Blog on Math Blogs

Math Digest

On Media Coverage of Math

Edited by Mike Breen and Annette Emerson, AMS Public Awareness Officers
Mike Breen (AMS), Claudia Clark (writer and editor), Lisa DeKeukelaere (2004 AMS Media Fellow), Annette Emerson (AMS), and Allyn Jackson (Deputy Editor, Notices of the AMS)

March Madness brackets

Mathematicians applied their skills to filling out brackets and figuring out how many brackets are possible. (Image: trendytron.)

"The news should start with mathematics, then poetry, and move down from there," from The Humans, by Matt Haig.

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Math Digest Archives || 2015 || 2014 || 2013 || 2012 || 2011 || 2010 || 2009 || 2008 || 2007 || 2006 || 2005 || 2004 || 2003 || 2002 || 2001 || 2000 || 1999 || 1998 || 1997 || 1996 || 1995

Click here for a list of links to web pages of publications covered in the Digest.

See also: The AMS Blog on Math Blogs: Mathematicians tour the mathematical blogosphere. PhD mathematicians Evelyn Lamb, Anna Haensch, and Brie Finegold blog on blogs that have posts related to mathematics research, applied mathematics, mathematicians, math in the news, mathematics education, math and the arts, and more. Recent posts: "Celebrating our sisters in STEM," and "Math in Pictures," by Anna Haensch, "The Pi Day Link Roundup of the Century," and "Topology Teaching Blogs," by Evelyn Lamb.

On the National Math Fest and the AMS, by Annette Emerson

The first National Math Fest was held in Washington DC, including a day of public events on Saturday April 18.

Really Big Numbers

On Friday April 17 Mathical: Books for Kids From Tots to Teens inaugural award winners were announced at the Mount Pleasant Neighborhood library. See the press release announcing the awards. Really Big Numbers by Richard Evan Schwartz and published by the AMS received the award in two categories, For grades 3-5 and 6-8. The prize "honors books that foster a love and curiosity for math."

Read a review of Really Big Numbers, by Sondra Eklund, Sonderbooks, 21 April 2015.

On Saturday the festivities drew families of all ages to the Mall. There were talks, the Math Midway (kids rode a square-wheeled tricycle), hands-on activities (art, mazes), interactive mime and magic performances, and the AMS's Who Wants to Be a Mathematician game.

See a video segment about the festival and game, with information about the book awards on ABC7 News (if you can't view the video embedded below in your browser go to ABC7). Featured in the spot are AMS Public Awareness Officer Mike Breen and two of the Who Wants to Be a Mathematician contestants, who were great examples of students who love math--countering the host's introductory remark about how almost every high school student dreads math class.

See "National Math Festival underway in D.C.," by Brett Zongker (Associated Press), ABC7, 17 April 2014. And on the topic of math in media, see a video of Schwartz reading from his book Really Big Numbers at the Mathical award event.

--- Annette Emerson

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On Persi Diaconis and playing card smooshing, by Annette Emerson

As science writer Klarreich talked with Persi Diaconis at the 2015 Joint Mathematics Meetings he was shuffling playing cards. Diaconis, a professor of mathematics and statistics at Stanford University, has also been a professional magician for decades. "At 24, he started taking college classes to try to learn how to calculate the probabilities behind various gambling games. A few years later he was admitted to Harvard University's graduate statistics program on the strength of a recommendation letter from the famed mathematics writer Martin Gardner that said, more or less, 'This kid invented two of the best ten card tricks in the last decade, so you should give him a chance.'" But in this interview Diaconis shares how he has "employed his intuition about cards" in other ways. "Once, for example, he helped decode messages passed between inmates at a California state prison by using small random "shuffles" to gradually improve a decryption key." He also explains "smooshing," a different method of shuffling used in gambling casinos. But he notes "a mathematical analysis of smooshing will likewise have ramifications that go far beyond card shuffling. 'Smooshing is close to a whole raft of practical life problems.' It has more in common with a swirling fluid than with, say, a riffle shuffle; it's reminiscent, for example, of the mechanics underlying the motion of large garbage patches in the ocean, during which swirling currents stir a large collection of objects."

Pacific Ocean garbage patch

Garbage accumulation locations in the North Pacific Ocean. Image by the National Oceanographic and Atmospheric Administration (NOAA).

Klarreich then explains more about smooshing, smooshing tests, randomness, smooshing models, and potential applications. "The model does provide a framework for relating the size of the deck to the amount of mixing time needed, but pinning down this relationship precisely requires ideas from a mathematical field still in its infancy, called the quantitative theory of differential equations.... Diaconis is optimistic that the work will lead him not just to an answer to the smooshing question, but to deeper discoveries. 'The other shuffles have led to very rich mathematical consequences, and maybe this one will too,' he said."

See "For Persi Diaconis' Next Magic Trick ...," by Erica Klarreich, Quanta Magazine, 14 April 2015.

--- Annette Emerson (Posted 4/23/15)

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On Escher, optical illusions, and math, by Annette Emerson

"The Mathematical Art of M.C. Escher," by the BBC. See a larger version on YouTube and other videos with the article.

Ian Stewart, professor of mathematics at University of Warwick, UK, author of many books, and recipient of the JPBM Communications Award, explains in the BBC video how M.C. Escher was able to connect art and mathematics. The online article includes images and embedded videos showing optical illusions and works by Escher, who was fascinated by the concepts of infinity, reflections, Möbius strips, Penrose tiles, and human perception, and whose works illustrate tessellations and symmetry.

Stewart rightly concludes, "Mathematicians know their subject is beautiful; Escher shows us it's beautiful."

See "Optical illusions: Is the cat walking up or down the stairs?," by Western Daily Press, 8 April 2015.

--- Annette Emerson (Posted 4/9/15)

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On sandpiles, by Allyn Jackson

Sandpile simulation Add a few grains of sand to a sandpile, and maybe nothing much happens. But add a few more, and you might suddenly find the structure of the pile shifting and morphing into a new shape. In mathematics, a sandpile is a model that captures the simplest aspects of the behavior of a real sandpile. In this article, Jordan Ellenberg describes the mathematical sandpile and its incredibly rich behavior. One can think of a mathematical sandpile as an infinite array of dots, each with a vertical pile of sand. The vertical piles cannot get too tall, so any pile with 4 or more grains must topple, sending one grain in each compass direction. Now imagine an infinite table onto which sand is dropped grain by grain in the center. A pile of 4 grains forms and topples; as more sand is added, an adjacent pile accumulates 4 grains and then topples, and so on. As the sand begins to spread over the table, patterns emerge in the sandpile. The article contains some beautiful computer-generated pictures showing sandpile patterns, as well as a fascinating video. The sandpile is one of the simplest examples of what is known as "self-organized criticality," a phenomenon that could be at the root of life itself. "Some biologists see self-organized criticality as a potential unified theory for complex biological behavior, which governs the way a flock of birds moves in sync just as genetic information governs the development of the individual birds," Ellenberg writes. (Image of "billion" grain pile provided by Wesley Pegden.)

See "The Amazing, Autotuning Sandpile," by Jordan Ellenberg. Nautilus, 2 April 2015. See also "What is a sandpile?", by Lionel Levine and James Propp, in the September 2010 issue of the AMS Notices.

--- Allyn Jackson (Posted 4/21/15)

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On the origin of numbers, by Lisa DeKeukelaere

Is mathematics invented or discovered? A bit of both, according to astrophysicist Mario Livio, who will delve into this question while hosting "The Great Math Mystery" on PBS’s NOVA program on April 15. In an interview with Discover, Livio explains that humans invented natural numbers by abstracting what they observed in the natural environment: two eyes, two legs, etc. Humans then discovered the relationships between those numbers, such as the Pythagorian theorem. Livio notes that fractions and imaginary numbers are human inventions followed by discoveries, as well. When asked about math education, Livio opines that math should be treated as part of the human culture, like literature and history, particularly in an age where so much of our daily lives involve technologies reliant upon mathematics. He notes as an example that cell phones rely on satellite communications that use Einstein's theories of special relativity and general relativity.

See "The Numbers Game," an interview with Mario Livio by Gemma Tarlach. Discover, April 2015, page 12, and a trailer of "The Great Math Mystery" NOVA program.

--- Lisa DeKeukelaere

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Media coverage of the 2015 Abel Prize, by Annette Emerson

Nash and Nirenberg, 2015 Abel laureates

(Photos: Nash (left): © Peter Badge/Typos 1 in coop. with the HLF - all rights reserved 2015 and Nirenberg (right): © NYU Photo Bureau: Hollenshead.)

As soon as the Norwegian Academy of Sciences and Letters announced 2015 Abel Prize winners John F. Nash Jr. and Louis Nirenberg, the news spread on Twitter and elsewhere--many not able to resist connecting Nash with 'A Beautiful Mind,' the book and film about his life. (Nature puts as its title "'Beautiful mind' John Nash adds Abel Prize to his Nobel," and underneath that, "Mathematician made famous by Hollywood will share US$765,000 award with Louis Nirenberg for work in the field of geometric analysis.") Nash, who spent most of his career at Princeton University, and Nirenberg, professor emeritus at New York University's Courant Institute of Mathematical Sciences, receive the Abel Prize "for striking and seminal contributions to the theory of nonlinear partial differential equations and its applications to geometric analysis." The Abel prize committee wrote with the citation: "Their breakthroughs have developed into versatile and robust techniques that have become essential tools for the study of nonlinear partial differential equations. Their impact can be felt in all branches of the theory." Nash and Nirenberg have separately received prestigious awards and honors for their work in mathematics, but were nevertheless surprised to receive the Abel. New Scientist quotes Nash's quip, "I must be an honorary Scandinavian," and Nirenberg as saying, "I'm overwhelmed. I was asleep when the phone range yesterday, and I was simply astonished, just flabbergasted."

Philip Ball's piece in Nature provides more depth--a summary of just some of the work of the laureates, and bit of their lives. He quotes from a past interview in which Nirenberg said how he enjoyed collaborating in mathematics: "It's a very nice, warm family," and "That's the thing I try to get across to people who don't know anything about mathematics, what fun it is!" The recipients will be presented with their awards in the Abel Prize ceremony in Oslo in May.

See "A Beautiful Mind mathematician wins Abel prize," by Jacob Aron. New Scientist, 25 March 2015; "'Beautiful mind' John Nash adds Abel Prize to his Nobel," by Philip Ball, Nature, 25 March 2015; and "'A Beautiful Mind' Mathematician, John Nash, Wins Prestigious Prize," by David Freeman, The Huffington Post, 25 March 2015; "Bluefield's Nash wins highest mathematics honor," (with video of Nash after he received the Nobel Prize in Economics) by Marcus Constantino, Charleston Daily Mail, 30 March 2015. Other media, such as the New York Times and ABC News, picked up the announcement on the Associated Press newswire.

--- Annette Emerson (Posted 3/27/15)

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In honor of Emmy Noether, by Annette Emerson

To mark the occasion of mathematican Emmy Noether's 133rd birthday, Google celebrated with a google doodle. Noether, born 23 March, 1882, made outstanding contributions to the field of abstract algebra and theoretical physics. She was asked to address the International Congress of Mathematicians in 1928 and again in 1932. After being dismissed from the University of Göttingen in 1933 by the Nazis because she was Jewish, she made her way to the U.S. where she accepted a professorship at Bryn Mawr College. She was highly respected by prominent mathematicians of the day and was praised by Albert Einstein as a "creative mathematical genius."

The video, "Emmy Noether and The Fabric of Reality," is a talk by Ransom Stephens about Noether's Theorem, which "ties the laws of nature--from Newton's laws to thermodynamics to charge conservation--directly to the geometry of space and time, the very fabric of reality."

See "Google doodle honors mathematician Emmy Noether," (+video) by Rowena Lindsay, Christian Science Monitor, 23 March 2015, which includes the above video and description of how doodler Sophie Diao went about incluiding mathemtics into the google doodle honioring Noether.

--- Annette Emerson (Posted 3/24/15)

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On generating memorable passwords with Markov models, by Mike Breen

It's not easy finding a password you can remember that is also secure. In New Scientist, Jacob Aron writes about a method created by John Clements that uses Markov models and, in this case, text from A Tale of Two Cities, to generate passwords that are long enough to be secure, but are much easier to remember than passwords garbled up with special characters. One example: The greed hispefters and. Using the Dickens' novel, Clements used pairs of adjacent letters and for each pair, determined a distribution for possible subsequent individual letters. Then given an intial pair of letters, the third letter in the password is chosen based on that distribution. Once the third letter is chosen, the second and third letters are used to determine the frequency and make the choice for the possible fourth letter (as was done initially with the first two letters), and so on. Clements uses Huffman trees, binary trees used in compression, to terminate the word. Starting with longer strings, rather than only two-letter strings, yields longer but more pronounceable passwords. He admits in his paper--"Generating 56-bit passwords using Markov Models (and Charles Dickens)"--that there are still questions about the method, but notes that its security is independent of the chosen text so that people could use their own email history to generate passwords.

See "Let Charles Dickens sort out your passwords," by Jacob Aron. New Scientist, 21 March 2015, page 28.

--- Mike Breen (Posted 4/7/15)

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On math and the NCAA men's basketball tournament

BracketWho's going to win the tournament? Math can't say with 100% confidence, but some math professors have applied their skills to filling out brackets and figuring out how many brackets are possible. Tim Chartier (Davidson College), who has been studying the tournament and having success with brackets for years, writes about his approach to picking teams in the bracket in The New York Times, which gives extra points for correctly picking upsets. Jordan Ellenberg, University of Wisconsin, also wrote an article in the Times. Ellenberg looked at a couple of fairly simple methods to pick winners and noted, "The math can boost your chances of scoring high; but in bracketology, as in life, there are no guarantees." Eduardo Cabral Balreira and Brian Maceli at Trinity College weigh in with their predictions using their program Oracle, and Jeff Bergen at Depaul University talks about the number of possible brackets and his experiences doing interviews with the press. (Image: trendytron.)

--- Mike Breen (Posted 3/19/15)

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Media coverage of Pi Day, by Annette Emerson

Pi Day

The AMS knows when Pi Day is approaching (and when the potential lottery winnings are high), as reporters call to get insights on the numbers. This year AMS Public Awareness Officer Mike Breen and other mathematicians (Steven Strogatz, Keith Devlin, Manil Suri, among others) were interviewed on what makes pi such a fascinating number, and why so this year in particular. "Pi is a great number, for many reasons. It is a mathematical constant that occurs in many different scientific applications, and it is a homophone for something that is delicious," said Stu Schmill, dean of admissions at the school," quoted in "Boston math lovers mark rare Pi Day". Devlin, interviewed on NPR, notes "The full date, 3/14/15, is pi to the first four places. At 9:26 a.m. and 53 seconds, you can even celebrate pi to nine places: 3.141592653." (This is so in the U.S., anyway, where dates are written by month, day and—in this case, abbreviated—year.) Devlin notes that pi is irrational and has been calculated to more than a trillion digits.

But as Strogatz writes in The New Yorker, "Pi does deserve a celebration, but for reasons that are rarely mentioned.... The beauty of pi, in part, is that it puts infinity within reach. Even young children get this. The digits of pi never end and never show a pattern. They go on forever, seemingly at random—except that they can't possibly be random, because they embody the order inherent in a perfect circle. This tension between order and randomness is one of the most tantalizing aspects of pi." He explains why pi matters: "Through the Fourier series, pi appears in the math that describes the gentle breathing of a baby and the circadian rhythms of sleep and wakefulness that govern our bodies. When structural engineers need to design buildings to withstand earthquakes, pi always shows up in their calculations.... In short, pi is woven into our descriptions of the innermost workings of the universe." His beautiful description of pi and its connection to cycles brings more appreciation to the number than the celebrations of who can recite the most digits of pi or who has baked the most creative pies (though those are good ways to celebrate Pi Day too!).

And Pi Day 2015 was the perfect time for Robert Burton, Jr. (a math teacher at Explorations Academy in New York) and Jaclyn Sawler (who teaches pre-K and kindergarten in Jersey City, NJ) to get married. Their wedding took place at the Liberty Science Center in New Jersey, starting at precisely 9:26:53 (a.m.), and was written up in the Sunday Styles section of The New York Times.

See "Why Pi Matters," by Steven Strogatz, The New Yorker, 13 March 2015; "The 'Math Guy' Presents 5 Facts About 3.14," an interview with Keith Devlin, Weekend Edition Saturday, NPR, 14 March 2015; " 'Super Pi Day' — 3.14.15 — will feature weddings, food specials as math nerds celebrate once-a-century date," by Sasha Goldstein, New York Daily News, 13 March 2015; "Don't Expect Math to Make Sense: On Pi Day, Celebrate Math's Enigmas," an Opinion by Manil Suri, New York Times, 13 March 2015; "Boston math lovers mark rare Pi Day," by Steve Annear, Boston Globe, 14 March 2015; "It pays to know Pi — often more than 6 figures," by Silvia Ascarelli, Marketwatch, 14 March 2015; "University of Portland professor says he has unraveled mysteries in pi," by Casey Parks, The Oregonian, 14 March 2015; "Pi Day Hits a Milestone That Comes Only Once a Century: 3/14/15," by Alan Boyle, NBC News, 14 March 2015.

And see a roundup of Pi Day coverage in the blogosphere in "The Pi Day Link Roundup of the Century," by Evelyn Lamb.

--- Annette Emerson (Posted 3/16/15)

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On chance, by Allyn Jackson

This issue of New Scientist takes a look at how probability and randomness arise in a variety of areas. One of the articles, "Chance: Is anything in the universe truly random?" by Michael Brooks, examines the question of whether the cosmos is predictable or ruled entirely by chance. The answer? No one knows. The issue contains articles on randomness in evolution, the problem of generating numbers that are truly random, and Bayesian probability. In addition, there are brief interviews with people from several walks of life, from "The Avalanche Predictor" to "The Gambler," who discuss how chance and randomness enter into the phenomena they work with. One of the people interviewed is David Hand, an emeritus professor of mathematics at Imperial College London, whose book The Improbability Principle appeared in 2014 (the book was reviewed in the AMS Notices by Andrew I. Dale). In his book, Hand argues that highly improbable events are actually commonplace. "At first glance, it sounds like a contradiction: if something is highly improbable, how can it possibly be commonplace?" he told the interviewer, Michael Bond. "But as you dig deeper you see it is not a contradiction, and that you should expect what appear to be extremely improbable events to occur quite often." One reason is the law of large numbers, which says, for example, that even though the probability of being struck by lightning is very small, every year thousands of people die of lightning strikes. "[T]here are 7 billion people in the world, so there are a lot of opportunities for it to happen," Hand said.

See "Chance: How randomness rules our world" (subscription required). Special feature in New Scientist, 14 March 2015.

--- Allyn Jackson (Posted 3/17/15)

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On number theory, algebra and string theory, by Claudia Clark

In this article, Erica Klarreich writes about the work that has led to the publication earlier this month of a paper that proves the colorfully named Umbral Moonshine Conjecture, first proposed in 2012. She begins by describing the discovery in 1978 by mathematician John McKay of a connection between the special dimensions of the monster group and the coefficients of the j-function. This lead to the publication the following year of the paper "Monstrous Moonshine," in which mathematicians John Conway and Simon Norton "conjectured that these relationships must result from some deep connection between" this group and this function. Then in 1992, some 10 years after University of Michigan mathematician Robert Griess constructed the monster, Fields Medalist Richard Borcherds proved that string theory was the "bridge between the two distant realms of mathematics in which the monster and the j-function live." Some 20 years later, the Umbral Moonshine Conjecture "proposes that in addition to monstrous moonshine, there are 23 other moonshines: mysterious correspondences between the dimensions of a symmetry group on the one hand, and the coefficients of a special function on the other." Read the proof of the conjecture.

To read more about this conjecture, and the mathematicians who have worked on and proven the conjecture, see "Mathematicians Chase Moonshine's Shadow," by Erica Klarreich, Quanta Magazine, 12 March 2015.

--- Claudia Clark

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On Einstein the math tutor, by Mike Breen

When 12-year old Betty Leedom struggled with math in 1941, she wound up with Albert Einstein as her tutor! This article gives delightful details about how Einstein became her tutor and his approach to teaching her math over the four years that they met. The two met almost daily and eventually Leedom got the hang of algebra and other math subjects. Near the end of the article, Leedom says, "Some people were afraid to talk to him because they thought he was a crazy old man, but he was just so nice. Even when I told him I hated math. He said, 'you shouldn’t hate math, math is the center of the universe, and anyone who knows math knows everything.’” [Emphasis added.]

See "Albert Einstein was a Princeton genius. And math tutor." by Jeff Edelstein. The Trentonian, 12 March 2015.

--- Mike Breen (Posted 3/18/15)

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On data in medicine, by Claudia Clark

This article, which is adapted from Lohr’s soon-to-be-published book "Data-ism: The Revolution Transforming Decision Making, Consumer Behavior, and Almost Everything Else," discusses the life and work of Harvard math major and "number cruncher" Jeffrey Hammerbacher. At the age of 32, Hammerbacher has already applied his quantitative skills to building sophisticated computer models on Wall Street, using data to improve Facebook's service, and founding Cloudera, "a fast-growing company that makes software tools for data science." However, a diagnosis of bipolar disorder several years ago led him to explore and eventually apply his talents to the field of medicine, and to work with Dr. Eric Schadt at Icahn School of Medicine at Mt. Sinai, which "has begun an ambitious, well-funded initiative to apply data science to medicine." The reason for the initiative, Dr. Schadt explained, is that chronic diseases "are not caused by single genes, but are 'complex networked disorders' involving genetics, but also patient characteristics such as weight, age, gender, vital signs, tobacco use, toxic exposure and exercise routines--all of which can be captured as data and modeled."

At Mount Sinai, researchers have been doing work on cancer treatments tailored to individual patients. Hammerbacher and his team work on the "'computational pipeline,'... with the goal of making [these] treatments more automated and thus more affordable and practical. 'It's ultimately what cancer cures are going to look like,' he said."

See "On the Case at Mount Sinai, It's Dr. Data," by Steve Lohr, New York Times, 7 March 2015.

--- Claudia Clark

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On A full-scale computer simulation of the galaxy, by Lisa DeKeukelaere

Three centuries after Isaac Newton solved the two-body problem for describing the gravitational pull between the Earth and the Sun, researchers in the Netherlands and Japan are endeavoring to solve the 100-billion-body problem to describe the motions of all of the stars in a galaxy the size and shape of the Milky Way. Solving systems with less than a dozen bodies is achievable with sets of equations that provide the position and velocity of a body at any given time. Larger numbers of bodies, however, require numerical simulation to calculate each star's acceleration—based on the gravitational force of each other star in the system—over a brief change in time. Such a large number of computations is unfeasible at present, so the researchers reduced the required number of calculations by dividing the galaxy into cubic subvolumes to simplify some of the pairwise computations. The researchers also adapted their software to run on special parallel computing devices originally produced for video games. The researchers already have succeeded in simulating a 51-billion-body problem, and they hope that solutions to the full problem will yield new insights when compared to the results of the European Space Agency's effort, using the Gaia spacecraft launched in 2013, to map a billion stars.

See "The 100-Billion-Body Problem," by Brian Hayes. American Scientist, March-April 2015, vol. 103, no 2, pages 90-93.

--- Lisa DeKeukelaere

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Math Digest Archives || 2015 || 2014 || 2013 || 2012 || 2011 || 2010 || 2009 || 2008 || 2007 || 2006 || 2005 || 2004 || 2003 || 2002 || 2001 || 2000 || 1999 || 1998 || 1997 || 1996 || 1995

Click here for a list of links to web pages of publications covered in the Digest.