school will be furnished with a new science lab worth $100,000.

]]>Monday’s Google Doodle honors what would have been the 200th birthday of famed mathematician George Boole, whose research played a significant role in the 20th century’s digital revolution.

Boole work, commonly referred to as Boolean algebra, went on to influence binary systems used in electrical circuits and computers.

The Doodle shows the “logic gates” derived from Boolean theories often used in modern computing.

Boole’s talents didn’t lie solely with mathematics, however. Born in Lincolnshire in the U.K., Boole ended his formal education at 14 but still managed to teach himself poetry and a slew of languages. By the age of 20 he had even opened up his own school.

His scientific successes came later — he was the first pure mathematician to receive the Gold Medal for Mathematics by the Royal Society in 1844, only three years after his first publication on the subject.

He then became the first mathematics professor at Ireland’s University College Cork, then known as Queen’s College Cork, in 1849 — a position which he retained for the rest of his life. He wrote his most famous work, *An Investigation of the Laws of Thought*, there in 1854.

Boole fell ill with pneumonia and passed away in Cork in 1864 at the age of 49. He was survived by five daughters, many of whom ended up making significant contributions to maths and sciences themselves.

]]>If the thought of calculating a tip at a restaurant makes you nervous, then you are not alone. Math anxiety is common worldwide.

Math anxiety can lead to poor performance and also deter people from taking math courses. This is because feelings of anxiety can tie up important cognitive resources (known as working memory), which are needed for solving math problems.

But why are some people more math anxious than others? And is there a link between parents’ math anxiety and their children’s math anxiety?

As researchers who study the role of cognitive and emotional factors in achievement, these are some of the questions that my colleagues and I have been examining. We find that when parents with math anxiety help with homework, it could have a negative impact on their kids.

**Social factors contribute to math anxiety**

Math anxiety can start early. Children as young as six can experience varying degrees of math anxiety which is linked to poor math achievement.

While recent research suggests that some people are predisposed to develop math anxiety, and that there may be a genetic component to this predisposition, the social factors that can lead someone to develop math anxiety are also important to understand.

Recently, we examined the link between parents’ math anxiety and their children’s math anxiety and math achievement.

We assessed the math anxiety and math achievement levels of 438 first- and second-grade children at both the beginning and the end of the school year. We assessed their parents’ math anxiety level. We also assessed how often they helped their children with their math homework.

Our research demonstrated that when parents are highly-math-anxious, their children learn significantly less math (over one-third of a grade level less than their peers in math achievement across the school year) and have more math anxiety by school-year’s end. But this is only if parents provide frequent math homework help.

When highly-math-anxious parents don’t help their children very often with their math homework, their children are unaffected by their parents’ anxiety.

**How parents transfer anxiety**

Why does the homework help of highly math-anxious parents backfire?

We can’t say for certain why the homework help of highly-math-anxious parents backfires, leading their children to learn less math and be more math anxious than their peers, but we believe that there are a number of possible reasons.

First, when helping with their children’s math homework, highly-math-anxious parents may be expressing their own dislike of math, perhaps saying things like “math is hard” or “some people are simply not math people.”

Finally, highly-math-anxious parents may become flustered when their children’s teachers use novel strategies that parents themselves never learned.

We believe that being exposed to negative attitudes about math and confusing instruction from parents might cause children to lose confidence in their math abilities and to invest less effort into learning math, resulting in lower math achievement by the end of the year.

**Couldn’t this just be genetics?**

While I mentioned earlier that there is a genetic link between math anxiety of parents and their children, our research indicates that parents have more than just a genetic influence on their children’s math outcomes.

If genetics were the only factor at play, then we would have seen that parents with higher math anxiety would also have children displaying similar anxiety. They would also have lower math achievement as compared to their peers.

But that was not what we found.

Rather, it was specifically in the case of children whose highly-math-anxious parents helped them often with math homework that we saw this trickling down of parents’ math anxiety.

Thus, while genetics may be part of the equation, it is certainly not the entire story.

**How can children be supported**

This research highlights the need for researchers and educators to work together to develop more effective tools to help parents – especially those who are anxious – support their children’s math success.

These tools may come in the form of worksheets, apps, and games, or parent-teacher workshops aimed at teaching parents the new strategies that are being used in the classroom to teach math today.

Fortunately, there are a number of research-based strategies that can be very useful in helping children and parents deal with their math anxiety. My favorite strategy is a simple, inexpensive, and very effective tool called expressive writing.

To use this strategy, students simply have to write about their worries regarding an upcoming math test (for example by answering the question “Explain in detail how this upcoming math test makes you feel”) for about seven minutes before they take the test.

This straightforward act of writing actually causes students to perform better on the math test than what they would have performed had they not written at all.

While it is true that even the best-intentioned parents may contribute to their child’s anxiety and lower achievement, the good news is that simple strategies, like expressive writing, can go a long way in helping children combat the negative effects of math anxiety.

Success in math requires more than just ability. It is also about developing the right attitude.

*This article originally appeared on The Conversation*

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A female mathematician has won the most prestigious prize in math for the first time, a hugely symbolic breakthrough for gender equality in one of the most male-dominated areas of academic research.

Maryam Mirzakhani, 37, will be awarded the Fields Medal — widely considered math’s Nobel Prize, since there is no Nobel for mathematics — at a ceremony in Seoul on Wednesday morning. Born and raised in Iran, she has been a professor at Stanford University since 2008.

All the previous 52 winners of the Fields have been men since its inception in 1936, one of the most visible indicators that at its highest level math remains a predominantly male preserve.

Ingrid Daubechies, president of the International Mathematical Union (IMU), said that Mirzakhani’s success was “hugely symbolic and I hope it will encourage more women to get into mathematics because we need more women. I am very happy that now we can put to rest that particular ‘it has never happened before.’”

The Fields Medal is awarded every four years at the IMU’s International Mathematical Congress to two to four mathematicians aged under 40. The medal honors “outstanding mathematical achievement for existing work and for the promise of future achievement,” which is why there is an age limit.

Besides Mirzakhani, the other recipients will be Manjul Bhargava, Princeton professor who was born in Canada but raised in the U.S.; Artur Ávila from Brazil; and Martin Hairer from Austria.

As well as honoring a woman for the first time, this year’s Fields also reflect the rise of the developing world in producing top mathematicians, even if they are working at universities in the West.

Ávila, who works in Paris, is the first winner from South America and Mirzakhani the first from the Middle East.

Yet it is the emergence of a female winner that is likely to cause the most discussion in math and science circles. Even though the percentage of math majors who are women is now approaching parity with men in the U.S., women make up less than 10% of full math professors at the top 100 universities in the U.S., according to Stephen Ceci and Wendy Williams, both Cornell University professors, in their book *The Mathematics of Sex.*

“In the U.S. about 30% of the graduate population at research departments are women,” said Daubechies. “But a higher percentage of women leave academia than men, so we have an even lower percentage of women postdocs and an even lower percentage of women in faculty. It is not just that the numbers are small, it is also that more leave percentagewise. I hope that will change.”

Daubechies, who is the first female president of the IMU, said that there have been excellent female mathematicians before but often they have not done their strongest work before age 40.

“I am of course chuffed that the first female Fields medalist has happened when I am president, but I think it is coincidence. I did not set it out as an agenda point. It would have been completely inappropriate to do that.”

Each Fields Medal comes with a citation, which can be hard to understand for those with no mathematical grounding — and even those with one, since the frontiers of math are such abstract places.

Ávila won “for his profound contributions to dynamical systems theory,” Bhargava won “for developing powerful new methods in the geometry of numbers,” Hairer won “for his outstanding contributions to the theory of stochastic partial differential equations,” and Mirzakhani won “for her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces.”

Daubechies added: “At the IMU we believe that mathematical talent is spread randomly and uniformly over the Earth — it is just opportunity that is not. We hope very much that by making more opportunities available — for women, or people from developing countries — we will see more of them at the very top, not just in the rank and file.”

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