April 30, 2004
DNA key to in-body device to aid diagnosis, treatmentSOLUTIONS IN SOLUTION: The `computer' is a liquid that changes its state based on a single variable, and then its `sticky ends' slice off offending DNA segmentsScientists have developed what they say could become the world's smallest medical kit: a computer made of DNA that can diagnose disease and automatically dispense medicine to treat it.The computer, so small that a trillion would fit into a drop of water, now works only in a test tube, and it could be decades before something like it is ready for practical use. But it offers an intriguing glimpse of a future in which molecular machines operate inside people, spotting diseases and treating them before symptoms appear. "Eventually we have this vision of a doctor in a cell," said Ehud Shapiro of the Weizmann Institute of Science in Rehovot, Israel, who led the research, whch was published online Wednesday by the journal Nature. DNA's role is to store and process information, the genetic code. So it is not surprising that DNA can be used for other computing tasks as well, and scientists have used it to solve mathematical problems. "I think it's very elegant -- it's almost like a beautiful mathematical proof," said George Church, professor of genetics at Harvard Medical School. "But it's not working in human cells yet." DNA has intrigued some computer scientists since 1994, when Len Adleman of the University of Southern California showed it could be used to solve a mathematical problem. People in the field then began envisioning billions of pieces of DNA undergoing chemical reactions, solving problems too complex for more conventional computers. Some scientists have since concluded that it will be difficult to get DNA computers to match the power of electronic computers. But Shapiro, who is also in the Weizmann Institute's department of biological chemistry, decided to focus on a DNA computer for use in the body, where silicon would have a hard time competing. The Weizmann DNA computer encodes both the software and the data in the four letters of the genetic code, A, C, G and T. The "hardware," the part of the computer that does not change, is an enzyme that cuts the strands of DNA in a particular way. The computer is made of double-stranded DNA with ends that are single-stranded. These so-called sticky ends can bind to specific other strands of DNA or RNA in the solution under the usual rules of DNA pairing. If binding occurs, the enzyme cuts the DNA a certain distance away, exposing new sticky ends. If those ends find something to bind to, the enzyme cuts in yet another location, and so on. If the chain reaction proceeds in a certain way, the enzyme eventually slices off the piece of DNA that acts as the drug. After the DNA encoding the problem is made and put in the test tube, the computer works automatically and arrives at the answer in minutes. "Basically," Shapiro said, "we just drop everything in solution and see what happens." DNA key to in-body device to aid diagnosis, treatment |
April 30, 2004
Academy elects Cal professorsFour University of California, Berkeley, professors and a mathematician from the Lawrence Berkeley National Laboratory have been elected to the National Academy of Sciences, considered one of the highest honors accorded a U.S. scientist or engineer. UC Berkeley's electees are A. Paul Alivisatos, Chancellor's Professor of Chemistry and Materials Science and director of the Molecular Foundry at the Lawrence Berkeley lab; Raymond Jeanloz, professor of earth and planetary science and astronomy; George F. Oster, professor of cell and developmental biology and environmental science, policy and management; and Peter H. Quail, professor of plant biology and research director of the Plant Gene Expression Center. Phillip Colella, senior staff mathematician and group leader with the Applied Numerical Algorithms Group at the Berkeley lab, was also elected. They were among 72 new members and 18 foreign associates from 12 countries elected to the National Academy of Sciences during its annual meeting in Washington, D.C. Academy elects Cal professors |
April 29, 2004
A hard-headed approach to selling a dreamBy Gary Silverman There was a time when advertising professionals lived in a dream world. David Ogilvy, founder of WPP's Ogilvy & Mather agency, said the imagery for his popular Pepperidge Farm bread commercials came to him in his sleep. But now, it takes more than a dream to satisfy the world's largest advertisers. They want numbers - Return On Investment figures to tell them how well particular forms of advertising are paying off in sales. The push for greater quantification of marketing results is symbolised by recent developments at Procter & Gamble. Using complex mathematical models, the consumer goods group in Cincinnati, Ohio, redeployed about $400m (£223m) of its $4.3bn global advertising budget last year. Of course, mathematical models have been used for years to gauge the effectiveness of advertising, particularly in the UK. But the P&G example suggests that the intensity of these efforts is growing. Behind the scenes, marketing services companies are preparing for the impact. "When they [P&G] do something like this, it is a huge signal that this is a serious subject," says Stephen Fajen, general manager of consultancy Morgan Anderson. "It almost automatically becomes a best practice. They are leaders." The embrace of ROI in marketing reflects the increasingly mathematical culture of large conglomer ates. These companies have grown so complex that they almost have to focus on activities that can be readily measured. At Citigroup, the management mantra boils down to "track it, control it, measure it". "Historically, we looked at the short-term effect of things," Mr Usitalo says. "In recent years, we [have been] more interested in the long-term impact on the consumer. We are moving to track the effects on at least a 12-month basis and close to a 36-month basis." Advertisers are gaining confidence in their mathematical models because technical advances are helping them sift through more data more quickly. Real-time sales information from stores is one of the most important advances helping this effort. A hard-headed approach to selling a dream |
April 29, 2004
Fun challenge for math whizzes, calculated risk for the restBY BRYAN ROURKE At yesterday's "Who Wants to be a Mathematician?" competition, sponsored by the American Mathematical Society, not only were the questions incomprehensible to mere non-mathematician mortals, so were the jokes. Miriam Klein, a junior at Classical High School, was on stage in a Providence College auditorium, competing and excelling. The appreciative precalculus crowd roared. They cheered. And one guy held up a sign saying: "Miriam, are you a differentiable equation?" Liberal arts enthusiasts looked lost. But the high-school math students competing here just laughed, and laughed. We wanted an explanation, some kind of proof those words equated with humor. Nick Chammas, a senior at Classical, gave us the answer, citing the Internet as the source for the postulate quip. So this guy walks into a bar. He asks a woman, "Are you a differentialable equation?" Naturally, she's confused: "Why do you ask?" And he says, "I want to be a tangent to your curves." The contest, now in its fourth consecutive year, culminates Math Awareness Month. No one's more aware of this than the Providence-based American Mathematical Society, which has a thing for celebrating the cerebral. "We like to reward these students," Breen says. "They may be doing their homework alone and doing well, but they're the only ones who know that. They're not performing in front of a big crowd at an athletic contest." While none of the competitors won the top prize, all won consolation prizes of calculators, software programs, and other items. And in the end, Breen says, the event accomplished its goal. It promoted the pursuit of mathematical excellence, which is relatively uncommon in this country compared with others. "In Europe, mathematicians are respected and rewarded," Breen says. "It's how a culture sees things. I don't know what it would take for mathematics to become popular here, but it would be good if that happened." Fun challenge for math whizzes, calculated risk for the rest |
April 29, 2004
Back to BASICs: College readies for program's 40thBy Mark Herman The Beginners' All-purpose Symbolic Instruction Code, an innovation of Dartmouth mathematics professors John Kemeny and Thomas Kurtz, was launched 40 years ago Saturday. The BASIC computing language went on to become the most widely used computing language in the world, bringing computer technology to the general public. At 4 a.m. on May 1, 1964 -- just hours after The Dartmouth published student election results and covered the controversy caused by a sociology professor's comments that Texas was just "semi-civilized" -- two undergraduates pulling an all-nighter quietly launched BASIC programs on several computers in the basement of College Hall, now part of the Collis Center. The event realized the vision Kurtz and Kemeny had to create an environment where computers were less intimidating for students, even those studying outside the sciences. Unlike the languages from which it was descended, FORTRAN and AGOL, BASIC used common sense commands, including PRINT, SAVE and RUN, which allowed users to more easily develop their own programs. Originally devised as a teaching tool, BASIC was integrated into the College curriculum at the time through two introductory mathematics courses. Beyond Dartmouth, BASIC brought technology to a network of high schools, colleges and corporate partners. Paul Allen and Bill Gates, who later formed Microsoft, used a form of BASIC to write the first programs for personal computers. Variations on the language are still used today. Following the development of BASIC, Kemeny became the 13th president of Dartmouth. Kurtz is now a professor emeritus of mathematics and computer science at the College. Their vision lives on today as the College continues to work for computing innovation and accessibility for students. Back to BASICs: College readies for program's 40th |
April 29, 2004
Maths boffins topple Certicom cryptoLucy Sherriff What do you get if you cross 109-bit elliptical curve cryptography with a very determined mathematician? If you have 2600 computers and 17 months and few more maths wizards to throw into the mix, you get a cracked key. Chris Monico, an assistant professor at Texas Tech university, and his team have solved the Certicom Elliptic Curve Cryptography (ECC)2-109 Challenge. There are three reasons that this is good news: firstly, it was brute forced, which means the algorithm is still sound. Secondly the CPU power it took to brute force the key is equivalent to an Athlon XP 3200+ working nonstop for about 1200 years. Lastly, commercial grade crypto uses 163-bit keys. To solve one of those is around one hundred million times harder. Maths boffins topple Certicom crypto |
April 28, 2004
Certicom Announces Elliptic Curve Cryptography Challenge WinnerMISSISSAUGA, ON, April 27 /PRNewswire-FirstCall/ - Certicom Corp. (TSX: CIC), the authority for strong, efficient cryptography, today announced that Chris Monico, an assistant professor at Texas Tech University, and his team of mathematicians have successfully solved the Certicom Elliptic Curve Cryptography (ECC)2-109 Challenge. The effort required 2600 computers and took 17 months. For comparison purposes, the gross CPU time used would be roughly equivalent to that of an Athlon XP 3200+ working nonstop for about 1200 years. Monico also led the team that won the ECCp-109 Certicom challenge in 2002. Although the same key length, this challenge was solved over a field of characteristic 2 rather than a prime field. For those people concerned about data security, this announcement is good news. The key solved in this challenge is well below the strength of commercial standards used by Certicom and many others today, which is ECC 163 or higher. In fact, it would be approximately one hundred million times harder to solve ECC 163. Why participate in the challenge? "I think public-key cryptography based on ECC is what we should and will be moving toward," said Monico. "And besides, the fact that this is likely the last of the ECC challenges to be solved in the next few years was a big motivator. The only way to get at the 130-bit level challenges are by a combination of Moore's law (wait around for computers to get faster) and gathering more computers. Personally, I think it's unlikely to happen soon." In addition to the professional incentives, Monico and his team will receive a US $10,000 prize for solving the challenge. Certicom introduced the ECC Challenge in November 1997. It was developed to increase industry understanding and appreciation for the difficulty of the elliptic curve discrete logarithm problem, and to encourage and stimulate further research in the security analysis of elliptic curve cryptosystems. Certicom Announces Elliptic Curve Cryptography Challenge Winner |
April 28, 2004
Floating Bodies from the Fourth DimensionSan Leandro, CA (PRWEB) April 28, 2004 -- According to latest theories, our universe has more than three dimensions. But is there a way to look into higher-dimensional spaces? Maybe not directly - but if we reverse the process, we could take a virtual object out of there, reduce it back into our 3D world, and then look at this. At least that's the approach that Vincent Stahl, computer artist from Germany, is taking in his images of the New Fractal Surrealism. The foundation for this isn't myth, but math - actually a formula invented by French mathematician Gaston Julia, in the early 20th century. It describes a mathematical object which can be visualized; in the 1970's, IBM mathematician Benoit Mandelbrot used this process to create 2D images. Today, the latest software generation allows to create 4D hyperspace objects, from which a small portion, or slice, is taken - resulting in a 3D form. Vincent Stahl is the first artist worldwide using this process in a professional manner. His sculptures are embedded within wide, silent landscapes, creating a unique surreal atmosphere. Every form is based on a set of input numbers, and by modifying those numbers, the form permutates - a principle made to create the most surreal short movies. This gives a real "look and feel" of the beauty and infinite complexity that 4D Fractal forms provide. His first internet movie, "Liquid faces", is now available for instant viewing: http://vincentstahl.com/movies/ "We're only at the beginning", states the artist, "it still is a matter of computing power, and the rendering takes quite a while. But with faster computers and future software, more and more artists and designers will explore the richness and beauty of Fractal forms taken from hyperspace." Within a few decades, the sculptures will be produced in real metal, and placed in public parks; industrial design will benefit from the strict symmetry and streamlines. Therefore, most of Stahl's images could be considered as a straight view into the future. The online gallery of Stahl's still images is available at: http://vincentstahl.com/gallery/ Floating Bodies from the Fourth Dimension |
April 28, 2004
Mathematical supermodels refine epidemic predictionsANDY DWORKIN Before the fire, Richard Crandall's computerized wilderness looks like a flag: one small red dot on a field of green. A quick click sets this silicon forest ablaze. The ring of fire spreads, leaving a ragged-edged red circle spattered with tiny green flecks. The green "survivors" seem randomly scattered through the dead zone. But complex calculations by Crandall and his Reed College students show that the survivors form a "fractal set," a nonrandom pattern in which subtle repetitions offer information about the crisis that created them. With some tweaks, that crisis can be a disease instead of a flame. The Reed group has already loosed smallpox through Conflagrator -- their name for the computer program that graphically plays out their disaster model. The smallpox also spreads in a fractal pattern, a fact that could help medics plan for outbreaks and suggests a new strategy for using limited vaccine supplies, Crandall said. The model is "a new tool that makes sharper predictions for some phenomena, such as sudden surges in an epidemic (or) vaccination strategies when you cannot vaccinate everyone," he said. Conflagrator represents a new way of thinking, fundamentally different than traditional disease models, that could influence public health efforts in Portland and perhaps the nation or world. An unusual collaboration produced this model. The main research arm of the U.S. Department of Defense gave two grants to explore how disease spreads. The investigators are Crandall and Reed biology professor Stephen Arch. Reed undergraduates studying biology, math and physics feed into the research, Crandall said. Mathematical supermodels refine epidemic predictions |
April 27, 2004
Mathematicians From Around the World Collaborate to Solve Latest RSA Factoring ChallengeBEDFORD, Mass., April 27 /PRNewswire-FirstCall/ -- RSA Laboratories, the research center of RSA Security Inc. (Nasdaq: RSAS) today announced that a team from the Scientific Computing Institute and the Pure Mathematics Institute in Germany, along with the National Research Institute for Mathematics and Computer Science in the Netherlands and several other organizations, has solved the RSA-576 Factoring Challenge. The worldwide team of eight solved the challenge using approximately 100 workstations in a little more than three months, and earned a cash prize of $10,000 from RSA Security for their efforts. Originally started in 1991 and relaunched with its current set of challenge numbers in 2001, RSA Laboratories' Factoring Challenge was established to encourage research into computational number theory and the practical difficulty of factoring large integers. "The information received during these challenges is a valuable resource to the cryptographic community and can be helpful for organizations in choosing appropriate cryptographic measures for a desired level of security," said Burt Kaliski, chief scientist and director at RSA Laboratories. To solve the factoring challenge, the consortium leveraged resources from around the world, including hardware from the Experimental Mathematics Institute in Essen, Germany, from the Bundesamt fur Sicherheit in der Informationstechnologie (BSI), and experts from the Number Field Sieve network of mathematicians throughout Canada, the United States and the United Kingdom. The factoring of RSA-576 was completed using the general number field sieve factoring algorithm (GNFS) to gather data, find dependencies among the data and ultimately leverage those dependencies to factor the number. RSA-576 is a smaller-scale example of the types of cryptographic keys that are recommended to secure Internet and wireless transactions. Typical keys are at least 1024 bits (310 decimal digits); RSA-576 is 576 bits (174 decimal digits). Larger numbers are considered to provide significantly greater security. The next challenge number in the series is RSA-640. "RSA Security extends our congratulations to the team for their efforts," said Kaliski. "This challenge demonstrates how the work of a few can have a broad impact on the development of the critical nature of cryptography. Their work reflects the kind of expertise and resources needed to factor large numbers. Such challenges are designed to track the evolution of cryptographic research and ensure businesses are protecting their intellectual property and critical data with the right levels of security." Mathematicians From Around the World Collaborate to Solve Latest RSA Factoring Challenge |
April 27, 2004
E-voting causes security and privacy concerns in the Netherlandsby Joe Figueiredo Following a damning report on a government-commissioned investigation into Dutch-produced automated voting machines in Ireland, internet voting is now facing criticism from Dutch security experts. The Dutch ministry of the interior’s pilot e-voting project involving overseas voters is about to be put to the test at the European parliamentary elections in June. Launched in 1999, but delayed due to an unsuccessful tender process and lack of experience, the distance-voting (KOA) project, of which e-voting is a part, also allows voting through a telephone-based voice-response system. The KOA project is still causing security and privacy concerns, as the risk analysis - a ministry-commissioned 48-page report covering 150 problem - revealed to the Dutch lower house. The ministry held an ‘expert meeting’ last year, to which Dutch experts were invited to review and comment on the proposed e-voting system. One of the participants, Berry Schoenmakers, a cryptographer and mathematician at the University of Eindhoven (whose experience includes the EU’s Cybervote project) was not impressed. "The cryptographic part of the system leaves much to be desired," he remarked afterwards. Mr Schoenmakers was also critical of the way election results are verified and the possibility of privacy breaches. Furthermore, Anglo-Dutch ICT consultants, LogicaCMG, developers of the e-voting system for which they also bear operational responsibility, were said to have little proven experience in such security matters. E-voting causes security and privacy concerns in the Netherlands |
April 27, 2004
Fadeout, pupils’ flair for figures |
April 26, 2004
Pentagon tests breakthrough system to detect airborne toxinsA breakthrough blend of high-tech instruments and weather forecasting models is being tested at the Pentagon April 15-May 15. Coordinated by scientists at the National Center for Atmospheric Research (NCAR), the tests scan for potential airborne toxins near the Pentagon and predict their motion and impact on the building. The knowledge gained from the tests will allow the development of improved systems for protecting Department of Defense facilities. "Knowing how to properly respond to an attack or a toxic industrial incident requires the best modeling tools and sensors available today, and these must all work in a coordinated fashion in real time," says NCAR project leader Scott Swerdlin. Understanding air circulation around the Pentagon is a unique challenge, says Swerdlin. The air circulations are very complex because of the building's size and unusual geometry. Temperature inversions, especially at night, could allow an airborne hazard to spread below rooftop height, which adds to the complexity of a monitoring system. To tackle the problem, NCAR and partners built a nest of concentric computer models--each with a different strength--that predict weather conditions from the entire Washington region inward to the Pentagon itself. Information is routed among them every 15 minutes. "The weather modeling system tested here is one of the most complex ever constructed," says NCAR's Thomas Warner, lead scientist on the project. Tests will occur between April 15 and May 15. In addition to the system's standard equipment (below), these tests will include A 23-foot-long instrumented balloon tethered above the Pentagon. Deployed by the University of Colorado, the setup includes sensors studded along the balloon's tethering wire. As the balloon rises and falls, the sensors sample air flow and turbulence. Periodic releases of sulfur hexafluoride (SF6). This inert, invisible, nontoxic gas helps scientists verify the accuracy of the computer models and sensors that track dispersal of airborne material. The releases are coordinated by the National Oceanic and Atmospheric Administration with assistance from the U.S. Army's Dugway Proving Ground. The dates of the SF6 releases hinge on day-to-day weather conditions. Scientists are taking advantage of wind directions and speeds that allow SF6 to be tracked from a release point directly toward the Pentagon. "It's a very challenging exercise," says Swerdlin. "We're calling on a lot of experienced players and advanced weather forecasting systems in order to precisely time the releases." Pentagon tests breakthrough system to detect airborne toxins |
April 26, 2004
Riverside math teacher gets national award, mementoGustavo Reveles Acosta Riverside High School teacher Nancy Arroyo has been certified as one of the top math instructors in the country -- and she's got a photograph with President Bush to prove it. Arroyo met the president in mid-March when she received the Presidential Award for Excellence in Mathematics and Science Teaching at the White House during spring break. "He's a very warm person ... very welcoming," she said. "He told us that since we face the future every day -- the students -- it is upon us to inspire them." The award is the country's highest commendation for math and science teachers. To win, teachers must be nominated and then selected in their respective states. "She's just a great teacher," said Elaine Cristan, a senior in Arroyo's calculus class. "She never gives up on us and makes learning a lot of fun." Arroyo, who also teaches geometry and algebra, said that math has changed over the years and that keeping up with it has been a challenge. "Math is much harder now than it was when I was in school. It's at a much higher learning level," she said. "But math is more relevant right now. We have to keep showing our students how math and science will apply to real-life situations," she said. Winners receive a $10,000 prize they may use to further science and math instruction. Arroyo said she will use the money to go through a master teaching certification program and begin her doctoral studies in education. Riverside math teacher gets national award, memento |
April 25, 2004
No wonder we stink at mathScott Maxwell Good news for Floridians arrived last week when we learned that only about a third of our elementary schoolers are scoring below grade level on standardized tests. Us is smarter now. Any education improvement is good news here in Flori-duh. But a news release from Gov. Jeb Bush and Education Commissioner Jim Horne made the improvements sound downright miraculous. Here's a sentence: Mathematics results for third graders also improved. In mathematics, 64 percent of third graders scored at or above Level 3, compared to 63 percent last year (a 20 percent improvement) . . . Um. Wait. Lemme get my calculator here. No, it turns out that going from 63 percent to 64 percent is, in fact, not a 20 percent improvement. It's a 1 percentage-point jump (or 1.6 percent improvement). Horne's and Bush's offices quickly responded to my questions. One theory was that I might be an idiot (a theory Mrs. Names has floated on more than one occasion). One even wearily remarked that there were "numerators and denominators" involved that I shouldn't try to decipher by myself. So they asked John Winn, an Education Department guru who's the governor's version of the royal mathematician, to set me straight. Winn explained that the increase was actually referring to improvements over the past three years. Ahhh. Fair enough. But wait. That's not what the governor's release said. "I think the parenthetical phrase was in the wrong place," he said. Well, in our leaders' defense, the poor sentence structure happened in the paragraph discussing math competency. No wonder we stink at math |
April 25, 2004
Art by numbersBy Rachel Grace Toussaint EXETER - Tiankai Liu sees math as an art, and his creative flair for this seemingly misunderstood subject has allowed him to color the canvas of his mathematical career with dynamic success. The senior at Phillips Exeter Academy has twice competed in the International Mathematical Olympiad (IMO), earning gold medals at both competitions. Most recently, Liu was among six high school students featured in a book for his involvement in the IMO. Titled "Count down: Six kids vie for glory at the world’s toughest math competition," the work by author Steve Olson chronicles the lives and experiences of the six members of the 2001 U.S. IMO team. As Liu explained it, those wishing to get to the IMO must first compete in two rounds of preliminary competition. First, they must compete among thousands of other high-schoolers in the American Math Competition. From there, judges take a certain number (those who show the highest level of skill) of competitors to the second round - the American Invitation Math Exam. From there, 250 of the best young mathematicians are invited to take the USA Math Olympiad exam. Lastly, judges invite the Top 30 highest scorers on this exam to a training that takes place over the summer, and from that group, they pick the final six to go to IMO. While some might view this intense process as stressful, Liu explained the experience as a time of growth for him. "To me, the Olympiad took my interest in math to a very high level," Liu said. "When I went to the summer training for the first time, I met people who were similar to me in that they had this interest in math competitions. But also, they were so much better than me that I looked up to them as role models. The experience of that was very exciting for me - just the sheer fact that I was the only ninth-grader there, and all the other members were in 12th grade, gave me a sense of wonder and possibility." Liu says, from his own experience, he’s seen the way that American teachers sometimes don’t do math much justice. "It should be taught as a creative thing - how can we play with numbers, how can we play with triangles," Liu said. "Whatever I do, there’s a high chance it will involve math, and even if I don’t end up doing something that has to do with math, I’m still very interested in math and want to learn as much about it as can," Liu said. "From then on, I guess we’ll see. I’m not really committed to doing a lifetime of math yet. There are other possibilities I want to think about." Art by numbers |
April 25, 2004
Real world mathSARAH EVANS Math. Just the mention of the word to many adults brings back memories of pages of homework problems or a teacher working out long equations on a blackboard. For some, the subject was fun and even useful in their later careers. For others, the topic still makes their palms sweat and their heads spin. But a look at math and the way many students learn it in today’s schools reveals a quite different classroom picture than what was seen just 10 years ago. Some students play games. Others sing and dance. Many don’t have homework. Sometimes they don’t even have a textbook. It’s all part of a push by educators to help students do better in mathematics by understanding what numbers mean, not just memorizing how to manipulate them. “I’ve often thought, ‘Man, if I would have learned algebra this way, I would have understood it,’” said Laura Lethe, a math program assistant for the Salem-Keizer School District. The thud of hammers hitting wood and the clink of nails hitting the floor are common sounds in Dave Anderson’s math classroom at North Salem High School. In March, Anderson’s students built a shed to go next to a Habitat for Humanity house. But before they pulled out their tools, they had to calculate the area and perimeter of several buildings on paper. The course is a combination of shop class and algebra review. The students are in the class because they had trouble passing algebra. Anderson decided to combine math with construction as a way to show the students how they could use algebra in their daily lives. “I thought, ‘These kids need something that’s tied to the real world,’” Anderson said. “They need something that’s meaningful.” Real world math |
April 24, 2004
Local man devises ‘God number’ |
April 23, 2004
Finding recombination hotspotsDaily News By Cathy Holding A new algorithm for revealing recombination hotspots, reported in the April 23 Science, has found that most recombination occurs outside genes. The mathematical method will be important in understanding the nature of recombination, according to the paper's authors. But others feel that claims that it will aid in mapping disease loci are unjustified. “If we have a better sense of the way in which recombination rates go up and down in various places across the genome, we have a hope of learning more about the molecular mechanisms involved,” said Peter Donnelly, coauthor of the paper and professor in the Department of Statistics at Oxford University. Donnelly told The Scientist that the team's algorithm revealed that recombination occurs, on average, once every 200 kilobase pairs, with up to four-fold increases in frequency in these hotspots. Until now, researchers used family pedigrees to manually count recombination events. “The idea here is that you use individuals that are unrelated,” said Carsten Wiuf, a professor at the Bioinformatics Research Center at the University of Aarhus in Denmark, who was not involved in the study. “Then you use some mathematical algorithm that helps you to do the counting; so they don't do it manually here. A second reason for developing the mathematical method was its use in designing disease association studies and in their interpretation, according to Donnelly. “The hope is we'll soon be able to do association studies on pretty large scales across the genome,” he said. Finding recombination hotspots |
April 23, 2004
Mathematician teaches visual aids to problem-solvingJeff Milgram Teaching John Witherspoon students to exercise the right sides of their brains. By his own admission, Tom Schersten is a right brain kind of guy. The left side of his brain — the half that controls reading and writing — is only so strong, he confessed. He was in remedial reading in the seventh grade. But the right half — the visual side — is something else entirely. And this past week, Mr. Schersten, of Randolph, Vt., was at the John Witherspoon Middle School teaching students and teachers how to use the right sides of their brains to learn modeling math — mathematics in a whole new light. "I see mathematics as largely a visual and spatial language," Mr. Schersten explained. Using "manipulatives" such as blocks, squares and pentominos — geometric shapes that look like letters — Mr. Schersten is modeling mathematical concepts and procedures for two sixth-grade classes at the school. "When we do math like this, we're using both halves of your brain," Mr. Schersten said. Mr. Schersten uses individual pentominos to teach linear space and area. He then has the kids copy the shapes on graph paper to reinforce the visual aspect of geometry. He also has the students combine the pentominos to create rectangles. "I try to make a good strong linkup between the concrete and abstract," Mr. Schersten explained. Manipulatives used to be used only in early grades, but that is changing, he said. Mr. Schersten's enthusiasm is catching, with the students raising their hands as they accomplish the most recent task. He admitted that he went through more Skittles than usual during this class. "I'm loving it," Mr. Schersten said. "I think my favorite thing to do is to be in front of kids and doing discovery math." Mathematician teaches visual aids to problem-solving |
April 22, 2004
Nonlinear nets approach runway to wireless appsBy Chappell Brown HANCOCK, N.H. — Recent research is revealing how to harness the nonlinear operation of biological neural networks to create a more powerful architecture for applications in telecommunications and robotics. The architectural network created by Herbert Jaeger in Germany and the mathematical model produced by Wolfgang Maass in Austria bring the promise of man-made devices with the speed and power of the brain one step closer to reality. A major hurdle for computer scientists and engineers alike is the recurrent feedback architecture of natural neural networks, which puts them in the terra incognita of nonlinear dynamics. Thus, the most widely used architecture-the back-propagation of errors network-is a linear system with only feed-forward connections. Now Jaeger at the International University Bremen (Bremen, Germany) has hit on a black-box tactic for getting around the need to model nonlinear networks. Nonlinear systems can be approximately simulated on computers, but most lack any comprehensive mathematical model, which makes it difficult to design them into systems. Jaeger has developed a type of feedback architecture he terms Echo State Networks. His ESNs are powerful nonlinear networks that look like back-propagation networks to the user. The black box contains a randomly connected echo-state network that remains fixed. This is connected to a number of inputs and a row of output neurons that have adjustable weights. The system is then trained in the same manner as a conventional back-propagation network with the output weights being adjusted to reproduce model input-output data sets. Jaeger likens the operation of ESNs to the standard mathematical technique of representing a nonlinear curve with a linear combination of nonlinear basis functions-Taylor series, Fourier series or wavelets being some of the most common basis sets. "You start from a collection of nonlinear functions or signals and linearly combine them to approximate a target. The larger the collection of basis functions you choose from, the finer the approximation," he said. Jaeger characterizes nonlinear networks as "beautiful beasts," since they would have a power far beyond current networks, but are essentially untamable. But will ESNs have a better chance of behaving more like neural networks do in biological systems than other approaches researchers have used to date? An answer to that question is being investigated by Maass at the Technical University of Graz (Graz, Austria). Maass independently discovered ESNs while trying to mathematically model the behavior of feedback circuits in the brain. While Jaeger's black-box networks only use a highly simplified model of a neuron, Maass' model has more realistic neurons that communicate using trains of voltage spikes. Maass called these nonlinear systems "liquid-state networks," comparing them with the surface of a liquid. For example, when a sugar cube is dropped into a cup of coffee, the surface begins to undulate in a complex pattern that gradually diminishes in amplitude until it reaches the original zero state. A similar phenomenon occurs when a reservoir of feedback neural nets are given a single-input set of data. Given a time-series of input events, the continual agitation of the liquid stores a running history of the input sequence, giving the network a built-in memory. Maass has formulated a general mathematical model called a liquid-state machine, similar to the universal Turing machine model of digital computers. Nonlinear nets approach runway to wireless apps |
April 22, 2004
Most advanced mathematics just doesn't compute in our brains, "Math Guy" saysAP State News By JOANN LOVIGLIO, Associated Press Writer, The Associated Press If someone offered you $1 million to complete a calculus problem or add a group of fractions, and you know you'd walk away with empty pockets, a well-known mathematician says don't be too hard on yourself. Our brains aren't well equipped to grasp those kinds of advanced mathematics _ and most people who can do such abstract number twisting don't even understand what they're doing at first, said Stanford University mathematician and National Public Radio's "Math Guy" Keith Devlin. Unlike what Devlin calls "natural mathematics," such as counting, algebra, geometry and simple arithmetic that the brain does naturally, "formal mathematics," such as adding fractions and calculus, seems counter to common sense to our brains. Because natural and formal math require different kinds of thinking, teachers may want to look for ways to teach them differently too, said Devlin, who was speaking at the annual meeting of the National Council of Teachers of Mathematics. The four-day conference of about 17,000 math teachers started Wednesday in Philadelphia. So how does one learn formal math? Fake it till you make it _ and not everyone does because it can take years of frustrating, repetitious and rote rule-following, Devlin said. "You have to be psychologically willing and able to just follow the formal rules, play the game and not try to make sense of it. Eventually, for some people, the meaningless game will eventually become meaningful," he said. Devlin said it was not until he was a graduate student that he really understood what he was doing. "I learned to play the game first ... to manipulate the symbols to get the right answer, and the understanding came later," he said. Maybe formalized math should be taught in a manner similar to the immersion method used for teaching language, in which a teacher just starts speaking in a foreign tongue and students eventually start figuring out what's being said, Devlin said. But not all students learn language that way _ and not all students will master formal mathematics, he said. "We shouldn't be surprised that there are parts of mathematics that the brain isn't suited for," Devlin said. "But if we're aware of the problem, then we can find ways around it and the strategies to deal with it." Most advanced mathematics just doesn't compute in our brains, "Math Guy" says |
April 22, 2004
ASA Announces Po-Shen Loh as Recipient of Prestigious Graduate HonorsAmerican Statistical Association ALEXANDRIA, Va., April 22 /PRNewswire/ -- Po-Shen Loh, son of ASA member Wei-Yin Loh and Theresa Loh is the recipient of multiple honors that will enable him to pursue his graduate study and research. A student a California Institute of Technology, Po-Shen grew up in Madison, Wisconsin, where his parents still reside. This academic year, Loh has been offered the National Science Foundation (NSF) award, a Churchill Scholarship, a Hertz fellowship, and a National Defense Science and Engineering Graduate Fellowship. Loh received the Churchill Scholarship to do graduate work in mathematics at Churchill College, University of Cambridge. He is one of only 11 students from across the country to receive this scholarship. The Churchill Scholarship Program, now in its 41st year, offers students an exceptional opportunity to pursue one year of graduate studies in engineering, mathematics, and the sciences at the university. Loh is the recipient of a silver medal at the 1999 International Mathematics Olympiad in Bucharest, Romania; represented the United States in informatics during a 1999 Computer Science Competition held in the Baltic region of Latvia where he was one of four U.S. representatives in the prestigious competition; a 2000-2004 Axline Merit Award; and the 2002 Morgan Ward Prize for developing original math problems and solutions. He was also a 2002 national semifinalist in the TopCoder Collegiate Championship, a 2003 finalist in the TopCoder Google Code Jam, and winner of a 2003 Barry Goldwater Scholarship. Po-Shen, 21, aspires to become a university professor in mathematics. He is the eldest in a trio of gifted children. Wei-Yin's daughter Po-Ling Loh, 16, and youngest son Po-Ru Loh, 18, have all excelled and demonstrated equal talent and ingenuity in the realm of mathematics. "I am pleasantly surprised and very happy with their achievements," says Wei-Yin Loh, University of Wisconsin, Department of Statistics and a long-time member of the American Statistical Association. ASA Announces Po-Shen Loh as Recipient of Prestigious Graduate Honors |
April 21, 2004
Singer Cool on Global WarmingBy Stephen Goode Fred Singer established the Science & Environmental Policy Project (SEPP) in 1990 after becoming fed up with what he calls "the distorted science" surrounding the question of atmospheric ozone depletion. Singer is a scientist. His undergraduate degree is in electrical engineering and he has a doctorate in physics from Princeton University. He has spent a lifetime in scientific research and development. So it is not surprising that bad science gets Singer excited and arouses his concern. Two things concern Singer about global warming. First is the questionable science that says global warming is taking place and it's a bad thing. The second is that the global-warming people argue government and society must now greatly expand the government's authority to enforce policies that will put an end to global warming or at least hold it in check. Singer has held prestigious scientific positions, such as director of the Center for Atmospheric and Space Physics at the University of Maryland and distinguished research professor at the Institute for Space Science and Technology in Gainesville, Fla. He's also published widely both in scientific journals and in the popular press. And Singer's list of scientific accomplishments is impressive. Q: What are some of the weak points about the global-warming argument? A: The fact that they don't properly take into account the effects of clouds in the atmosphere. Clouds will cool the climate rather than warm the climate. When you try to warm the ocean, I argued - and the argument is still sound - you evaporate more water and create more clouds and this reduces the amount of solar radiation. What you have is a kind of negative feedback which keeps the temperature from rising very much. Q: "Look before you leap" means let's not adopt large government programs to deal with a problem that the evidence says isn't taking place but which theory and mathematical models say must take place? A: If we don't see anything happening despite the fact that carbon dioxide is increasing, then maybe something else is happening and the effect of the increase will be minimal. I won't say an effect won't be there, but that maybe it is minimal - or not even enough to be detectable. If it's not detectable, it means it probably can't do you any harm. There's an additional argument, which is this: Supposing it did warm up, is that good or bad? You cannot automatically assume it is bad, because we've had warming in the past and coolings. Climate is always changing. Every time the climate has been warm, it's been good for mankind, and every time it has been cold it has been bad. Singer Cool on Global Warming |
April 21, 2004
Cooling killed dinosaursJoanne Laucius Dinosaurs became extinct because cool temperatures caused too many male babies and not enough females to hatch, says an article in this month's Fertility and Sterility, a respected medical journal which normally limits itself to reproduction issues of the human variety. The authors, who included U.S. fertility specialist Dr. Sherman Silber, used evolutionary biology, fossil evidence and mathematical modelling to bolster their theory: the sex of dinosaurs, like crocodilian species today, was determined by the temperature while the eggs were incubating. If, as many scientists believe, a meteor hit Earth about 65 million years ago leading to a rapid cooling of the climate, the change would have wreaked havoc on animals that depended on temperature to determine the sex of their young. Mathematical models show that if more males than females were born, the dinosaur population would have slid into a quick and irreversible decline within a few generations. For most modern animals, the sex of offspring is determined by genes, not temperature. In mammals, for example, all female eggs carry the X chromosome. The male sperm can contribute another X, resulting in a female, or a Y, resulting in a male. But the Y chromosome is notoriously unstable and in the long run undermines male fertility. Dr. Silber and his fellow researchers, who included a molecular biologist and a mathematician, posed the question: if the Y-chromosome threatens the long-term survival of the species, why did it survive for millions of years? "We realized . . . it protects against extinction linked to global temperature change," Silber said Tuesday. For millions of years, sex determination was prompted by small changes in temperature. For some species, including crocodilians, some lizards and many species of turtles, temperature still determines whether an embryo will develop male or female organs. Cooling killed dinosaurs |
April 21, 2004
OP-ED: The queen of sciencesMunir Attaulla Increasingly, beauty -- and delight -- is sought in the pure manipulation of the tools of the trade, be they colours, words, or the musical scale. Mathematicians have always known this form of intellectual pleasure. Most people find mathematics a forbiddingly dry and boring subject. I suspect that that is because, to quote Russell’s famous epigram, "mathematics is a subject where we never know what we are talking about or, whether what we are talking about is true". That flippant remark, nevertheless, aptly sums up what a mathematician does. Mathematics is the finest method we know for generalised and abstract thinking and is, without doubt, the supreme construct of the human mind. Without it, nothing of any significance would have been achievable in any of the sciences. Those school years spent in tedious struggle with decimal fractions, square roots, and learning mysterious formulae by rote, are necessary because nothing worthwhile is ever achieved by anyone without first painstakingly mastering the tools of his trade. For the mathematician, the tools are numbers and the great advance which made this possible was the decimal system of numbering and its modern Arabic notation. ‘Art for art’s sake’ is a relatively modern concept which inspires much of abstract art, free verse poetry, and even atonal music. The emphasis is on form rather than content. Increasingly, beauty - and delight - is sought in the pure manipulation of the tools of the trade, be they colours, words, or the musical scale. Mathematicians have always known this form of intellectual pleasure. Can you see anything beautiful about an apparently ordinary number such as 142857? No? Well, if you multiply it successively by 2,3,4,5,and 6 you get the following numbers: 285714, 428571, 571428, 714285, and 857142. Notice anything odd about these numbers? Amazingly, they are all made up of the same digits as the original number. What is even more interesting, all the digits maintain their relative order vis-a vis the other digits. But what happens when you multiply the number by seven? Surprise! You get 999999! Intriguing? Certainly. Beautiful? I think so. It is as if Shane Warne, the magician, lulls you with five perfect leg-spinners before foxing you with a googly. An endless source of delight is the mysterious and subtle ways the realities of Nature are mirrored in mathematics. We humans instinctively seem to find certain proportions pleasing to the eye. Coffee tables of roughly eight by five look good. The pyramids of Giza and the Parthenon exhibit a similar base to height ratio. The Greeks called this ‘the golden ratio’ (1.618 or 0.618 to be exact, depending on which dimension is being compared to which). Even artists pay homage to this mysterious number when they focus the attention of the eye not on the centre of the canvas but to one side. Your credit card and Mona Lisa’s face form a ‘golden rectangle’. Consider next the series of numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55... called the Fibonacci series, where each number is the sum of the previous two numbers. As uninteresting a set of numbers as you could ask for, till you notice that the further down the series you go, the closer two adjoining numbers approximate to the golden ratio. Curious. In the last hundred years Naturalists have unearthed the deep interconnections between cell growth, Fibonacci numbers and the golden ratio. The number of petals on most flowers are Fibonacci numbers (three on lilies, 34 on sunflowers, 13 on marigolds, 34, 55, or 89 on daisies etc.); If you count the clockwise and anti-clockwise spiral patterns on a pinecone or sunflower seed packing, you will find them to be two adjoining Fibonacci numbers; leaves around a stem and the spiral shell of a snail share a common growth pattern (a factor of 1.618 per whole turn) etc. etc. From there it took some simple mathematics to show that cell growth based on the golden ratio was the optimal way of packing seeds on a flower bud, ensuring maximum sunlight for each leaf on a stem and collecting the most rainwater for the plant! If such deep interconnections fail to move you it is time for your siesta and time for me to say goodbye. OP-ED: The queen of sciences |
April 20, 2004
Selected works of mathematician Madan Puri published in three volumesBLOOMINGTON, Ind. -- Madan Puri was once called "the Michael Jordan of statistics" by a fellow mathematician, according to David Hoff, professor and chair of the Department of Mathematics at Indiana University Bloomington. It doesn't take a degree in statistics to see that the compliment was deserved. Puri was ranked the fourth most prolific statistician in the world for his writings in the top statistical journals in a 1997 report by the Natural Sciences and Engineering Research Council of Canada. Among statisticians in universities such as IU which do not have separate departments of statistics, Puri was ranked number one in the world by the same report. In an unusual tribute for any scholar, International Science Publishers recently published three volumes titled Madan Lal Puri: Selected Collected Works. The editorial board of ISP, consisting of Peter Hall of the London School of Economics, Marc Hallin, director of the Institute of Statistics at the European Center for Advanced Research in Economics and Statistics, Brussels, Belgium, and George Roussas of the University of California, made the determination to publish the three volumes. Not more than three researchers nationwide have been accorded this publication honor in the past 15 to 20 years. Statistical knowledge is a national resource for efficient planning for the future, whether the subject is medicine or agriculture or urban infrastructure, Puri pointed out. It allows for optimal decision-making in many areas of practical importance. "Statistical thinking," wrote futurist H.G. Wells, "will one day be as necessary for efficient citizenship as the ability to read and write." An example of how Puri's work can be applied to ordinary life is the concept of fuzzy sets, one of the many areas in which he has made pioneering contributions. "Fuzzy sets are effective tools for dealing with uncertainties due to vagueness," he explained. "In everyday life, we often deal with imprecisely defined properties or quantities -- a few books, a long story, a young woman, or a tall man, as examples. A fuzzy set is a class of objects with a continuum of grades of membership." Each object in a fuzzy set is assigned a grade of membership ranging between 0 and 1. This concept was first introduced so that imprecisely defined notions could be properly formulated and manipulated. Its use is widespread, particularly in the fields of pattern recognition and information processing. In statistics, Puri said, "we quantify the uncertainties due to randomness. With quantification of uncertainty, we have found a means to express and convey knowledge in a meaningful way. For instance, weather forecasts are made nowadays in terms of probabilities. 'There is a 30 percent chance of rain tomorrow' is a more useful way of conveying information about the atmospheric conditions than the assertion 'It will rain tomorrow' or 'It will not rain tomorrow.' In other words, chance is no longer an expression of ignorance. It is a way to present our knowledge. Selected works of mathematician Madan Puri published in three volumes |
April 20, 2004
Smalltalk Creator Wins 'Nobel Prize' of ComputingBy Jim Wagner One man's work to bring a biological model to the computer world has, 34 years later, led to a 2003 Turing Award by the Association for Computing Machinery (ACM), officials announced Monday. Dr. Alan Kay will receive the "Nobel Prize of Computing" in a ceremony in June, as well as $100,000, for his pioneering work on Smalltalk, the first complete dynamic object-oriented programming (OOP) language. Today, the language is credited as the model for C++ and Java; Kay is considered the first to coin the phrase "object-oriented." Kay said he was happy to receive the award, especially since most of his personal heroes have already made the roster. He also said he's surprised at the lasting power of languages such as Smalltalk in the business world. "Of course, it's an incredible thrill, I'm quite surprised to get it," he told internetnews.com. "It's hard to describe the last 20 years or so in a few sentences, but it's interesting that in spite of the enormous change downward in the kinds of machines that can run on it, dynamic languages like Smalltalk and (List Processor), both of these languages still hung in there." The award is named for Dr. Alan Turing, the British mathematician who is most famously known for the "Turing Machine," an abstract logic exercise published by Turing in the mid-1930s to describe a mechanical device taking information in a systematic way. It turns out the paper anticipated many common computer functions like input, output, coded programs and compilers/interpreters. Smalltalk was Kay's idea of using "cells" of individual objects communicating with one another to solve problems. In 1972, he took his work to Xerox's Palo Alto Research Center (PARC), where he began work using Smalltalk as an educational tool for children. He concluded children learned best when information was presented in graphics and sound, rather than just dry text. Kay is the second computing pioneer in as many weeks to be recognized for efforts conducted in the 1970s. On Thursday, Sir Tim Berners-Lee took home the Millennium Award and $1 million Euros by a Finnish organization for his work to bring the World Wide Web (WWW) to the masses. Smalltalk Creator Wins 'Nobel Prize' of Computing |
April 19, 2004
Judge Itô’s Lemma for YourselfBy Christopher Faille, Reporter Book Review “Financial Derivatives: Pricing, Applications, and Mathematics,” by Jamil Baz & George Chacko, Cambridge, U.K.; Cambridge University Press, 2004, 338 pp., $40. (cloth). ENFIELD, Conn. (HedgeWorld.com)—Anyone who believes that “Itô’s lemma” was responsible for the O.J. Simpson acquittal will benefit mightily from this book, which explains the mathematics of derivatives in ways non-quants, or at least those non-quants familiar with standard calculus, can understand. Co-author Jamil Baz is the head of global fixed-income research at Deutsche Bank, London, and George Chacko is associate professor of finance at Harvard Business School, Cambridge, Mass. In the book, they aim to provide intuitive (heuristic) explanations of the basic concepts behind the pricing of both conventional and exotic derivatives. The target audience includes “advanced undergraduates in mathematics, economics, and finance” as well as asset-management “practitioners afflicted with an interest in derivatives pricing and mathematical curiosity. Their first chapter explains such concepts as volatility and time, random walks, geometric Brownian motion and, of course, Itô’s lemma. It also explains some of the “paradoxes of finance,” such as why success in portfolio management might have more to do with luck than skill. One of the barriers to understanding Itô’s lemma is that financial mathematics depends not upon ordinary calculus, the sort many a bright college undergraduate has mastered, but upon stochastic calculus. Kiyoshi Itô, a Japanese mathematician, was concerned with the issue of defining the expected value and variance of the outcomes of random—or, in mathematician-speak, stochastic—processes. Although Mr. Itô apparently had no interest in finance, his work on this point proved crucial in the development of the Black-Scholes/Merton stock option pricing model. A “lemma” is a mathematical theorem of interest chiefly because it is a bridge to another theorem, and Itô’s lemma is a bridge to stochastic calculus as such. To understand Itô’s work, Jamil Baz and George Chacko suggest, first imagine a particle sitting on the origin point, zero, of a line. The particle can move in either of the two available directions, in a series of discrete hops. In any hop, it either moves right (positive) one or left (negative) one unit. The probability of a rightward move is p, that of a leftward move is q, and 1-p = q. After two hops (when t=2) the particle (X) can either be at 2, at –2, or at 0. When t=3, X can be at 3, 1, -1, or –3. Note that if t=3, 0 will still be the mean in this range, the “expected value of X,” although X can’t possibly be there. If p is .5, then there is no drift” the expected value of X will not change. It will stay at 0, the high point of the familiar bell-shaped probability curve. But what if p doesn’t equal q? Ah, in that case the expected value of X will drift over time, with a speed that will depend both on the difference between the two probabilities and the size of each step. As these considerations are generalized, mathematicians relax the assumption that the size of each step is always 1, and they represent the step size by a lower-case sigma. The difference between p and q, multiplied by step size, then is drift, represented by a lowercase mu. That’s the first step toward Itô’s lemma, which is the formula used to find the differential of a function of certain stochastic processes, including the drifting random-walks of asset prices. But be warned. From here the going gets rougher. Still, the authors stay true to their promise to present their material in a way that requires no mathematical background beyond differential and integral calculus, probability and statistics. The second chapter discusses pricing techniques for assets and derivatives, including the Black-Scholes/Merton model. The third chapter applies those techniques to interest-rate markets: bonds, swaps and other interest-rate derivatives. It explains the two families of pricing models for these markets, factor models and term-structure-consistent models. The final chapter returns, more rigorously, to the underlying mathematics. Judge Itô’s Lemma for Yourself |
April 18, 2004
Believing in God is logical decisionLetter to the Editor Keith Hall Hobart On the subject of atheists, philosopher and mathematician Blaise Pascal (1623-1662) came up with the definitive conclusion. Pascal realized there are essentially only two choices you can make: believe in God or not. And there are two possible realities after you die: God exists or God does not exist. Now take each choice and examine the consequences for both possible realities. For example, if you believe in God and God does exist, that leads to a positive outcome. There are only four possible combinations. If you work it out, you will discover there is only one bad combination: not believing in God and there is a God. So any rational person would choose to believe in God to avoid that one bad outcome. All other outcomes are either positive or neutral. Granted, most religious leaders would prefer that you base your beliefs on faith, not the arguments of a logical thinker. However, the reasoning, though debated many times, remains sound. Pascal's conclusion? Those who believe in God have the only chance at the ultimate human success, and those who don't believe in God risk the chance of the greatest possible failure. Believing in God is logical decision |
April 18, 2004
SAT mania grips studentsBy Michelle Maitre SAT. It's such a simple three-letter combination, but those three little characters spell big-time grief each year for more than 1 million college-bound high school students. The three-hour standardized test, which nearly 80 percent of the nation's colleges and universities now use in admissions decisions, has been a rite of passage since it first gained widespread use in the 1950s. Today, however, more students than ever before are taking the SAT. The test has taken on near mythic proportions for high school students and their parents, who view a high score on the SAT as a magical Golden Ticket that, if it doesn't guarantee access to the most prestigious colleges, will at least boost a students' application to the top of the pile. Students are doing more than just worrying. SAT tutoring and test preparation businesses are booming, and it's not uncommon for students to begin SAT prep in their freshman year. Some students begin preparing in middle school. Last year, nearly half of the nation's 3 million high school students took the SAT, a new record. The average math score - 519 out of a possible 800 - was the highest it is has been in more than 35 years. SAT prep sessions in math and English at Mill Creek Academy in Fremont run $550 each - $1,100 for both - although scholarships are available. SAT mania grips students |
April 18, 2004
Everyday math adds up for studentsBy Claudia Balint For the Press-Journal to discuss Everyday Math in its March 28 editorial in such a glib manner is unfair. Math standardized test scores are some of the highest in Florida. Student demographics are not the reason for these scores. This idea discounts student, parental, and professional effort. In the case of Everyday Math, it works well at our school because teachers at Osceola are fully vested in it. We do not expect the whole district to change to suit us. As a magnet school, though, we should be allowed to continue using Everyday Math, because of its documented success, which isn’t merely because our students come from families economic advantages. Our students are from all walks of life. While some students do come from families with two parents who can spend time with their child working on homework, many students come from either single parent homes or homes where both parents must work. Our parents, no matter what their economic situation, want what is best academically for their children. They know that this means their involvement with school work is essential. Initially, Everyday Math is not an easy program to use. It takes time and patience for teachers to become comfortable with it. Since this is a comprehensive program, beginning when a child is in kindergarten and continuing through fifth grade, positive results may not be seen immediately. While mastery of basic number sense, computation, technology, algebra, geometry, and measurement is important in Everyday Math, it is understood that children learn differently. The program re-teaches concepts over and over during the year, every year. Children become comfortable with all math concepts, knowing that they will comprehend them, rather than feeling tense and insecure because they are lagging behind their classmates. Initially, it can be difficult for parents to understand. This is not how we were taught math. But adults come to see that math is an exciting and beautiful realm, not the threatening, forbidden discipline we once thought it was. A math program should not be discounted merely because a generation doesn’t "get it". Let’s hold our children to higher standards and encourage them to go where we didn’t. We might find that they’ll light the way for us. The beauty of a curriculum like Everyday Math is that it forces all of us to open our minds and imagine the incredible possibilities in a math-filled world. The Press-Journal characterizes the debate about Everyday Math as the same as the phonics/whole language instruction, a disturbing idea since there is so much research to the contrary. Even educators in the trenches dare not minimize the debate to such rudimentary and shallow terms, either about Everyday Math or phonics/whole language. Everyday Math works well for students who are not proficient with numbers because it relies so heavily on everyday, real life experience. Students who operate better in the verbal realm of knowledge do very well with Everyday Math, since there is a strong emphasis on math stories and word problems. The School Board and administration should ask why we must even consider giving- up a rich curriculum that is so successful for our students? Why must the teachers in this district "fight" for the curriculum they feel best suits their students? It should be enough to know that Everyday Math meets and fulfills the Sunshine State Standards and Benchmarks that our students are required to master each year. Teachers and parents have the right to question not just the curriculum at individual schools, but also the necessity of a unified curriculum. Everyday math adds up for students |
April 17, 2004
Sri Lankan Mathematical OlympiadA Sri Lankan Mathematical Olympiad, arranged by the Sri Lanka mathematics Olympiad Foundation will be held in May to popularise mathematics among schoolchildren and selecting a team to represent Sri Lanka at the International Mathematic Olympiad to be held in Athens, Greece from July 4 to 18. The Sri Lankan Mathematical Olympiad consists of two competitions - the Sri Lankan mathematics competition and the Sri Lankan Mathematics Challenge Competition. The Sri Lankan Mathematics Competition will consist 30 multiple choice questions designed for students in Grades 9 to 13. The problems are set in situations to which students can relate indicating relevance of mathematics in everyday life. High Distinction and Distinction Certificates will be awarded to successful students. This competition will be held on May 15 at 10.30 a.m. at the University of Colombo. It is open to any student born on or after July 14, 1984. The first 25 in the Sri Lankan Mathematics Competition will be entitled to sit the Sri Lankan Mathematics Challenge Competition that consists five essay type problems. In addition to certificates to participants three medals, gold, silver and bronze will also be offered. Applications for participation with name, birth date, address, and school, either directly by individuals or through schools along with a bank-draft or money-order (payable at Cinnamon Gardens Post Office) for Rs. 250 drawn in favour of Sri Lanka Olympiad Mathematics Foundation for each applicant should be forwarded to reach by May 7, to the Chief Executive Officer, Sri Lanka Olympiad mathematics Foundation, Department of Mathematics, University of Colombo, Colombo 3. Applicants should be at the Department of Mathematics, University of Colombo on the day of competition (May 15) by 9.45 a.m. with their national or postal identity cards. Sri Lankan Mathematical Olympiad |
April 17, 2004
Mathematics Teachers On Way To Active LearningBy Maya Salleh Bandar Seri Begawan - A Workshop on "The Effective Teaching and Active Learning in Secondary Mathematics" launched in conjunction with SEAMEO RECSAM came to a close yesterday. The Sultan Mohammad Jamalul Alam Secondary School organized the workshop. It commenced on April 12. Over 50 teachers from 25 secondary schools across the country took part in the workshop. The workshop was facilitated by two specialists from SEAMEO RECSAM, Dr. Ida Karnasih and Dr. Cheah Ui Hock. Covered were mathematical teaching concepts which included the current trend in teaching and learning mathematics for secondary school, effective teaching and active learning in secondary mathematics, and developing mathematical thinking, to name a few. The workshop also saw the participants putting theory into practice when they conducted presentations on lesson plans to be shared among them. -- Courtesy of Borneo Bulletin Mathematics Teachers On Way To Active Learning |
April 16, 2004
What's the domain of function given by f(x) = sec(cos x)?Doug Erickson There were no spinning wheels or showcase showdowns. But Friday's local production of "Who Wants to be a Mathematician" did offer one game show staple: gobs of quick money. Tailored after the television show that creates millionaires out of trivia buffs, the competition at Madison Area Technical College gave 10 of the state's top high school math students a chance to turn their knowledge into hard cash. The sponsors, including MATC and the American Mathematical Society, gave away $6,000 in cash and thousands more in prizes during the hour-long contest. "What a nice change - to show kids that it's good to be smart," said Sue Ishihara, whose son, Andrew, a sophomore at Marquette University High School in Milwaukee, took home $1,000. The goal was to have fun, promote math and reward smart students, said J. "Sri" Sriskandarajah, an MATC math instructor and the event's coordinator. Erik Saunders, a senior at Rufus King High School in Milwaukee, was the first to answer a speed-round question and get a shot at the winner's circle. To reach the top prize of $2,000, which he did, he had to answer 15 questions. Each correct answer came with a prize. (The first correct answer won him a "graphite computer," i.e. a pencil.) Just like on television, Erik could tap three "lifelines," including help from his math teacher. The $2,000 question he won on: What is the domain of the function given by f(x) = sec(cos x)? Answer: All reals. (If you have to ask what that means, you might want to skip the "Who Wants to be a Mathematician" home version.) What's the domain of function given by f(x) = sec(cos x)? |
April 16, 2004
Waking up to Algebra |
April 16, 2004
Minac, Shoesmith pursue innovative researchby Mitchell Zimmer Jan Minac of the Department of Mathematics and David Shoesmith of the Department of Chemistry are recipients of the Distinguished Research Professorships in the Faculty of Science. These awards release faculty from teaching for one year to focus on innovative research. “It’s quite an honor but especially it’s a great opportunity for me.” says Minac, who focuses on a branch of abstract algebra that studies the symmetries of the roots of polynomials known as Galois theory. The theory, although developed in the 19th century by French mathematician Evariste Galois, continues to play a role in mathematics. “What is amazing is that this theory is still, even today, one of the central parts of mathematics,” says Minac. Part of that development includes the recent solving of what was known as the Milnor conjecture by Vladimir Voevodsky. Milnor believed there was an equivalence between different ways of describing the properties of different kinds of surfaces. Voevodsky created new tools that, in 1996, enabled him to solve the problem. Minac will spend a year at the Princeton Institute of Advanced Study to assess the impact of this conjecture in various areas of mathematics. Minac, Shoesmith pursue innovative research |
April 16, 2004
Space Commission Gets Advice on Sustaining Public Interest in Bush VisionBy Tariq Malik If NASA plans to sustain its mission of sending humans to other worlds in the next few decades, it must encourage schoolteachers to fold space into lesson plans that inspire students to pursue careers in science, education professionals told a presidential commission Thursday. "The moon-Mars initiative offers us a tremendous opportunity for education if we make sure from the beginning that teachers see themselves as part of the effort," said Barbara Morgan, NASA's educator astronaut and former schoolteacher, told commissioners during a discussion on education. Morgan told commissioners that the best way to inspire the next generation of astronauts and scientists is to start at their education source. "During the average school year, teachers might spend more time with a child than parents," Morgan said. "No one can offer the lifelong enthusiasm better than someone who is teaching a subject for which he or she has a passion for." Education experts said that while NASA must obviously encourage students to pursue careers in science and mathematics, areas critical not only to the space vision but to the nation's technological growth as a whole, the agency must also stress the continuous need for new and qualified teachers. "We are facing a teacher shortage in mathematics and science," said Jim McMurtray, executive director of the National Alliance of State Science and Mathematics Coalitions. "And a scientifically illiterate populace is something that no nation can afford." Space Commission Gets Advice on Sustaining Public Interest in Bush Vision |
April 15, 2004
The universe is not round, say scientists - it is shaped like a trumpetBy Charles Arthur, Technology Editor At first they thought it was flat. Then that it was shaped like a football. But now, scientists believe the universe could be shaped like a flat-sided trumpet. That would lead to strange effects in some parts of the universe, where time and light would be so curved that you could see the back of your own head. Also, a long-held theory about the universe - that it looks much the same anywhere - would have to be abandoned. And finally, the universe would be finite, rather than extending in every direction forever. The new shape, predicted by careful mathematical modelling to fit with known astronomical data, would have the universe stretched out into a long funnel, flaring into a bell-like shape at one end. The thin end would be infinitely long - but so narrow that it would have a finite volume. The research by a team of German physicists led by Frank Steiner at the University of Ulm is reported today in New Scientist magazine. Their theory uses a complex mathematical model called a "Picard topology", named after a mathematician rather than the Star Trek character. It would mean the universe has a finite volume, although you would not be aware of its "edges"; they would seem to be part of the rest of space. The universe is not round, say scientists - it is shaped like a trumpet |
April 15, 2004
Chair of math dept. honored |
April 15, 2004
Milford's Brookside school hosts math nightBy Patricia A. Russell MILFORD -- It was all about math. In one corner of the library last night, Brookside School's assistant principal, Terrie Sharp, read a book. Halfway through, she asked if anyone recognized any math terms that were used in the story. Six-year-old Abby Kline's hand shot up. "Patterns," she said. Down the hall and in the gymnasium, a mathematical games jamboree was going on. Kids and parents sat on the floor huddled over floor games that reinforced math skills. Some played a game with dollar bills (the fake kind), while others sorted shapes by size and weight. Another three students had fun playing spin a number game. Integrating mathematics into activities helps promote family involvement and introduce math concepts to children, said Sharp. It also shows parents what their children are doing in the classroom. Bassett said it is important to keep math interesting and exciting in the lower grades so it will be less intimidating later on. "The teachers find a lot of ways to emphasize math with the kids and make it fun in creative ways," she said. Milford's Brookside school hosts math night |
April 14, 2004
Caraiani wins prestigious Putnam prize at math competitionEllen Young Ana Caraiani '07 earned the title of Individual Putnam Fellow and won the prestigious Elizabeth Lowell Putnam Prize at the Putnam Mathematical Competition. Results of the competition were announced over spring break. The Putnam exam, held in December, was taken by 3,615 undergraduate students from 479 colleges and universities across the U.S. and Canada. The University entered 46 students into this year's competition, which awards scholarships of up to $25,000 to the highest scoring team and up to $2,500 for the individuals with the top five scores. Caraiani was one of those top five finishers, all of whom were automatically designated Putnam Fellows by the Mathematical Association of America. In addition, she received the Elizabeth Lowell Putnam Prize and an additional $1,000, which is awarded to the top-performing female in the competition. Caraiani won two gold medals in the International Math Olympiad prior to entering the University. "Ana's a genius," said Matthew Ferszt, undergraduate administrator of the math department. The exam administered in the Putnam competition consists of 12 questions worth 10 points each. The problems "cut across algebra, geometry, analysis, statistics and are meant to be cross-disciplinary," Ferszt said. Some questions involve deeper concepts such as lattice theory and cardinal arithmetic, but Caraiani said the time constraints presented by the exam format were the most difficult part of the competition. "You can understand the text of the problems but the hard part is doing six problems in three hours," she said. "It requires a lot of intuition." The test is divided into two three-hour sessions and one two-hour break. Caraiani, an aspiring math concentrator, scored somewhere between 80 and 110 out of a possible 120 points. The exact scores and rankings of each year's Putnam Fellows are not disclosed, even to the winners, she said. Caraiani plans to participate in the Putnam competition as long as she remains an undergraduate, but anticipates there will be more pressure to repeat her performance in years to come. "This year I didn't care about [the competition] too much," she said. "I had other things on my mind besides just math, so I was relaxed during the exam." "I'm really happy, but I have to think about my classes now too," she added. "Problem-solving isn't all there is to math. It requires a lot of hard work." Caraiani wins prestigious Putnam prize at math competition |
April 13, 2004
They've got it! Science grasps eureka momentBy Mark Henderson, Science Correspondent THE secret of the “eureka moment”, when a flash of inspiration suddenly resolves a tricky problem, has been explained by scientists for the first time. The “light bulb” or “aha!” experience, in which an answer seems to appear from thin air, relies on a very different method of thinking from standard problem- solving, according to research in the United States. Abrupt insights such as Archimedes’ discovery of water displacement, which supposedly prompted the mathematician to jump from his bath shouting “eureka”, produce a characteristic pattern of activity in a specific region of the brain’s right hemisphere, scans have shown. When people work out an answer in deliberative, methodical fashion, however, this eureka centre remains quiet, suggesting that the brain has at least two distinct ways of solving difficult problems. In the study, details of which are published today in the journal Public Library of Science Biology, Dr Jung- Beeman and Dr Bowden asked volunteers to solve a series of word problems. Participants were given a series of three words, such as “fence”, “card” and “master”, and told to think of a single word that would go with each to form a compound word. The answer in this example is “post” — “fencepost”, “postcard”, “postmaster”. The problems were designed so that most people would solve them methodically and by insight about half of the time each. The volunteers’ brains were scanned using functional magnetic resonance imaging (fMRI) as they solved the problems. When the subjects reported having an “aha! moment”, a region of the brain known as the anterior superior temporal gyrus, in the right temporal lobe, tended to fire with activity. When they solved the problems through methodical working, that region was inactive. They've got it! Science grasps eureka moment |
April 13, 2004
Suhrit Dey: Mathematical Model of Breast Cancerby: Francis C. Assisi “Mathematics is my religion, I Preach it, Practice it and Promote it.” That’s what Suhrit K Dey, of Eastern Illinois University, claims. Considering the teaching track of this professor of mathematics, it is not a tall claim. Dey has had long innings at the EIU campus at Charleston, where he’s been since 1970, and is considered a superior teacher by his students and his peers. Dey has math teaching experience in Calcutta from where he came in 1966 to earn his Ph.D. (1970) in Aerospace Engineering from Mississippi State University. Actually he says he is following his family tradition as an educator. Besides Mathematics, Dey has a yen for teaching yoga and meditation on campus. But more recently, according to NASA publication Gridpoints, Dey teamed with computer scientists at NASA Advanced Supercomputing (NAS) Division at Ames, to create three-dimensional mathematical models for predicting how cancer spreads — and how it may be contained or even cured. As Dey explained: Cancer cells are activators. They activate the lymphocytes to respond as inhibitors. This model consists of two coupled nonlinear partial differential equations, which were solved numerically. If the activator prevails, cancer spreads and if the inhibitor prevails the immune system overpowers cancer. Dey is computing one-dimensional cancer models using a set of eight mathematical equations. These models include variables such as the number of lymphocytes (cells in the human body that attack cancer), number of cancer cells, types of medical treatments, angiogenesis (the development of new blood vessels), and glucose levels in the body. Dey’s mathematical models are based, in part, on his theory that there is a direct correlation between stress levels and the development of breast cancer. “I am building these models based on information I’m gathering in scientific journals, which is qualitatively accurate. Once the models are complete, I will input an individual’s data to provide us with some quantitative results – this will enable us to predict if that individual will get cancer, or if their body’s immune sys-tem can revert the process,” explains Dey. “Dr. Dey is developing elaborate models of tumor growth, incorporating multiple features of tumor cell and immune cell interactions. The most interesting feature of these models is their exploration of the importance of the immune system in controlling tumor growth,” says Webb, who has worked on mathematical modeling of cancer for 30 years. Although these mathematical models for cancer prediction are qualitatively accurate, Dey emphasizes that they are designed only to accompany clinical studies on breast cancer — not to replace them. “We need a combination of mathematical models, statistical models, and clinical studies, so we can see breast cancer from every possible angle,” he says. "I can see the light at the end of the tunnel. The solution is there, but I need help from others so breast cancer can be contained,” says Dey. “If 10 percent of the people take an interest in this and protect themselves, that’s a large number of women being saved." Suhrit Dey: Mathematical Model of Breast Cancer |
April 12, 2004
STAGE 3 SETS CALCULATING DRAMANotices and reviews of Mother Lode theatrical productions. "Lead us not into temptation," says the prayer. Sometimes temptation is too great. But heed a word of warning: Before you take another step, you better check your math. The Stage 3 Theatre Co. is one of those courageous theater companies willing to take a risk on bringing exciting new works to the stage. In this case, the gamble pays off in the form of Alex Lewin's captivating intellectual thriller, "Twin Primes," playing through May 9 at the Sonora theater. Winner of Stage 3's 2003 Festival of New Plays, "Twin Primes" is a psychological spine tingler in the vein of Alfred Hitchcock and Orson Welles that features taut, gripping storytelling that's filled with surprises and a dash of humor. Brilliant mathematician Linda Ruether has spent her life trying to unlock the age-old mathematical mystery of the Twin Prime Conjecture. She has sacrificed everything, but this tantalizing dream has remained just out of reach. When an 18-year-old genius stumbles upon the solution, she can't resist the temptation to gain her own intellectual immortality, whatever the cost. She might just succeed; she might be able to join the pantheon of giants. Or is there something that she has overlooked that was before our eyes the entire time? Can ambition blind us to the obvious? Perhaps, but the audience has to wait until the last few seconds of this exciting play to find out. STAGE 3 SETS CALCULATING DRAMA |
April 12, 2004
It adds up ... mathematicians are better at using their headsPEOPLE with a gift for maths really are better at using their heads, scientists claim. Research shows they employ both the left and right sides of their brain when tackling a problem; most people tend to prefer one side or the other. Psychologists in America and Australia studied 18 mathematically-gifted children with an average age of 14. Their performance in tests was compared with 18 children of average maths ability and 24 college students aged around 20. The students were shown letter patterns flashed on the left or right hand sides of a computer screen. Their ability to match patterns indicated how they used the left or right sides of their brains. There were two types of tasks, "local" and "global". "Local" involved deciding whether small components of big letters matched each other, and "global" involved saying whether whole big letters matched. For average teens and college students, the left brain hemisphere performed the task faster for local matches while the right side was quicker at global matches. This fitted in with previous research which indicated that the left side was adept at processing visual "parts" while the right side tended to focus on "wholes". However, mathematically-gifted students showed no such difference between the two halves of their brains. The study, reported in the journal Neuropsychology, supports the growing theory that people with a head for maths are better at relaying and integrating information between the cerebral hemispheres. It adds up ... mathematicians are better at using their heads |
April 12, 2004
Boris Levitan, mathematician, dies at age 89Neal Gendler Boris Levitan, 89, a world-renowned mathematician and winner of the former Soviet Union's highest civilian honor, the Lenin Prize, died April 4 after suffering a stroke at his home in Minneapolis. He was buried Friday in Adath Chesed Shel Emes cemetery in New Hope. Levitan came to the United States in 1992, after many years of teaching and research at Moscow State University, Russia's highest degree-granting institution. He became an adjunct professor at the University of Minnesota at age 77 and stayed active until about five years ago, when Parkinson's disease made him unable to work. His stepson, Leonid Glazman, is a physics professor at the University of Minnesota. "Professor Levitan was an absolutely outstanding person," said Grigory Barenblatt, a mathematics professor at the University of California at Berkeley. "He was my first mentor." Levitan and Vladimir Marchenko were awarded the Lenin Prize in 1961 for "a great work, the inverse scattering problem," Barenblatt said, adding that it is too complicated to explain, but was "very important in various aspects of physics for the next 50 years." Levitan was born in Berdyansk, in southern Ukraine, and became a doctor of science -- a level above an American Ph.D. -- at age 26, "which was absolutely unusual," Barenblatt said. "Simultaneously, he received the title of full professor." He fought in the Battle of Stalingrad and was removed from combat in 1944 to teach at an artillery academy in Samarkand. After the war, the academy moved to Moscow, but for a Jew to become a professor at the university, "it was almost impossible," Naiman said. Restrictions loosened after Stalin's death, and Levitan was taken onto the faculty in 1961, while still working at the artillery academy part time. "Every, every evening and every free minute was research, research, research," she said. "His life was mathematics." Winning a Lenin Prize in a nation with official and unofficial anti-Semitism also was remarkable, Barenblatt said. But he was among other Jewish recipients whose "work was so strong and important," that giving them the prize "could not be avoided." Boris Levitan, mathematician, dies at age 89 |
April 12, 2004
Why Babies Love MusicBy Heather Moors Johnson Shortly before my first child was born, the governor of my state -- Zell Miller, now a U.S. Senator -- made a startling announcement: Every baby born in Georgia would receive a free classical music CD at the hospital. This wasn't just some bonus prize for being born; it was a start to making Georgians smarter. "Listening to music at a very early age affects the spatial, temporal reasoning that underlies math and engineering and even chess," the governor's statement said. Wow, I thought, all that from a CD? My soon-to-be Georgia peach would be smarter than her mom and dad combined. In addition to the myths about the Mozart Effect -- and the ensuing number of musical toys with grand claims about making babies smarter -- there was a lot of ink devoted to the importance of the first three years of life. Parents were sold on the "use it or lose it" theory -- the notion that unless certain areas of the brain (those that would turn Johnny into a brilliant mathematician, for instance) were stimulated in those crucial early months of life, the window of opportunity would snap shut, never to open again. Classical music was considered an important stimulus, so a parent who failed to play hours of the stuff for her infant was clearly irresponsible. Well, all those parents out there can relax. "There is no scientific research on the effect listening to music has on a baby's intelligence," says Frances Rauscher, PhD, a psychologist with the University of Wisconsin and the lead researcher on the college-student study that launched all the brouhaha. Our Mozart Effect research was blown way out of proportion." None of this, of course, implies that exposing our children to music pays no intellectual dividends. Rauscher and her colleagues have continued their research and found that there is a positive effect on children's spatial-temporal (puzzle-solving) and math skills when those as young as 3-years-old are given formal musical instruction -- when they actively study and play music, not merely listen to it. According to Norman Weinberger, PhD, a professor of neurobiology and behavior at the University of California in Irvine, "Music learning and practice benefit many mental and behavioral processes, including cognitive development, language learning, reading ability, creativity, motor skills, and social adjustment." Why Babies Love Music |
April 11, 2004
A prodigy's fun, and prizes, with numbersBY YVETTE BUENO Ryan Williams has become a living math legend at Miami Springs Senior High. Ryan, a senior on the school's Calculus Team, has participated in more than 75 math honor society competitions during his years at Springs. He is also the 2004 class valedictorian and has been accepted to MIT, Harvard, Yale and Stanford. On his SAT college entrance test, Ryan scored a 750 in verbal and a perfect 800 -- what else -- in math, his family said. Summers were spent attending math programs at the University of Nebraska, where he was trained by top math instructors. But Ryan's world is not exclusively math-bound. He is also captain of the water polo and swimming teams and likes playing racquetball, basketball and chess in his spare time. His forte, though, is solving complicated mathematical equations. A prodigy's fun, and prizes, with numbers |
April 11, 2004
Count Down |
April 11, 2004
Francis Cape and DrawingsBy David Bonetti The proportions of Francis Cape's installation "Forest Park" were generated by the Fibonacci series, invented by a 13th-century Italian mathematician. The series is a sequence of numbers based on adding the previous two integers to derive the next. (It starts 1, 1, 2, 3, 5, 8, 13, 21 and continues ad infinitum.) You probably won't notice that - I didn't, even though I knew to look for it - and you really don't have to. But to understand that the work, which looks like a misplaced architectural project, is not merely arbitrary endows it with a certain seriousnea matter of reaching and being reached. She's not reachable; she can be seen but she cannot be heard. So maybe this is narcissistic; she's happy to be isolated." And indeed, the doll-like girl, drawn with ink on pink paper, smiles contentedly if idiotically, as so many women of that era did because they were expected to. (Sylvia Plath's famous novel, "The Bell Jar," wasn't published until 1963.) The museum smartly reprints Bourgeois' comments on her work, when they exist, on the wall labels. Francis Cape and Drawings |
April 9, 2004
BHS, Brook Hill teachers take students to math competitionBy Lauren LaFleur "Math never gets to have fun," said Donna Nicholson, a math teacher from Bullard High School, when asked about the trip her students recently took to Tyler Junior College's 20th annual Mathematics Competition. She said she and fellow teachers Diana Sowell and Jane Medley took their students to CiCi's Pizza before the event to make sure they had a good time, though. In addition to having a good time, however, Michelle Rozell, head of the Department of Mathematics at The Brook Hill School, said "it's important to take the students to these competitions to build their confidence." In team competition, Bullard High's Team 3 won first place honors and Team 1 placed second in the Division II competition which is designated for 1, 2 and 3A schools. Brook Hill's Team 1 placed sixth in the Division III competition, which is composed of private schools. In the competition of individual students, 22 of the 50 Bullard High students who competed won honors in their division, while six Brook Hill High students placed in their division. The individual winners from Bullard High are as follows: in Algebra I, Aaron Miller placed first, Krugler Williams placed second, Kevin Sylestine placed third, Timothy Lackey placed fourth, James Ragsland placed fifth and Sandy Burris placed sixth; in geometry, Kira Langsjoen placed first, Amanda Kuckinsky tied for third and Eric French placed fifth; in Algebra II, Molly Moody placed first, Chance Moore placed second, Elly Baker placed third, Melissa Chamness placed fourth and Phil Kuchinsky placed fifth; in pre-calculus, Patrick Newburn placed first, Amber Palmer placed second, Sandra Smith placed third, Sarah Droddy placed fourth and Callie Sheffield placed fifth; and in calculus, Dane Langsjoen and John Miller tied for first place and John Perry placed fourth. BHS, Brook Hill teachers take students to math competition |
April 9, 2004
The Golden RatioBy Dr. Sami POLATOZ It is very obvious that there is an amazing system at work in the universe. Words are usually insufficient to explain this perfection. Therefore, one must refer to the different language and approach of mathematics. Characteristics found in events and structures that are similar, but seem unconnected with one another indicate that there is a Creator who is the Absolute Ruler of the entire universe. In this article, we will discuss a unique number in mathematics, the Golden Ratio, and its place in the universe, as well as its history, its usage in art and in aesthetics. What makes the Golden Ratio special is the number of mathematical properties it possesses. The Golden Ratio is the only number whose square can be produced simply by adding 1 and the reciprocal of which can be arrived at by subtracting 1. If you take a Golden Rectangle – that is a rectangle where the length-to-breadth ratio is equal to the Golden Ratio, and take out a square, what remains is another, smaller Golden Rectangle. Also, think of any two numbers. Make a third by adding the first and second, a fourth by adding the second and third, and so on. If you start with 7 and 11, then what you have is: 7, 11, 18, 29, 47, 76... When you have written down approximately 20 numbers, calculate the ratio of the last to the penultimate: the answer should approximate the Golden Number. It was the elusive nature of the Golden Ratio that led the Italian friar and mathematician Luca Pacioli to equate it with the incomprehensibility of God. In the 15th century, he wrote a three-volume treatise, Divina Proportione (Divine Proportion), that was crucial in the dissemination of the Golden Ratio beyond the world of mathematics. After him, many artists, architects, and musicians used the Golden Ratio in their works; for example, musicians such as Debussy and Bartok and the architect Le Corbusier. The Golden Ratio also crops up in hard sciences. Let’s take a look at the growth of “quasi-crystals.” These maintain a five-fold symmetry, which means that they make a pattern that looks the same when rotated by multiples of one-fifth of 360 degrees. Since the time when these crystals were discovered in 1984, many physicists have been researching their properties. In Brookhaven National Lab in New York State, Tanhong Cai imaged the microscopic terrain of the surface of such crystals made from alloys of aluminum-copper-iron and aluminum-palladium-manganese. It is found that flat terraces are punctuated by abrupt vertical steps. The steps come in two predominant sizes, with the ratio of the heights of these two steps being the Golden Ratio. This fact was discovered in 2002. The most surprising place where the Golden Ratio appears is in black holes, a discovery made by Paul Davies of the University of Adelaide in 1989. Black holes and other self-gravitating bodies, such as the sun, have a negative specific heat. This means that they get hotter as they lose heat. In a spinning black hole there is an outward centrifugal force acting to prevent any shrinkage of the hole. The force depends on how fast the black hole is spinning. It turns out that at a critical value of the spin (when the ratio between the square root of the mass value and the square root of the spinning parameter is equal to the golden ratio), a black hole flips from having negative to positive specific heat. In other words, the Golden Ratio determines the character of the black hole. The Golden Ratio |
April 9, 2004
They know what you're thinking |
April 8, 2004
Education: Cowbell Maths Contest Winners Emerge April 21Wale Ajao The overall winners of the Cowbell National Mathematics Competition will emerge at a colourful ceremony in Abuja on April 21. The first stage of the examination started on February 7, 2004 at 126 centres around the country. Officials of the Federal Ministry of Education, officials of the various states ministries of education and staff of Cowbell milk monitored the first stage of the examination. After the first stage the best three students (1st, 2nd and 3rd positions) in both the junior and senior categories in each state and the Federal Capital Territory, a total of 222 students from across the country emerged as state winners. The state winners, that is, first, second and third positions were awarded cash prizes of N15,000, N10,000 and N5,000 respectively. They also got branded gift items like Cowbell milk, school bags, certificates of recognition, notebooks and writing materials. The second and final stage of the examination was held on March 20, 2004 at the Lagos Airport Hotel Ikeja. 74 students duly accompanied by either their parents or mathematics teachers were at Lagos Airport Hotel. Education: Cowbell Maths Contest Winners Emerge April 21 |
April 8, 2004
Education:- Mathematics: Most Hated Subject By PupilsEmmanuel Edukugho No subject in the school curriculum particularly at basic education (primary and secondary) is as important more feared and dreaded by learned than Mathematics. Ordinarily defined as the "science of numbers and of shapes, including Algebra, Geometry and Arithmetic," it has to do with calculating things in a careful exact way." Some knowledge of mathematics is needed in almost all spheres of human endeavour. An aura of invincibility surrounds mathematics, with a phobia created especially by many teachers that it is a difficult subject and therefore can't be passed. For many pupils in primary schools, arithmetic turns them off, while students in secondary institutions are often scared by mathematics - (Algebra, Geometry, Arithmetic). Attention was drawn to the need for a good teacher/student relationship in the mastery of the subject. Pupils should have the patience to listen and possess individual determination. Vanguard survey showed that students don't get close enough to their maths teachers. Some pupils are slow, while others are fast in learning. One student said: "I don't pass maths, not that I don't like it. There can be better ways of teaching it. Let government provide materials for effective teaching in schools and libraries. Teachers should use dramatic style and not making it magical. They need to tell the pupils to believe in themselves. Teaching ought to be more practical, and less of theory." Education:- Mathematics: Most Hated Subject By Pupils |
April 7, 2004
What's it all about: The DinerBy Bobby Neal Winters Spring is the time of year when mathematical conferences are in bloom, and I've just been to one. This particular conference meets every year, usually in the South. Tradition, you know. People come from all around the world to be there, so they can feed their minds, and share their discoveries in every imaginable accent. We mathematicians have language all our own. We discuss "semi-locally simply connected spaces" and "linearly Lindeloff spaces that are locally compact." These are just ways of saying "nice" in a particular, technical way. When mathematicians say technical, we know of whence we speak. The motel where many of us at the conference stayed was just off the interstate. There was a diner by the motel that was a handy place to have breakfast. We theoretical mathematicians could walk in, sit down, and wait to be served. The waitresses hustled out our orders, the cook fried some more eggs, and the cashier made change for a $20 for another one of group. The waitress came around one last time to refill my coffee, and I told her, "Thank you." She smiled and said, "You're welcome." She brought the check, and I put down a dollar for a tip, paid the cashier, and left. I went to hear more about hyperbolic manifolds and unknotting numbers. A new girl who came on shift as I was leaving had eight hours to put in on her feet slinging waffles, sausage, and grits, and during that time I would be on my backside watching Ph.D.'s talking about slide after incomprehensible slide. She was doing something everyone recognizes as useful, I was doing something very few would recognize as useful, and yet I am paid substantially more, have fringe benefits, and a retirement plan. What's it all about? I shook my head and returned to the world in which I have one foot. It is comfortable, prosperous, and semi-locally simply connected. What's it all about: The Diner |
April 6, 2004
In Math, Computers Don't Lie. Or Do They?By KENNETH CHANG A leading mathematics journal has finally accepted that one of the longest-standing problems in the field - the most efficient way to pack oranges - has been conclusively solved. That is, if you believe a computer. The answer is what experts - and grocers . have long suspected: stacked as a pyramid. That allows each layer of oranges to sit lower, in the hollows of the layer below, and take up less space than if the oranges sat directly on top of each other. While that appeared to be the correct answer, no one offered a convincing mathematical proof until 1998 - and even then people were not entirely convinced. For six years, mathematicians have pored over hundreds of pages of a paper by Dr. Thomas C. Hales, a professor of mathematics at the University of Pittsburgh. But Dr. Hales's proof of the problem, known as the Kepler Conjecture, hinges on a complex series of computer calculations, too many and too tedious for mathematicians reviewing his paper to check by hand. Believing it thus, at some level, requires faith that the computer performed the calculations flawlessly, without any programming bugs. Because of the ambiguities, the journal, the prestigious Annals of Mathematics, has decided to publish only the theoretical parts of the proof, which have been checked in the traditional manner. A more specialized journal, Discrete and Computational Geometry, will publish the computer sections. In a new policy, The Annals has decided that computer-assisted proofs have merit, but the journal will accord them a lower status than traditional proofs, regarding them more like laboratory experiments that provide supporting evidence. Mathematicians like Dr. Larry Wos of Argonne National Laboratory use "automated reasoning" computer programs: they enter axioms and the computer sifts through logical possibilities in search of a proof. Because of the huge number of possibilities, a human still needs to tell the computer where to search. "The human mind will never be replaced," Dr. Wos said, butthe advantage of computers is their lack of preconceptions. "They can follow paths that are totally counterintuitive," he said. In a 2003 book, "Automated Reasoning and the Discovery of Missing and Elegant Proofs," Dr. Wos described new proofs and more elegant versions of known proofs discovered by computers. Dr. Hales has embarked on a similar project called Flyspeck -- the letters F, P and K stand for "formal proof of Kepler" -- to put to rest any last doubts about the computer proof. Current software, however cannot handle anything nearly as complex as the Kepler Conjecture. Dr. Hales estimates that it will take 20 years of cumulative effort by a team of mathematicians to complete. As for his 1998 proof of the Kepler Conjecture, Dr. Hales said that final publication, after a review process, originally expected to last a few months, would be almost anticlimactic. "For me, the big moment was when I completed the proof," Dr. Hales said. "And I don't think anything will change when I see it in print." In Math, Computers Don't Lie. Or Do They? |
April 6, 2004
Mobile phones 'harm blood cells'Mobile phone radiation may damage cells by increasing the forces they exert on each other, scientists have said. The finding could be the key to claims that mobile phones cause cancer and other health problems. Swedish physicists looked at the effect of electromagnetic radiation on red blood cells using a mathematical theory, New Scientist reported. The simplified mathematical model investigated the effect of electromagnetic radiation in the field of 850 megahertz - about the range used by mobile phones - on the blood cells. The molecules all ended up with their poles aligned in the same direction. The forces between the cells unexpectedly jumped by about 11 orders of magnitude. Katie Daniel, deputy editor of the journal Physical Chemistry Chemical Physics, said the finding was important. "It highlights the idea that electromagnetic radiation might act on cells by affecting the attractive forces between them rather than simply causing heat damage to tissue," she said. Mobile phones 'harm blood cells' |
April 6, 2004
Math professor granted distinguished fellowshipBy Deborah Meron A Northwestern assistant professor of mathematics will join 116 of the nation's top scientists and economists as a recipient of the prestigious Sloan Research Fellowship. Roman Bezrukavnikov, 31, will receive a grant of $40,000 from the Alfred P. Sloan Foundation over the next two years. He was awarded the grant for his research in "representation theory," an area of algebra he cites as his expertise. Twenty-eight former Sloan Fellows have gone on to receive Nobel Prizes and hundreds have received other distinguished awards and honors. Bezrukavnikov said he will use his grant money toward developing his work in representation theory, the study of "abstract structures of symmetries and the representation of those structures." Born in Kaluga, Russia, Bezrukavnikov moved on to pursue math in Moscow, Boston, Israel, New Jersey and Chicago. Bezrukavnikov attended School No. 57, a well-known mathematics magnet high school in Moscow where he was a member of the Mathematics Olympics. "This high school really determines your outcome," Bezrukanikov said. "It instilled the idea that math is one of the most important and beautiful things in life." Math professor granted distinguished fellowship |
April 6, 2004
The shape of thingsCindy Tumiel Juhasz, who just turned 90, speaks with a thick Hungarian accent.. He is an expert in heat transfer and engineering communication who spent 30 years as editor of a technical journal on mechanical engineering. Juhasz organized his interactive geometry exhibit in the fall of 2002 on the Southwest Research Institute campus with the idea of keeping geometry alive. Inside his small portable trailer, shelves are stacked with everything from simple cubes to complex, multisided shapes called octahedrons (eight sides) and icosahedrons (20 sides). Several times a month, students and teachers fill the 20 or so chairs in the room for a 90-minute discussion that jumps around a full semester of geometry, moving from the infinity of points on a straight line to Pythagoras' theorem of right triangles to the principles for a properly built nuclear plant cooling tower. They learn how to calculate the formula for dividing a wooden cube into six equal pieces. Students go home with instructions and a kit that enables them to build a three-dimensional open-sided cube using little more than straws, rubber bands and paper clips. The shape of things |
April 5, 2004
Theological Researcher Announces Release of Mathematical and Scientific Proof That God Exists!The debate about whether or not God exists, beyond your belief or faith, has an astounding new element. Don Sneed, a private Theological Researcher for the last 35 years, has announced the release and premiere of a new educational video entitled: "The God Number: Mathematical and Scientific Proof of the Existence of God." "The God Number" will premiere, locally, in Dallas, Texas (sometimes referred to as the Buckle of the Bible Belt) on Easter Sunday, April 11th at 8:00 p.m., on Dallas Community Television (DCTV) carried by Comcast Cable. During recent private advance previews of the program, audiences have walked away in a state of bewilderment, alternating with enlightenment, with no one being able to refute the scientific and mathematical evidence presented in the video. Mr. Sneed has developed an associated scientific theorem: "Definity-Uninity-Infinity" that substantiates the identification of the specific number that represents God. The theorem has been registered with the United States Copyright Office and has been issued a certificate as an original work. "Definity-Uninity-Infinity" sets forth a new, more realistic and sensible view of the innate structure and order of the Universe, Mr. Sneed states: "is created, sustained and controlled by God; then, now and forever." The viewer is able to easily understand Mr. Sneed's mathematical and scientific proof of God's existence. Theological Researcher Announces Release of Mathematical and Scientific Proof That God Exists! |
April 5, 2004
Riding on Square WheelsMath Trek Ivars Peterson Stan Wagon, a mathematician at Macalester College in St. Paul, Minn., has a bicycle with square wheels. It's a weird contraption, but he can ride it perfectly smoothly. His secret is the shape of the road over which the wheels roll. A square wheel can roll smoothly, keeping the axle moving in a straight line and at a constant velocity, if it travels over evenly spaced bumps of just the right shape. This special shape is called an inverted catenary. It turns out that for just about every shape of wheel there's an appropriate road to produce a smooth ride, and vice versa. Just as a square rides smoothly across a roadbed of linked inverted catenaries, other regular polygons, including pentagons and hexagons, also ride smoothly over curves made up of appropriately selected pieces of inverted catenaries. As the number of a polygon's sides increases, these catenary segments get shorter and flatter. Ultimately, for an infinite number of sides (in effect, a circle), the curve becomes a straight, horizontal line. Interestingly, triangular wheels don't work. As an equilateral triangle rolls over one catenary, it ends up bumping into the next catenary . However, you can find roads for wheels shaped like ellipses, cardioids, rosettes, teardrops, and many other geometric forms. You can also start with a road profile and find the shape that rolls smoothly across it. A sawtooth road, for instance, requires a wheel pasted together from pieces of an equiangular spiral. Riding on Square Wheels |
April 4, 2004
In search of a formula |
April 4, 2004
On science, Bob Newhart and the 'butterfly effect'James McCusker Like Newhart's decision to turn on the TV, seemingly inconsequential events, chance meetings and trivial decisions have been the stuff of dramas for centuries. But it is only recently that they have become the stuff of science. In 1972, Edward Lorenz gave a talk to the American Association for the Advancement of Science titled "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Ofered just how sensitive systems could be when he was using a computer to solve a set of differential equations in a large, complex weather model. Like any good scientist, he decided to rerun his stuff on the computer to check the accuracy of the calculations. Thinking that he could save some computer time, when he re-entered one of the numbers he rounded it off from .506,127 to .506. No big whoop, as we might say. But the difference in the results was huge, leading Lorenz to the conclusion that the model was extremely sensitive to the initial conditions, which in turn led him -- and an entire generation of scientists -- to embrace the idea of dynamic instability and the "butterfly effect." On science, Bob Newhart and the 'butterfly effect' |
April 3, 2004
Geometric swimsuits cover all body typesKerry Dougherty It’s the same every spring. Doesn’t matter how skinny you are. Or how long it’s been since you last tasted pasta. Everyone over 40 looks funny in a bathing suit. Especially last year’s suit. But there’s good news. Mathematicians have joined forces with the garment industry to produce swimsuits that could turn Rosie O’Donnell into Sarah Jessica Parker. With just a few strategically placed polygons. It’s the minimizing magic of geometry. Everywhere you look, bathing suits are made up of complex geometrical patterns designed to disguise the size of your rhombus and keep you from looking like a hypotenuse. Call this the bisector theorem of thinning if you will, but it seems there are now bathing suits that can actually shrink your circumference, reduce your radius and diminish your diameter. Unlike slimsuits of old, which simply cinched the flab and shoved it into your kidneys, these optical-illusion suits comfortably address trimming and slimming. Oh, happy day. Geometric swimsuits cover all body types |
April 3, 2004
Puzzles + Math = MagicBy EDWARD ROTHSTEIN ATLANTA — In a room off the Japanese-style entryway of a house here, a small mahogany coffee cup is firmly attached to a polished wooden saucer. A wooden spoon sits on the plate. So do two white sugar cubes, also made of wood. But can the cup be lifted off the saucer? It seems locked in place. There are no obvious joints, no hidden pieces that can be turned. And what is the first thing done when faced with a cup and sugar cubes? One puts the cubes into the cup and stirs. That is precisely what works. The cubes sit on the flat surface of cup's wooden liquid and seem drawn to particular spots near the rim. And the cup is released from the saucer's locked grasp. And is the house itself not a source of wonder? Just outside is a Japanese rock garden and waterfall, landscaped by Takeo Uesugi using boulders from Tennessee; nearby, a humidity-controlled garage houses a collection of more than 1,200 dictionaries from before 1800. It is the home of Tom Rodgers, an Atlanta investor and businessman. Under his stewardship and partial sponsorship, devotees of mathematics, magic and games come for three days every two years from as far as Japan and England. They meet each other in Mr. Rodgers's house and in a hotel's conference halls, sharing their analyses and inventions, paying tribute to the man who inspired them all: the one-time columnist for Scientific American, Martin Gardner. Mr. Gardner, 89 and living in Oklahoma, attended only the first two Gatherings for Gardner, as these meetings are called, and missed the sixth, from March 26 to March 28, as well. But as a writer who redefined the nature of recreational mathematics, and inspired many hundreds of careers, he remains its guiding spirit. From the start of his "Mathematical Games" column in 1956 until he retired in 1991, Mr. Gardner must have discussed the work of at least half of the 180 or so people in attendance. Now younger generations are joining in, making this the largest gathering yet. Mr. Rodgers arranges the program with the guidance of Mr. Setteducati and the mathematician Elwyn Berlekamp. But aside from the influence of Mr. Gardner, which is bound to recede over time, what is the common ground for these participants and their puzzles? Mr. Berlekamp, a professor of mathematics at the University of California at Berkeley readily acknowledges that "most mathematicians would consider this on the P.R. side of mathematics; most magicians would consider it on the mathematical side of magic." The mathematician and puzzler dissent, of course, insisting that the best experience is in knowing. The goal is not illusion, but disillusion. See the coffee cup as a mechanism with magnets, show the palmed cards, explain why certain series of numbers act in a certain way. The truth, they believe, is its own magic. At one magic show, a mathematician, Arthur T. Benjamin, able to perform stunningly fast calculations in his head, took a four-digit number, asked calculator-wielding guests to multiply it by any three-digit numbers they wished. They were then asked to read off all but one digit of the result in any order. In each case, he guessed the remaining digit. Astonishing as magic, but even more astonishing as puzzle — the method has a simple mathematical explanation (which can be sought, for those interested, in the properties of numbers divisible by 9 — which the original number was). Not all solutions are easy or even possible, of course. But the mathematician, the magician, the inventor and the puzzler, for all their different attitudes, are always at play in this shape-shifting world, believing that if something is well understood, like Mr. Kamei's cup, perhaps, its secrets can be revealed, or manipulated, or applied. The task may always end up far easier, or far harder, than it looks. As the mathematician Peter Winkler said in one talk: "No matter how simple something is, there's room for it to be too hard to do." Puzzles + Math = Magic |
April 3, 2004
Divided on Connected MathBy Lee Sensenbrenner A seventh-grader at a Madison middle school is posed with the following situation: A gas station sells soda in three sizes. A 20-ounce cup costs 80 cents, a 32-ounce cup is 90 cents and a 64-ouncer goes for $1.25. The first question, which appeared in similar form on a recent exam, is as traditional as any mathematical story problem: What size offers the most soda for the money? But the second question carries the spirit of the Connected Math Program, which has developed strong undercurrents of controversy, both here and nationally, and plays prominently in one of the Madison School Board races Tuesday. This question asks: If the gas station were to offer an 84-ounce Mega Swig, what would you expect to pay for it? There's really no concrete answer. A student, for instance, could argue that the 84-ouncer would cost what the 20-ounce and 64-ounce cups cost together. Another student could say that soda gets cheaper with volume, and then choose an answer based on some per-ounce price slightly less than what was given for the 64-ounce drink. University of Wisconsin-Madison math and computer science Professor Jin-Yi Cai began to become concerned with Connected Math when he saw the questions on his seventh-grade son's test. He went to the UW Math Library to investigate the textbooks, and he said that he was dismayed to find them "thicker than the collected works of Tolstoy." Where the Chinese math books he remembers fondly were thin and contained concise explanations of math's fundamentals, these books were cumbersome and full of long story problems and written passages. "It goes around and around and things never really get down to the really crisp, elegant, basic fundamental principles," Cai said of the Connected Math texts. "It takes away the elegance, it takes away the beauty, it takes away the most basic logic structure. And the students are left with a vague, touchy-feely idea," he said. Divided on Connected Math |
April 1, 2004
Logic from chaos?QUANTUM computing (see article) is not the only game in town when it comes to creating a new computing paradigm. Speaking at the American Physical Society's annual March conference, William Ditto of the University of Florida told of his efforts to create a “chaotic computer”. This is saner than it sounds. Chaos, in the mathematical sense, is not unpredictability: chaotic systems can behave in a predictable and reproducible way. The catch is that the evolution of a chaotic system depends very sensitively on its starting conditions, which leads in the long term to behaviour that is ultimately unpredictable. But by choosing those starting conditions carefully, and only letting the system evolve for a short time, Dr Ditto thinks he can harness chaos to be computationally powerful. Dr Ditto proposes using “chaotic elements”—which could be specific types of electric circuits, lasers or even neurons—to replace the logic gates that are the basic building blocks of conventional computers. The inputs to each chaotic element, as with a conventional logic element, are binary: that is, either 0 or 1. If the element outputs a value that exceeds a threshold that Dr Ditto chooses, then the result is a 1, while if it is less than that threshold, the result is a 0. This is exactly what happens in a conventional logic gate as well. The theory is intriguing, but these circuits are not just theoretical. The team has built an electronic logic element using a collection of simple components, such as resistors and capacitors, which behaves chaotically. They have also made a logic element out of a pair of leech neurons (nerve cells from blood-sucking worms) placed on a microchip. Dr Ditto readily admits that, like quantum computing, this technology is still in its infancy. But it certainly has potential—even though many people feel that existing computers are quite chaotic enough already. Logic from chaos? |
April 1, 2004
The Jekyll and Hyde of granular materials uncoveredUniversity of Melbourne Granular materials – which include everything from coal to coco pops – are physical substances that don’t quite fit into any of the known phases of matter: solid, liquid, or gas. Keep the grains under pressure, vacuum-packed coffee for example, and you have solid-like behaviour; open the pack and pour it into a container and suddenly the grains flow freely like a liquid. The changing personalities of granular materials can have devastating implications, for example the disturbance of the earth following an earthquake can be enough to trigger solid ground to turn to mush with catastrophic consequences. Dr. Antoinette Tordesillas, a senior lecturer at the Department of Mathematics and Statistics at the University of Melbourne says, "Even a fractional advance in our understanding of how granular media behave can have a profound impact on the economic and general well-being of nations worldwide." "At the correct level of resolution it is possible to see critical microstructures, called ’shear-bands’, which give insight into the failure properties and personality shifts of such materials." "In a sense, we are endeavouring to understand what triggers the personality change in granular materials and the shear band is the key or signature microstructure that these materials manifest as they undergo a transition from solid to liquid." Nobody has successfully managed to understand the nature of shear bands to date. Now, the Mechanics and Granular Media Group of the Department of Mathematics and Statistics at the University of Melbourne, led by Dr. Tordesillas, have pioneered the first enriched continuum model capable of seeing shear bands. Dr. Tordesillas says, "We have found a way to capture and predict not only the split personality but also the key transition mechanism." The Jekyll and Hyde of granular materials uncovered |
April 1, 2004
Alfred Putnam, 88, influenced mathematics educationAlfred Putnam, a University Mathematics professor who helped influence the direction of U.S. mathematics education in the 1950s and 1960s, and who played a leading role in disseminating mathematical literature research from the former Soviet Union during the Cold War, died Thursday, March 11, at his home in Chesterton, Ind. He was 88. Putnam began examining the state of mathematics education in Eastern Europe even before the Soviet Union shocked the Western world with its technological prowess by successfully launching the Sputnik satellite in 1957. The previous year, Putnam had received a grant from the National Science Foundation to conduct the Survey of Recent East European Mathematical Literature. At that time, such a grant was almost unheard of. “You had to convince the NSF that there were excellent developments in mathematics education and literature in the Soviet Union,” said Izaak Wirszup, Professor Emeritus in Mathematics and the College. “After Sputnik it was much easier. Putnam was born March 10, 1916, in Dunkirk, N.Y. He received his B.S. degree from Hamilton College in Clinton, N.Y., in 1938, and his Ph.D. from Harvard University in 1942. At Harvard he studied under Saunders Mac Lane, now the Max Mason Distinguished Service Professor Emeritus in Mathematics at the University. Putnam became an instructor at Yale University in 1942 and joined the Chicago faculty as an Assistant Professor in Mathematics in 1945. He became Professor Emeritus in Mathematics in 1987. He twice received the University’s Llewellyn John and Harriet Manchester Quantrell Award for Excellence in Undergraduate Teaching, in 1952 and 1985. Alfred Putnam, 88, influenced mathematics education |
April 1, 2004
Fun with numbersBy Shannon Darling After spending three hours solving 46 math problems, 12-year-old Tie Shema Morgan said the subject was still her favorite. "It's fun," said Tie Shema, a seventh-grader at Alice G. Mulcahy School in Tulare. She joined about 750 seventh- and eighth-grade students Wednesday at the Math Super Bowl. Students compete in three math events, including the Pro Bowl, where students from different schools work for 45 minutes on one challenging problem; the Team Bowl, where team members from a school work together to solve 15 multiple-step problems; and the Power Bowl, where individual students work on 30 enhanced multiple-choice problems. The Cherry Avenue team members said they were tired after solving so many math problems. "I don't think I'd be able to go back to school and work," Kristi said. But her teammate Jake Coday, 12, said he was just glad he didn't have to go to school because math is what interests him. "Everything else is boring," he said. And if math isn't your best subject, Jake has one word of advice. "Work harder at it," he said. "It's the only way to get better." Fun with numbers |