Posts about Math

Mathematicians Top List of Best Occupations

These lists are basically silly but here is one sites opinion on the best occupations. I don’t really accept the methodology used as providing anything very meaningful about the “best jobs” but at least the spell it out. Best jobs

  1. Mathematician
  2. Actuary
  3. Statistician
  4. Biologist
  5. Software Engineer
  6. Computer Systems Analyst

Their criteria really value being able to sit at a desk and not having to do physical work. High salary and limited stress are also significant factors.

Related: The Economic Benefits of MathWho Killed the Software Engineer?Knowledge Is Power – Teaching MathThe IT Job Market in the UK

Making Magnificent Mirrors with Math

At Drexel, he designs amazing mirrors

Could math provide the path to better reflection? Perline asked.

Indeed it could. Eight years and numerous calculations later, Hicks is now testing a prototype mirror – for a car, not a bike – and he is in talks with a foreign manufacturer. As with the bike mirror, the rounded surface provides a wide field of view – so wide that it eliminates the dreaded, driver-side “blind spot” – yet the subtle mathematics of his design result in little or no distortion.

He didn’t stop there. The 42-year-old mathematician went on to design half a dozen other reflective surfaces for various applications – a few of them in collaboration with Perline – and they are like nothing you’d ever see on the bathroom wall.

Panoramic mirrors. Mirrors for use with high-tech surveillance cameras. Mirrors with odd, undulating surfaces that are fashioned with a computer-guided milling machine. And one wacky mirror that doesn’t yield a mirror image at all. If you raise one hand while looking into the curved surface, your reflection appears to be raising the opposite hand.

It’s not clear what use that one will have, beyond entertainment – Perline calls it “the vampire mirror” – but with his driver-side prototype, Hicks may be onto something.

Related: Innovation with MathThe Emperor of MathTimemath related posts

Evolution, Methane, Jobs, Food and More

photo of sunset on Mars
Photo from May 2005 by NASA’s Mars Exploration Rover Spirit as the Sun sank below the rim of Gusev crater on Mars.

Science Friday is a great National Public Radio show. The week was a great show covering Antimicrobial Copper, Top Jobs for Math and Science, Human-Driven Evolution, Methane On Mars, Fish with Mercury and more. This show, in particular did a great job of showing the scientific inquiry process in action.

“Fishing regulations often prescribe the taking of larger fish, and the same often applies to hunting regulations,” said Chris Darimont, one of the authors of the study. “Hunters are instructed not to take smaller animals or those with smaller horns. This is counter to patterns of natural predation, and now we’re seeing the consequences of this management.” Darimont and colleagues found that human predation accelerated the rate of observable trait changes in a species by 300 percent above the pace observed within purely natural systems, and 50 percent above that of systems subject to other human influences, such as pollution

Very interesting stuff, listen for more details. A part of what happens is those individuals that chose to focus on reproducing early (instead of investing in growing larger, to reproduce later) are those that are favored (they gain advantage) by the conditions of human activity. I am amazed how quickly the scientists says the changes in populations are taking place.

And Methane On Mars is another potentially amazing discovery. While it is far from providing proof of live on Mars it is possibly evidence of life on Mars. Which would then be looked back on as one of the most important scientific discoveries ever. And in any even the podcast is a great overview of scientists in action.

This week astronomers reported finding an unexpected gas — methane — in the Martian atmosphere. On Earth, a major source of methane is biological activity. However, planetary scientists aren’t ready to say that life on Mars is to blame for the presence of the gas there, as geochemical processes could also account for the finding. The find is intriguing especially because the researchers say they have detected seasonal variations of methane emissions over specific locations on the planet.

Martian Methane Reveals the Red Planet is not a Dead Planet
The Mars Methane Mystery: Aliens At Last?

Related: Mars Rover Continues ExplorationCopper Doorknobs and Faucets Kill 95% of SuperbugsViruses and What is Lifeposts on evolutionScience and Engineering Link Directory

Data Analysts Captivated by R’s Power

Data Analysts Captivated by R’s Power

data mining has entered a golden age, whether being used to set ad prices, find new drugs more quickly or fine-tune financial models. Companies as diverse as Google, Pfizer, Merck, Bank of America, the InterContinental Hotels Group and Shell use it.

Close to 1,600 different packages reside on just one of the many Web sites devoted to R, and the number of packages has grown exponentially. One package, called BiodiversityR, offers a graphical interface aimed at making calculations of environmental trends easier.

Another package, called Emu, analyzes speech patterns, while GenABEL is used to study the human genome. The financial services community has demonstrated a particular affinity for R; dozens of packages exist for derivatives analysis alone. “The great beauty of R is that you can modify it to do all sorts of things,” said Hal Varian, chief economist at Google. “And you have a lot of prepackaged stuff that’s already available, so you’re standing on the shoulders of giants.”

R first appeared in 1996, when the statistics professors Ross Ihaka and Robert Gentleman of the University of Auckland in New Zealand released the code as a free software package. According to them, the notion of devising something like R sprang up during a hallway conversation. They both wanted technology better suited for their statistics students, who needed to analyze data and produce graphical models of the information. Most comparable software had been designed by computer scientists and proved hard to use.

R is another example of great, free, open source software. See R packages for Statistics for Experimenters.

via: R in the news

Related: Mistakes in Experimental Design and InterpretationData Based Decision Making at GoogleFreeware Math ProgramsHow Large Quantities of Information Change Everything

Educating the Biologist of the 21st Century

An Introductory Science Curriculum for 21st Century Biologists by David Botstein (webcast)

At Princeton’s new Lewis-Sigler Institute, Botstein is spearheading an innovative effort at interdisciplinary undergraduate education. Students will take advantage of state of the art laboratories and computers capable of crunching vast amounts of data generated by actual research. Professors will “provide essential fundamental concepts as required, using the just-in-time-principle” – no more of the “learn this now, it will be good for you later” approach, which Botstein likens to hazing. Botstein says there is “lots of overhead in teaching historical and traditional origins” so his students will learn instead “with ideas and technologies of today.” He wants to create a new basic language that will enable his biology students to make sense of the fundamental issues of other disciplines.

Very good look at future of biology education.

Related: MIT Faculty Study Recommends Significant Undergraduate Education ChangesThe Importance of Science EducationWebcast: Engineering Education in the 21st CenturyEducating the Engineer of 2020: NAE Report

Brain Reorganizes As It Learns Math

Brain reorganizes to make room for math

It takes years for children to master the ins and outs of arithmetic. New research indicates that this learning process triggers a large-scale reorganization of brain processes involved in understanding written symbols for various quantities.

The findings support the idea that humans’ ability to match specific quantities with number symbols, a skill required for doing arithmetic, builds on a brain system that is used for estimating approximate quantities. That brain system is seen in many nonhuman animals.

When performing operations with Arabic numerals, young adults, but not school-age children, show pronounced activity in a piece of brain tissue called the left superior temporal gyrus, says Daniel Ansari of the University of Western Ontario in London, Canada. Earlier studies have linked this region to the ability to associate speech sounds with written letters, and musical sounds with written notes. The left superior temporal gyrus is located near the brain’s midpoint, not far from areas linked to speech production and understanding.

In contrast, children solving a numerical task display heightened activity in a frontal-brain area that, in adults, primarily serves other functions.

Related: Brain DevelopmentThe Brain Hides Information From Us To Prevent MistakesHow The Brain Rewires Itselfposts about brain research

Engineers and Scientists in Congress

I started maintaining a list of Congressmen with PhDs and graduate degrees in science, engineering and math awhile back.

Please comment with any additions that you know of.

The following were re-elected:
Vernon Ehlers, Michigan, physics PhD; Rush Holt, New Jersey, physics PhD; John Olver, Massachusetts, chemistry PhD; Brian Baird, Washington, psychology PhD; Bill Foster, Illinois, physics PhD.

Other scientists, engineers and mathematicians that were reelected include: Ron Paul, Texas, biology BS, MD; Jerry McNerney, California, mathematics PhD; Dan Lipinski, Illinois, mechanical engineering BS, engineering-economic systems MS; Todd Akin, Mississippi, management engineering BS;Cliff Stearns, Florida, electrical engineering BS; Louise Slaughter, New York, microbiology BS; Joe Barton, Texas, industrial engineering BS, Pete Stark, California, engineering BS, Mike Honda, California.

Lost: Nancy Boyda, Kansas (BS chemistry).

Newly elected: Bill Cassidy, Louisiana (BS Biochemistry, MD); Pete Olson, Texas (BA computer science); Kurt Schrader, Oregon (Doctor of Veterinary Medicine); Martin Heinrich, New Mexico (BS engineering), Gregg Harper, Mississippi (BS chemistry), Joseph Cao, Mississippi (BA physics); Brett Guthrie, Virginia (BS mathematical economics); Erik Paulsen, Minnesota, mathematics BA; Parker Griffith, Alabama (BS chemistry, MD); Cynthia Lummis, Wyoming (BS animal science and biology).

Before you leap to the conclusion that scientists are taking over Congress, remember 2 things: 1) I have probably been missing plenty that were in congress already and 2) this is still a total of less than 10% with even a BS in science, math or engineering. I attempted to determine the status of all those newly elected this year.

Please comment, if you know of others in Congress with science and engineering backgrounds. If we get this list to be relative close to accurate then we can start tracking the total representation in congress and see if it is increasing, decreasing or randomly fluctuating over time.

Related: Scientists and Engineers in CongressChina’s Technology Savvy LeadershipScience and Engineering in PoliticsThe A to Z Guide to Political Interference in Science

Compounding is the Most Powerful Force in the Universe

A talking head with some valuable info. I remember my father (a statistics professor) getting me to understand this as a small child (about 6 years old). The concept of growth and mathematical compounding is an important idea to understand as you think and learn about the world. It also is helpful so you understand that statistics don’t lie but ignorant people can draw false conclusions from limited data.

It is unclear if Einstein really said this but he is often quoted as saying “compounding is the most powerful force in the universe.” Whether he did or not, understanding this simple concept is a critical component of numeracy (literacy with numbers). Also quoted at times as: “Compound interest is the eighth wonder of the world.” My guess is that people just find the concept of compounding amazing and then attribute quotes about it to Einstein.

I strongly encourage you to watch at least the first 2 segments (a total of 15 minutes). And then take some time and think. Take some time to think about compounding in ways to help you internalize the concepts. You can also read his book: The Essential Exponential For the Future of Our Planet by Albert Bartlett.

Related: Playing Dice and Children’s NumeracySaving for Retirement (compound interest)Bigger Impact: 15 to 18 mpg or 50 to 100 mpg?Sexy MathThe Economic Benefits of Math

National Girls Collaborative Project for STEM

The National Girls Collaborative Project for science, technology, engineering, and mathematics (STEM) collaborates with those seeking to increase the participation of girls in STEM feeder activities. The goal is to encourage girls to pursue careers in science, technology, engineering, and math.

Collaboration as a Means to Building Capacity: Results and Future Directions of the National Girls Collaborative Project:

The purpose of the NGCP is to extend the capacity, impact, and sustainability of
existing and evolving girl-serving STEM projects and programs. The NGCP is structured to bring organizations together to compare needs and resources, to share information, and to plan strategically to expand STEM–related opportunities for girls.

Although we are still refining it, the NGCP collaborative model has shown its effectiveness through increased collaboration and minigrant projects with sustained results. As we have described, the success to date of the NGCP in developing collaborations has been demonstrated via data from the collaboration rubric, mini-grant reports, and metrics that show how collaborative activities have increased over the duration of the NGCP projects. As NGCP expands over the next few years to provide regional collaboratives across the entire United States and Puerto Rico, we will continue our assessment of its impact and hope to be able to report its influence on building capacity to attract and retain girls in STEM.

I support programs encouraging STEM activities for girls – and boys. NSF data shows for 2005 shows women outnumbered men in undergraduate degree in science and engineering. For post-graduate degrees men still outnumbering women but that gap has been reducing and seems like it will continue to. And the representations in the workplace seem poised to continue to show a reducing number of men and increasing number of women. Engineering is an example of an area with far more men than women graduating – the imbalance is equivalent to the imbalance the other way for psychology.

Related: Girls Sweep Top Honors at Siemens Competition in Math, Science and TechnologyFIRST Robotics in MinnesotaKids in the Lab: Getting High-Schoolers Hooked on Science

Problems Programming Math

Arithmetic Is Hard – To Get Right by Mark Sofroniou

I’ve been working on arithmetic in Mathematica for more than 12 years. You might think that’s silly; after all, how hard can arithmetic be?

The standard “schoolbook” algorithms are pretty easy. But they’re inefficient and often unnecessarily inaccurate. So people like me have done a huge amount of work to find algorithms that are more efficient and accurate. And the problem is that these algorithms are inevitably more complicated, and one has to be very careful to avoid insidious bugs.

Take multiplying integers, for example. The standard “schoolbook” long-multiplication algorithm uses n^2 multiplications to multiply two n-digit numbers. But many of these multiplications are actually redundant, and we now know clever algorithms that take n^1.58, n log n, or even fewer multiplications for large n. So this means that if one wants to do a million-digit multiplication, Mathematica can do it in a fraction of a second using these algorithms–while it would take at least a few minutes using standard long multiplication.

It’s not easy to get reliable numerical computation, and it’s not something one can “bolt on” after the fact. It’s something one has to build in from the beginning, as we’ve done in Mathematica for nearly 20 years.

Related: Who Killed the Software Engineer?Sexy MathFreeware Math Programs1=2: A ProofThings You Need to be a Computer Game Programmer

The Rush to Save Timbuktu’s Crumbling Manuscripts

The Rush to Save Timbuktu’s Crumbling Manuscripts

Fabled Timbuktu, once the site of the world’s southernmost Islamic university, harbors thousands upon thousands of long-forgotten manuscripts. A dozen academic instutions from around the world are now working frantically to save and evaluate the crumbling documents.

The Ahmed Baba Library alone contains more than 20,000 manuscripts, including works on herbal medicine and mathematics, yellowed volumes of poetry, music and Islamic law. Some are adorned with gilded letters, while others are written in the language of the Tuareg tribes. The contents remain a mystery.

Manuscript hunters are now scouring the environs of Timbuktu, descending into dark, clay basements and climbing up into attics. Twenty-four family-owned collections have already been discovered in the area. Most of the works stem from the late Middle Ages, when Timbuktu was an important crossroads for caravans.

Archaeologists have shown that an incredible system of underground canals up to 20,000 kilometers (12,422 miles) long once existed at Wadi al-Hayat in Libya. Thanks to such hydraulic marvels, the desert blossomed and crops sprouted in the fields of the Tuareg.

Related: digital library of scholarly resources from and about AfricaAfrican Union Science Meeting

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