Five Winners Receive Inaugural Breakthrough Prize in Mathematics

The Breakthrough Prize Foundation announces five winners of the inaugural Breakthrough Prize in Mathematics:

Simon Donaldson, Stony Brook University and Imperial College London, for the new revolutionary invariants of 4-dimensional manifolds and for the study of the relation between stability in algebraic geometry and in global differential geometry, both for bundles and for Fano varieties.

Maxim Kontsevich, Institut des Hautes Études Scientifiques, for work making a deep impact in a vast variety of mathematical disciplines, including algebraic geometry, deformation theory, symplectic topology, homological algebra and dynamical systems.

Jacob Lurie, Harvard University, for his work on the foundations of higher category theory and derived algebraic geometry; for the classification of fully extended topological quantum field theories; and for providing a moduli-theoretic interpretation of elliptic cohomology.

Terence Tao, University of California, Los Angeles, for numerous breakthrough contributions to harmonic analysis, combinatorics, partial differential equations and analytic number theory.

Richard Taylor, Institute for Advanced Study, for numerous breakthrough results in the theory of automorphic forms, including the Taniyama-Weil conjecture, the local Langlands conjecture for general linear groups, and the Sato-Tate conjecture.

The Breakthrough Prize in Mathematics was launched by Mark Zuckerberg and Yuri Milner at the Breakthrough Prize ceremony in December 2013. It aims to recognize major advances in the field, honor the world’s best mathematicians, support their future endeavors and communicate the excitement of mathematics to general public.

The laureates will be presented with their trophies and $3 million each at the Breakthrough Prize ceremony in November.

All five recipients of the Prize have agreed to serve on the Selection Committee, responsible for choosing subsequent winners of the prize from the pool of contenders nominated by the mathematics community. From 2015 onwards, one Breakthrough Prize in Mathematics will be awarded every year.

Mark Zuckerberg said: “Mathematics is essential for driving human progress and innovation in this century. This year’s Breakthrough Prize winners have made huge contributions to the field and we’re excited to celebrate their efforts.”

Yuri Milner commented: “Mathematics is the most fundamental of the sciences – the language they are all written in. The best mathematical minds benefit us all by expanding the sphere of human knowledge.”

Source: www.BreakthroughPrize.org

About the Breakthrough Prizes

The Breakthrough Prizes were founded by Sergey Brin and Anne Wojcicki, Jack Ma and Cathy Zhang, Yuri and Julia Milner, and Mark Zuckerberg and Priscilla Chan. The prizes aim to celebrate scientists and generate excitement about the pursuit of science as a career.

Universities Ease Off on Tuition Hikes

by Mary Beth Marklein

USA TODAY  |  October 23, 2013, 7:01 a.m. EDT

Average sticker prices at the nation’s four-year public universities rose 2.9% this year, the smallest annual increase in more than three decades, suggesting that the steeper increases over the past few years “did not signal a new era of accelerating prices,” says a report out Wednesday.

Still, the smaller rates of increase this year — across public, private non-profit and for-profit colleges — are tempered by recent declines in federal grant aid, it says.

* Preliminary estimate
Source: The College Board
The Wall Street Journal

“This does not mean that college is suddenly more affordable,” says economist Sandy Baum, co-author of Trends in Higher Education reports on tuition and financial aid, released by the non-profit College Board. “It does seem that the (upward tuition) spiral is moderating. Not turning around, not ending, but moderating.”

The increase in published rates for in-state students at public four-year colleges comes after increases of 4.5% last year and 8.5% the year before, the report says. Tuition this fall averaged $8,893. With estimated grant aid, the net price averaged $3,120. Average published tuition and fees for out-of-state students is $22,203, up 3.1% from last year.

The smaller increases serve as a reminder of the cyclical nature of price increases, Baum said. In 1983-84, for example, the first year for which the College Board began tracking annual costs, tuition and fees at four-year public institutions increased 11.3% over the previous year, to $1,148 in current dollars (not adjusted for inflation). Federal data show a dip in 1974-75, when annual tuition and fees fell from $514 to $512 in current dollars (not adjusted for inflation).

Even as sticker prices have climbed, the average amounts students pay out of their own pockets in recent years have been moderated by larger infusions of grant aid and tax benefits, the report says. In 2009, for example, net price dropped for undergraduates attending four-year public universities.

That began to change a few years ago. Total federal grants, for example, increased from $26 billion in 2008-09 to $51 billion in 2010-11, but dropped to $46 billion in 2011-12. Preliminary data show a drop this year to about $45 billion.

Highlights in other sectors:

  • Sticker prices at public community colleges, are up 3.5%, to $3,264, this year. With estimated grant aid, students would have $1,550 left after paying tuition to put toward books and living expenses.
  • Published rates at private four-year colleges, are up 3.8%, to $30,094, this year. With grant aid, the average net price is $12,460.
  • Average tuition at for-profit colleges increased just 0.5%, to $15,130, and net prices average about $3,420. The study urged caution in interpreting those numbers because most for-profit institutions do not participate in the survey.

Just as tuition has steadily climbed over the years, the number of people going to college has steadily increased, though it dipped slightly in 2011. Typically, enrollments increase in a weak economy and dip again when the employment picture brightens.

Source: National Center for Education Statistics
Tory Hargro, USA TODAY

Meanwhile, a College Board report published earlier this month noted that a college degree pays off in the job market. For example, median earnings for bachelor’s degree recipients with no advanced degree working full time in 2011 were $56,000 compared with $21,000 for high school graduates.

Also, the unemployment rate for four-year college graduates ages 25 to 34 was 7.1 percentage points below that for high school graduates.

ACE director of national initiatives Melanie Corrigan said economic and job growth will be key factors in enrollment trends while state appropriations and legislatures are the largest determinant of tuition levels. “For more than 40 years, we have seen increases and declines in enrollment — but the long-term trend has always been toward increasing enrollment. We don’t see year-to-year fluctuations in enrollment having a big impact” on tuition,” she said.

Source: The College Board, Trends in College Pricing
Tory Hargro, USA TODAY

 

Four Positive Integers with Equal Sum and Product

Q: For how many positive four‐digit integers is the sum of its digits equal to the product of its digits? (MathCounts Problems of the Week, July 22, 2013)

Since repetition is not excluded, the set of {1, 1, 2, 4} fulfills the restriction of all positive integers.  (There is a mathematical proof to show that this is the only set.)

The question here goes one step further to inquire how many unique ways to arrange these four numbers.  This is essentially identical to question asking how many distinguishable permutations the letters in OHIO have.

There are 4! = 4 x 3 x 2 x 1 = 24 ways of arranging 4 letters or numbers in 4 spots.

But number 1 or letter O is repeated twice: 2! = 2

Therefore, the number of unique or distinguishable ways is 4! / 2! = 24 / 2 = 12.

Poor Math Skills Contribute to Foreclosures

http://money.cnn.com/2013/06/25/real_estate/mortgage-math/index.html

Bad at math? You’re more likely to lose your home

By Les Christie @CNNMoney June 26, 2013: 5:55 PM ET

Borrowers with poor math skills made up a higher percentage of homeowners in foreclosure during the housing bust than those who were skilled at arithmetic.

According to a study released Monday, math-challenged borrowers were five times more likely to default on their loans.

“Whether you’re good with numbers predicts how likely you are to default,” said Stephan Meier, an associate professor of business at Columbia Business School, who authored the report along with economists from the Federal Reserve of Atlanta and the University of Lausanne.

The study examined several hundred borrowers who held mortgages issued in 2006 and 2007 — right before the mortgage meltdown. Of the study subjects, 25% of the borrowers who scored in the lowest bracket for math skills had defaulted on mortgage payments within five years of getting the loans. Meanwhile, only 5% of those in the top tier for math skills defaulted.

Related: Homebuyers clueless about mortgages

The survey sample included homebuyers from a variety of backgrounds, from blue collar workers to corporate professionals. Their math ability covered the gamut — from those with very limited abilities to a mathematician with a six-figure salary, according to Kristopher Gerardi, an economist with the Federal Reserve of Atlanta.

The researchers controlled for differences in overall intelligence by measuring for verbal and general IQs, as well as math skills, and controlled for socioeconomic factors, such as age, sex, income, ethnicity and local labor market conditions.

Surprisingly, it did not seem to matter what kind of mortgage the borrowers had, the researchers found. “Those lacking [math skills] will still get in more trouble later on even if they pick a plain vanilla mortgage,” said Meier.

The researchers asked the survey participants a series of five basic questions. The simplest question asked them how much a $300 sofa would cost at a half-price sale. The most difficult asked how much a savings account of $200 would grow to after earning 10% interest for two years.

Related: How smart are you about mortgages?

Determining why those with poor math skills default on mortgages more often than others will take more research, but previous studies suggest that people who struggle with simple math also struggle with handling their finances, according to Gerardi. This group tends to budget less carefully, misuse credit cards and mishandle financial emergencies, such as temporary income losses. When they hit a rough financial patch, they may not understand the math well enough to negotiate the most favorable settlements with lenders.

“When bad events happened, they don’t react optimally,” said Meier.

The report suggested that benefits could come from improved financial education. The more homeowners understand money matters, the less likely they are to mishandle them.

The Early Bird Catches the Worm

by Matthew Ting

Starting early and becoming successful are strongly correlated.  There is a proverb in the English language: “The early bird catches the worm.”  A British interpretation asserts, “Success comes to those who prepare well and put in effort.”  An American explanation claims, “If you wake up and get to work early, you will succeed.”

Financial literacy relies on the foundation of numeracy.  In other words, someone possessing a strong number sense should know how to manage money well.  The concept of principal and interest is introduced and taught in middle and high school math curriculum of Pre-Algebra, Algebra 1, and Algebra 2.  For simple interests, the formulas are I = Prt, or Interest = Principal x annual interest rate x number of years; and A = P + I = P + Prt = P(1 + rt), or Cumulative Amount = Principal + Interest.  For compound interests, which are widely used in real world, the formula is A = P(1 + r/n)^(nt), in which n is number of times the interest is compounded each year.

Albert Einstein was quoted declaring that compounding is the eighth wonder of the world and the most powerful force in the universe.  Whether our physics genius really said it or not, the simple math speaks for itself: at 7% interest rate, our money roughly doubles every 10 years.  Many Home Economics textbooks repeat such an investment scenario: if a 25-year-old invests $380 a month (that is $4,560 a year) at a 7% compound annual interest rate for 40 years (total contribution $182,400), he or she will have exceeded $1 million in personal wealth by age 65.

If a person starts later at age 35, the compounding factor will be far less robust.  He or she will not have amassed even half a million under the same conditions.  In order to reach the goal of $1 million, the person will have to be more aggressive and contribute $820 a month or $295,200 total for 30 years.  On the other hand, if a person starts five years earlier at age 20, then he or she will have $1.45 million on hand at age 65.  Or, the person can lower the monthly contribution to $270 and still reach the million dollar goal under the same conditions.

The Library of Economics and Liberty claims: “Saving and investing is one of 51 key economics concepts identified by the National Council on Economic Education (NCEE) for high school classes.”  Readers of this blog post can use any physical or virtual compound interest calculator to discover and determine the “dollars and sense” at any age.  Below is one of many useful sites: http://www.thecalculatorsite.com/finance/calculators/compoundinterestcalculator.php

The “early bird = success” axiom applies to learning math or any other subject, but probably more so for math, because math concepts and skills constrict the grey area between numeracy and innumeracy (mastery or the contrary) to nearly nonexistent.  Either you know it, or you do not know it.  If I hear a student saying with hesitance, “I kinda know what Laws of Sines are …” I usually pressure for an example, then will hear, “I forgot.”  That is no mastery.  That is innumeracy.  Having heard the term does not mean much.

Those students who preview in a solid fashion tend to succeed easily at school.  They typically spend far less time on assignments and retain far more content knowledge than their counterparts moving along or falling behind the teacher’s pace.

Being or becoming an “early bird” is essentially habit-forming and confidence-building.  Some of my university students would raise their hands on the first day of class asking whether the weekly readings listed on the syllabus are due before or after each class meeting.  The answer is before.  To encourage the habit and enhance the confidence level, I routinely give reading and lesson quizzes.  Full and through, “early birds” command our respect by having the fewest emergencies and performing at optimal levels most steadily.  They are simply persons, cases, and anecdotes of successes.

Are you an “early bird”?

(Inspiration and input by Steve)

Eight-Letter Permutations

Eight‐letter permutations can be made by using four letters from the word MAINE and four letters from IDAHO.  How many unique eight‐letter permutations are there?  (2013 National MathCounts Competition Team Round #3)

Choosing 4 letters from the word MAINE or IDAHO is 5 C 4 = 5; combining these two choices is 5^2 = 25.  Positioning 8 letters is 8 P 8 = 8! = 40,320 ways.  Positioning the 8 chosen letters has a total of 25 x 8! = 1,008,000 ways.

If 2 A’s are chosen among the 8 letters, then there are 7 + 6 + 5 + 4 + 3 + 2 + 1 = 28 ways of placing them.  In the meantime, the remaining 6 slots have 6! = 720 ways of arranging the other distinct letters.  Positioning 2 A’s and 6 other distinct letters has a total of 28 x 6! = 20,160 ways.  If 2 I’s are chosen, then positioning 2 I’s and 6 other distinct letters has an identical total of 20,160 ways.

Now let us explore the possibility of 2 A’s and 2 I’s are chosen simultaneously:  There are 8 C 4 = 70 ways of placing 4 letters in 8 slots.  There are 6 distinct ways of ordering 2 A’s and 2 I’s from left to right — AAII, AIAI, AIIA, IIAA, IAIA, and IAAI.  Therefore, positioning 2 A’s, 2 I’s, and 4 other distinct letters has a total of 70 x 6 x 4! = 10,080 ways.

In conclusion, there are 1,008,000 – (20,160 + 20,160 + 10,080) = 957,600 unique eight-letter permutations.

(Partial credit to Ethian)

Teacher Quality + Student Discipline + Repetition = Achievement

by Matthew Ting

Oftentimes we hear parents, educators, and elected officials complain that our students are not achieving their academic goals, whether individually or collectively.  In this day and age, many readily play the blame game — parents blame teachers for their students’ poor grades; math teachers blame English teachers for students’ inability to comprehend and solve word problems; current teachers blame former teachers for not covering the proper content; primary-grade teachers blame low family involvement, big class size, and inclusive instruction for students with special needs; school board members blame budget shortfalls … The vicious cycle goes on.

When a student gets an F … yell at the teacher with mom and dad
(Source: http://artofeducation.wordpress.com/tag/teacher-parent-relations/)

The salient question to ask should be, “What are the key factors for student success?”

Teacher quality is utmost important.  An ancient Chinese saying sums it up well: 名師出高徒 — literally “a renowned teacher cultivates outstanding students.”  In my work with math teachers around the nation, I found many fell short of basic expectations.  If an elementary school teacher claims “1 is the smallest prime number,” if a middle school teacher needs a calculator to square 12, if a high school teacher fails to properly plot square root of 2 on the number line, if a math instructional coach or curriculum specialist is promoted to the rank not based on meritocracy, then our math education system is in jeopardy.

Teaching, especially math and science teaching, may not attract the best and brightest in America, but a rigorous teacher preparatory program followed by continuing professional development will definitely produce the best and brightest teachers.  That is the long-term goal for the nation, and certainly takes time, funding, and concerted effort of policymakers, universities, school districts, and other stakeholders.  In the short run, the best solution for families with school-age children is finding and sending their students to the best math teachers.

I recently attended the AERA (American Educational Research Association) annual meeting in San Francisco and exchanged ideas with many other attendees from all over the world.  The most memorable of all was my interaction with Dr. Freeman A. Hrabowski, III, president of the University of Maryland, Baltimore County (UMBC) since May 1992.  He was once on the short list for secretary of education by the Obama administration and the recipient of the 2013 AERA Distinguished Public Service Award.  (Secretary of Education Arne Duncan was also one of the AERA keynoters; Hrabowski may not have Duncan’s job salaried at $196,700, but certainly enjoys his at more than $520,000 a year.)

with Dr. Freeman A. Hrabowski, III, UMBC president and 2013 AERA distinguished public service award recipient

President Hrabowski commands my respect, not only due to the fact that he earned his B.S. in Mathematics at age 19 then M.S. in Mathematics and Ph.D. in Statistics by age 24, but also because he has been a staunch promoter for excellence in math education.  He reminded me how a teacher’s attitude could make or break a student’s motivation in learning.  Growing up in the deep south in the 1960s as an African American boy, he shared that some of his high school math teachers would roll their eyes and say or use their body language to say “Isn’t that obvious?” when he asked questions on math.  Adversities, including an arrest for his civil rights involvement at age 12, did not crush the young Freeman but motivated him to excel and pursue a career in math.

Student discipline is the second key factor for academic success, asserted President Hrabowski in his featured AERA award lecture last Monday morning.  Students at UMBC do not cut classes nor even arrive fashionably late to classes, which is unheard of on any other university campus.  Hrabowski, dubbed by Time in 2009 as “a hard-discipline powerhouse,” maintains his presence in the attendance enforcement squad on campus.  He would tell some grumpy students: “It would be pretty hard to study the second derivative or applications to trusses on your own.”  Tough discipline yields impressive outcome — more than half of the 11,000 UMBC students majoring in the fields of STEM (science, technology, engineering, and mathematics) — a national record.

It has been a huge and rewarding privilege for me to coach thousands of talented students for math competitions since 1990.  Nothing is more thrilling than witnessing a talented and hardworking mathlete proudly winning a trophy after an arduous period of preparation time.  On the contrary, it always saddens me to see math geniuses come out empty-handed because they thought they could pull it off just being so smart.

What is the first word that comes to your mind when you hear “the few, the proud, the Marines”?  Discipline, probably.  Such a value is many times pushed aside in our land of the free.  I instilled “Perfect Attendance” in my own children from an early age.  It is far less for the badge of honor or ADA (average daily attendance for state funding), but for the moral fiber.  Involving in a few activities for a set period of time, giving full dedication, doing the best, taking pride, and staying as far away as possible from the flexible and the failing.  We all know who won the race between the hare and the tortoise.  What is the moral of the fable?  Self-discipline.

Repetition is the third leg of the tripod for student success, according to Dr. Hrabowski. Most colleges and universities allow students to retake and replace a D or F grade up to four or five courses.  UMBC breaks the barrier and allows far more, because the president firmly believes many students need more time and repetition to master STEM concepts and applications regardless of their ethnicity or college preparatory background.

I thought that is profound wisdom especially in math learning.  Each of my children repeated Pre-Algebra and Algebra 1 three times, not because they were “low and slow,” but because I wanted them to have a rock solid foundation.  Those repetitions have paid off.  Some of the parents I work with insist on tracking up their children’s progress in leaps and bounds without much repetition, but that is harmful and prone to regression.  There is a bright senior who completed AP Calculus BC in her junior year and wanted desperately but failed to score perfect on SAT and ACT math.  I ran some diagnostics last summer and was surprised by her profound weaknesses in Fraction Operations and Plane Geometry Area Formulas.  Why the discrepancy?  Not enough repetition in Math 6 and Pre-Algebra, I bet.

La Cathédrale de Chartres, France (photo credit: Alexander Eisenman)

I visited Chartres Cathedral at a young age.  This Roman Catholic cathedral is located about 50 miles southwest of metropolitan Paris, and is the oldest and best preserved Gothic architecture in the world.  I remember vividly what the cathedral guide told us, the architect did not allow the bricklayers to lay more than one layer each day, and the day had to be in fair condition, not rainy, snowy, or windy.  Many times he ordered the previous day’s layer removed and relayed because it failed his inspection.  He angered the workers as well as the archbishop who accused him of straddling for extra pay.  Should the architect have compromised, we would never have the opportunity to marvel at his masterpiece 900 years later.

“We are what we repeatedly do,” said Aristotle, “Excellence, therefore, is not an act but a habit.”

Congratulations to Our Mathletes!

by Matthew Ting

What a wonderful weekend that some of the current and former Math Competition Club members enjoyed at the annual MathCounts South Bay / Santa Monica Chapter Competitions!  Edward, Jeannie, Dennis, Richard, Brandon, Megan, David, Sarah, Andrew, Michelle, Peter, Vanessa, Ted (not in any particular order; did I leave anyone off?) represented their schools and competed along with nearly 400 other Mathletes at Northrop Grumman (NGC) Space Park Campus.  Several of them will advance to the State Competitions as Team Members or Individuals (I have not received the full and updated list yet).

Adams Middle School in Redondo Beach, another local school where I have also volunteered since 2008, followed last year’s suit — placing #1 in the Division and sending two Team Members onstage for the Countdown Round.  My students in other Chapters will compete in the weekends to come — February is MathCounts Chapter Competition month throughout the nation.  It is indeed the most meritorious and crowning achievement for any middle schoolers who are truly advanced to show off their math prowess through participation in MathCounts!

After the jubilant celebrations, it is most noteworthy to thank the parents, because without your dedication and encouragement in the first place, our Mathletes would not be able to stand a chance.  Two NGC directors and I had a working lunch together last week.  They regard all Mathletes as the future pillars of our national security and assure me the defense contract giant’s continuing support to MathCounts in South Bay!

Most of our kids are involved in many extracurricular activities — soccer, basketball, swimming, cross country, tennis, golf, piano, violin, marching band, dance, karate, art, etc.  Each and every one of them is terrific.  But to me, one of the 50 from the nation and one of the three from California commissioned by the National Governors Association in 2009-10 to write the Common Core State Standards for Mathematics (which will be fully adopted in California starting this fall), I am convinced that math will truly and fundamentally propel our kids to the top!

Math-Based 10 Best Jobs in America

CNNMoney / PayScale.com’s list of great careers

  1. Biomedical Engineer
  2. Marketing Consultant
  3. Software Architect
  4. Clinical Research Associate
  5. Database Administrator
  6. Financial Adviser
  7. Market Research Analyst
  8. Physical Therapist
  9. Software Developer
  10. Occupational Therapist

(中文簡譯)

1. Biomedical Engineer

Median pay: $79,500
Top pay: $124,000
10-year job growth: 61.7%
Total jobs: 15,700

What they do all day? Science fiction is a little less fictional in the day-to-day work of biomedical engineers, who design prosthetic limbs and artificial organs or regenerate tissue. They also create drug formulations, develop pharmaceuticals or collect and analyze biological data, among other work. In this field lies the intersection of biology and engineering skills, which helps crack tough problems in medicine and health.

How to get the job? A bachelor’s, master’s or Ph.D. in biological engineering will get prospects in the door, but engineers with more traditional degrees — such as electrical, mechanical and chemical — are also a good fit.

What makes it great? Not only is it one of the highest-paid engineering jobs, it’s a career that gives back to society by helping to improve world health. It’s also highly flexible, with positions in universities, hospitals, labs, industry and regulatory agencies.

What’s the catch? Rapid technological changes mean engineers have to work hard to stay abreast of new developments — so this isn’t the field for those looking to coast through their careers. –Kate Ashford

2. Marketing Consultant

Median pay: $92,100
Top pay: $208,000
10-year job growth: 41.2%
Total jobs: 282,700

What they do all day? Many business owners with great products have no idea how to get them out there. Enter the marketing consultant. Companies hire them to set up a plan that generates the right kind of buzz to attract the right kind of customers.

How to get the job? A flair for creative promotion runs side by side with a head for analyzing customer data. Expertise in the latest marketing technologies — web ads, SEO and Google Adwords — is also key. And most importantly: A savvy consultant needs to be well-versed across a wide range of industries to understand different clients’ needs.

What makes it great? That wide range of expertise is what makes the job so exciting. Unlike an in-house marketer, a consultant isn’t tied to one field. A variety of knowhow creates more opportunities for new accounts.

What’s the catch? Hustle is mandatory. Whether one works independently or for a consultancy, there is no such thing as job security, and regular income is never a sure bet. –Tom Ziegler

3. Software Architect

Median pay: $119,000
Top pay: $162,000
10-year job growth: 24.6%
Total jobs: 3,426,000

What they do all day? Great software architects are designers and diplomats. They create innovative and valuable programs, but they also translate highly technical plans into a vision the C-suite can understand. They are a crucial link between a company’s tech unit and management.

How to get the job? Unless one’s last name is Gates or Zuckerberg, a computer-related degree is strongly advised. A high-level position, it requires lots of experience, technical smarts and fluid communication skills.

What makes it great? It’s an opportunity to create and shape a company’s computer strategy. More responsibility also brings higher pay for a designer who wants to trade a PC screen for the conference room.

What’s the catch? Tech teams and management often speak very different languages that can lead to misunderstandings and even flare-ups. Putting out fires on both sides is crucial. –T.Z.

4. Clinical Research Associate

Median pay: $90,700
Top pay: $129,000
10-year job growth: 36.4%
Total jobs: 100,000

What they do all day? Where there’s a clinical trial, clinical research associates are making sure it’s going the way it should. That means monitoring procedures and results and making sure that researchers are following proper protocols at every step.

How to get the job? A bachelor’s in science, sociology or psychology is a good foundation, as is experience in a clinical trial environment or in health sciences. Some employers look for a CRA certification, such as the one offered by the Association of Clinical Research Professionals (ACRP).

What makes it great? Since there are so many different types of clinical trials, the work environment can be dynamic with tasks varying from day to day. CRAs can specialize in a particular subject area, or go for a broad base of knowledge and hop from topic to topic. And growth potential is strong: As personalized medicine becomes more common, clinical trials will increasingly be needed to make sure drugs and devices work properly.

What’s the catch? Most CRA jobs require at least some travel regionally, if not nationally or internationally, which can mean long hours and lots of time away from family. –K.A.

5. Database Administrator

Median pay: $87,200
Top pay: $122,000
10-year job growth: 30.6%
Total jobs: 110,800

What they do all day? It’s no understatement to say that corporate America is in the middle of an information explosion. Somebody has to keep track of it all. A database administrator (DBA) minds all the data in a company’s storehouse, keeps it safe and makes sure it’s easily accessible.

How to get the job? A degree in computer science is recommended, followed by years of experience. Many employers require certification in the most widely used programs, including MySQL, Oracle and DB2. And since the technology is always changing, re-training is a constant.

What makes it great? More data means more opportunities — DBAs are among the top-growing jobs on our list. They also command high paychecks, compared even to other tech jobs.

What’s the catch? The job requires long periods in front of the computer — especially during crunch times for big projects. And computers crash. Be prepared to come in late at night or on weekends when things go wrong. –T.Z.

6. Financial Adviser

Median pay: $90,200
Top pay: $206,000
10-year job growth: 32.1%
Total jobs: 206,800

What they do all day? You can DIY a lot of things, but big money decisions are sometimes best left to professionals. Financial advisers step in where many people fear to tread, offering advice on investments, savings, taxes and insurance decisions.

How to get the job? Although certification isn’t required to become an adviser, employers are more likely to hire prospects with letters after their names, such as CFP (Certified Financial Planner), CFA (Chartered Financial Analyst) or CPA (Certified Public Accountant). Once they pass their test of choice, advisers may have to work for a certain number of hours before the certification is official.

What makes it great? Advisers help clients achieve financial success, which feels pretty warm and fuzzy. And they can hang a shingle for themselves, work as part of a larger firm or even work virtually if their clients are comfortable with it.

What’s the catch? In an up market, financial advisers can be heroes. In a down market, they can be scapegoats. Handling someone else’s life savings can be daunting, especially when things are headed south. –K.A.

7. Market Research Analyst

Median pay: $63,100
Top pay: $97,700
10-year job growth: 41.2%
Total jobs: 282,700

What they do all day? Coke or Pepsi? Android or iPhone? Chevy or Toyota? You know what you like. It’s the job of market research analysts to find out why. From direct surveys to dissecting buckets of data, they track what consumers want — and what it would take to change their minds.

How to get the job? A head for numbers with a background in statistics, computer science and economics are essential to being more, um, marketable, as it were. The ability to distill those numbers into useful reports is a must.

What makes it great? An analyst is a key member of the team that develops great new products. The position runs across all industries that need research. And it’s got the second-highest growth rate of all the jobs on our list.

What’s the catch? Analysts who don’t need glasses yet, will soon enough. They spend hours poring over facts, figures and numbers. It’s a detail-driven field that operates under tight deadlines and has potential for long hours. –T.Z.

8. Physical Therapist

Median pay: $76,700
Top pay: $99,000
10-year job growth: 39.0%
Total jobs: 198,600

What they do all day? For people suffering from injuries or illness, physical therapists can be key to their recovery. They design tailored exercise and prevention programs, teach patients how to perform them safely, and help them regain movement and function.

How to get the job? A doctoral degree in physical therapy is usually required — and it typically takes two to three years to get one. Candidates without a strong background in math and science may have to take some prerequisite courses first. PTs also need a license. Patience and a sense of humor are pluses.

What makes it great? The workday is filled with small triumphs — a patient with a brain injury who learns to hold his head up again, an athlete whose range of motion improves after rotator cuff surgery.

What’s the catch? There’s paperwork aplenty, thanks to federal guidelines and the home health aspect of this job. Therapists who do in-home visits may deal with a couple of hours of documentation each night. –K.A.

9. Software Developer

Median pay: $84,200
Top pay: $121,000
10-year job growth: 24.6%
Total jobs: 3,426,000

What they do all day? From the games in a smartphone to the tools that map a genome, software developers write the programs that run our lives. The work runs across all levels of the process — research, design, writing and testing — and all the way to the final product.

How to get the job? Most developers have some sort of degree in computer science, but it’s a field that welcomes self-starters with practical experience and the right certifications. Check with local colleges to get going.

What makes it great? A developer can fly solo as a freelancer or work for a company as part of a team. And with a technology boom that sees no end in sight, firms are having a hard time filling positions.

What’s the catch? Those positions aren’t always in the U.S. In the search for talent (and to cut costs), more companies are heading overseas for their development needs. It’s also an ever-evolving field that requires a constant keeping up on what’s new. –T.Z.

10. Occupational Therapist

Median pay: $74,900
Top pay: $102,000
10-year job growth: 33.5%
Total jobs: 108,800

What they do all day? If it involves helping people perform daily activities on their own, occupational therapists have done it. While physical therapists might help someone with a hip injury learn to walk safely again, OTs would work on everyday tasks, such as getting out of bed or putting on shoes. They might also work with a child with OCD who has trouble at school, or help a patient with schizophrenia communicate more effectively.

How to get the job? Recruits must have a master’s degree in occupational therapy, and most programs take two to three years. They also need a license.

What makes it great? OTs can help people and develop strong relationships with clients without the rigmarole of becoming a doctor. OTs can work a flexible or part-time schedule and still earn decent money.

What’s the catch? It’s not always the most glamorous job. Occupational therapists might have to help someone learn how to shower or use the bathroom again, and that’s not everyone’s cup of tea. –K.A.

Math-Based 10 Best Jobs in America 十大最佳工作

November 29, 2012 06:00 AM

CNNMoney網站考量成長機會、薪資、滿意度、彈性等因素,找出2012年十大最佳工作

1、生物醫學工程師,中位薪水: 7萬9500元,最高薪水: 12萬4000元,十年工作成長: 61.7%,工作總數:1萬5700個。

生物醫學工程師設計義肢和人工器官,或使組織再生。這個領域是生物和工程的交集,幫助解決醫學難題。持有生物工程的文憑就能進入該領域,但較傳統的電力、機械和化學工程文憑也適合。

2、行銷顧問,中位薪水: 9萬2100元,最高薪水: 20萬8000元,十年工作成長: 41.2%,工作總數:28萬2700個。

公司聘請行銷顧問制定計畫,以製造人氣吸引顧客。擅長設計有創意的推銷手法,加上善於分析顧客數據的腦袋,就可找這行工作。精通最新行銷科技也是關鍵。最重要的是了解不同行業,以回應不同顧客的需要。

3、軟體架構師,中位薪水: 11萬9000元,最高薪水: 16萬2000元,十年工作成長: 24.6%,工作總數:342萬6000個。

軟體架構師創造革新和有價值的程式,並把極為技術性的計畫轉化為管理高層可以了解的願景。最好擁有與電腦相關的文憑,這個高階職位需要經驗豐富、技術高超、善於溝通。

4、臨床副研究員,中位薪水: 9萬700元,最高薪水: 12萬9000元,十年工作成長: 36.4%,工作總數:10萬個。

臨床副研究員監控臨床實驗的程序和結果,並確保研究員遵守規定。有關科學、社會學或心理學的大學文憑,是找工作的好基礎。在臨床實驗或醫療環境的經驗也有幫助。

5、資料庫管理員,中位薪水: 8萬7200元,最高薪水: 12萬2000元,十年工作成長: 30.6%,工作總數: 11萬800個。

資料庫管理員管理公司的資料庫,確保安全並容易取得資料。最好有電腦文憑和經驗,很多雇主要求在最普遍使用的程式獲得認證。

6、財務顧問,中位薪水: 9萬200元最,高薪水: 20萬6000元,十年工作成長: 32.1%,工作總數: 20萬6800個。

財務顧問提供投資、儲蓄、稅務和保險的建議。最好獲得認證 (CFP、CFA、CPA),較易找工作。

7、市場研究分析師,中位薪水: 6萬3100元,最高薪水: 9萬7700元,十年工作成長: 41.2%,工作總數: 28萬2700個。

從直接調查到分析數據,市場研究分析師追蹤消費者的喜好,以及如何改變他們的喜好。有統計學、電腦和經濟學的背景,加上精通數字,較易找工作。

8、物理治療師,中位薪水: 7萬6700元,最高薪水: 9萬9000元,十年工作成長: 39%,工作總數: 19萬8600個。

物理治療師為病人設計復健活動和預防計畫,教病人如何安全的進行這些活動,並助病人恢復運動和功能。需要物理治療的博士文憑。

9、軟體開發人員,中位薪水: 8萬4200元,最高薪水: 12萬1000元,十年工作成長: 24.6%,工作總數: 342萬6000個。

軟體開發人員撰寫程式。多數開發人員有電腦文憑,但這個領域歡迎有實務經驗和認證的自學者。

10、職能治療師,中位薪水: 7萬4900元,最高薪水: 10萬2000元,十年工作成長: 33.5%,工作總數: 10萬8800個。

職能治療師協助病人自己做日常活動,例如起床、穿鞋。需有職能治療的碩士文憑和執照。