
A Supplemental Introduction to Algebra  Rick Garlikov
Some things algebra books don't tend to tell students, but which Garlikov thinks are important for them to know so that they can understand what algebra is about and see, in a sense, how it works. Also The Way Algebra Works.
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 Automated Deduction  William McCune
Research on applications of automated deduction to problems in abstract algebra and algebraic geometry, algorithms and strategies for searching for proofs and for counterexamples, highperformance implementation of automated deduction algorithms, and
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 "Average" Temperature (Math Chat)  Frank Morgan, MAA Online
Answering the challenge: The National Weather Service approximates the daily average temperature by the average of the daily high and low temperatures. Why is this such a good approximation? Mathematically, the approximation is good because Earth's warming
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 Averting Instant Insanity  Ivars Peterson (MathTrek)
Once called "The Great Tantalizer," the puzzle looks innocuous and sounds quite simple. It consists of a set of four cubes with one of four colors on each of their six faces. Your goal is to arrange the four cubes in a row so that all four colors appear
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 Aviezri Fraenkel
Aviezri Fraenkel is an Israeli mathematician investigating combinatorial game theory. This page offers preprints and recent reprints in postscript format; a comprehensive bibliography on combinatorial games; and links to information on conferences and
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 Axiom (Encarta Encyclopedia 2000)  Robert M. Baird; Microsoft Encarta Online
Axiom, in logic and mathematics, a basic principle that is assumed to be true without proof. The use of axioms in mathematics stems from the ancient Greeks, most probably during the 5th century BC, and represents the beginnings of pure mathematics as
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 The Aztec Calendar: Math, Geometry, and Design  Charles William Johnson
A site that explores the relation between the mathematics of ancient reckoning systems, expressed in historically significant numbers (cited in the historical record), and designs within the geometry of ancient artwork. The complexity of design within
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 Azulejos Que Ensinam  Museu Nacional de Machado de Castro
Catálago sobre uma coleção de azulejos que mostram Os Elementos de Euclides e otras figuras de matemáticas.
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 Babylonian and Egyptian Mathematics  MacTutor Math History Archives
Linked essay describing the character and accomplishments of these two early mathematical systems, with references and other related web sites.
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 Babylonian numerals  MacTutor Math History Archives
Linked essay exploring the development of the Babylonians' number system, with ideas inherited from the Sumerians and the Akkadians. From them came base 60, or the sexagesimal system, but neither the Sumerian nor the Akkadian system was a positional system
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 The Bakhshali manuscript  MacTutor Math History Archives
Linked essay on the discovery and history of an early mathematical manuscript. The Bakhshali Manuscript is a mathematical work written on birch bark, found in the summer of 1881 near the village Bakhshali in Mardan tahsil, 50 miles from the city of Peshawar
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 Balanced Assessment in Mathematics  The Concord Consortium
From 1993 to 2003, the Balanced Assessment in Mathematics Program existed at the Harvard Graduate School of Education. The project group developed a large collection of innovative mathematics assessment tasks for grades K to 12, and trained teachers to
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 Balducci's Actuarial Home Page  David P.M. Scollnik; Dept. of Mathematics and Statistics, Univ. of Calgary
Links to popular actuarial resources: Balducci's List of Actuarial, Risk, and Insurance Links; Actuaries ( with Home Pages ) on the Web; Actuarial Programs in Academia; Actuarial ( Statistical ) Research Papers. Also information relating to actuarial
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 Barcode Encoding  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Barcodes are used with various encodings all over the world to simplify product identification, especially in retail. The site explains the most popular encodings, like UPC (Universal Product Code), ISBN (Intenational Standard Book Number), and EAN13
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 Barry Garelick, Author at Education News  EducationNews
Articles by Garelick, who teaches middle and high school math in California, have included "The Myth About Traditional Math Education," "Fran, Henderson & Pingry, and Me: A Tale of Problems vs Exercises," "Mathematics Education: Being Outwitted by Stupidity,"
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 Bartlett Corrections  F. CribariNeto
Introduction to and compilation of resources on Bartlett corrections: scalar transformations "applied to the likelihood ratio (LR) statistic that yields a new, improved test statistic which has a chisquared null distribution to order O(1/n). This represents
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 Base Considerations  Keith Devlin (Devlin's Angle)
A discussion of base systems, including negative bases, used in computers. "We are so used to computers nowadays that it seems obvious that computer arithmetic should be performed in a binary fashion. After all, this is the most natural form for a computer,
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 BaseGroup Labs  data analysis, forecasting, free analytical components
A commercial software company that creates systems for information analysis and forecasting, and develops custom integrated circuits. The site offers scientific articles concerning data analysisneural nets, selforganizing maps, filtration, decision
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 The Battle of The Frog and The Mouse  John Hays
In the 1920s, Albert Einstein heard of a Foundational debate between Formalist
David Hilbert and Intuitionist L.E.J. Brouwer, and asked: "What is this frog and mouse battle between the mathematicians?" This fable presents Brouwer as the frog, Hilbert
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 Beeneet Kothari Wins First $1000 National High School Calculus Student Award (Math Chat)  Frank Morgan, MAA Online
Beeneet Kothari of Half Hollow Hills High School West, Long Island, has been awarded the first $1000 National High School Calculus Student Award by ecalculus.org, based at the University of California at Davis and Williams College. In ninth grade he wrote
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 ... Before This Decade Is Out ...  Keith Devlin (Devlin's Angle)
With four thousand professionally active mathematicians gathered together, the January Joint Meeting provides an opportunity to check the pulse of the US mathematical community and to look for any significant new trends... "Make the preparation of K12
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 The Beginnings of Set Theory  MacTutor Math History Archives
Linked essay describing the rise of set theory from Cantor (with discussion of earlier contributions) through the first half of the 20th century, with another web site and 25 references (books/articles).
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 Behind the Numbers  Jonathan Sills; ESPN SportsZone
A monthly column that explores the gray area between math and sports and what happens when exact calculations meet the human, unpredictable factors that make sports so entertaining. A combinatoric and probabilistic analysis of changes in World Cup soccer
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 Benchmarks for Optimization Software  Mittelmann, Spellucci
I: Several codes, one computer  linear and quadratic programming; quadratically constrained quadratic programming; geometric programming; boundconstrained nonlinear programming; nonlinear programming; largescale nonlinear system benchmark; benchmarks
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 The Benefits of MixedAge Grouping (ERIC Digest)  Lilian G. Katz
"Goodlad and Anderson, who introduced the modern notion of the nongraded elementary school in 1959, raised our awareness of the fact that age is a crude indicator of what learning experiences children are ready for... The terms 'ungraded' and 'nongraded'
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 The Benezet Centre  Richard Hake & Sanjoy Mahajan
In 1929, Louis Benezet tried an experiment, "abandoning all formal instruction in arithmetic below the seventh grade and concentrating on teaching the children to read, to reason, and to recite." The experiment was successful; this site includes Benezet's
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 Bernhard Kutzler's Collection: Technology in Mathematics Education  Bernhard Kutzler
Read or download the author's articles: "Algebraic Calculators as Pedagogical Tools for Teaching Mathematics"; "Indispensable Manual Calculation Skills in a CAS Environment"; "TwoTier Exams as a Way to Let Technology in"; and "Interconnectivity  Derive
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 The Bertrand Russell Editorial Project  McMaster University
These archives, at McMaster University, house the complete papers of Bertrand Russell (18721970), British Philosopher, logician, essayist and renowned peace advocate. His Collected Papers include logical and philosophical works, Toward the "Principles
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 Bessel, Friedrich Wilhelm (Funk & Wagnalls Multimedia Encyclopedia)  Lycos Zone: Mathematics
A short biography of Friedrich Wilhelm Bessel (17841846), the German astronomer and mathematician, best known for making the first accurate measurement of the distance to a star.
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 The Best Two Points in a Square (Math Chat)  Frank Morgan, MAA Online
Solution to the challenge: Where do you think you should you place two points in a unit square to minimize the average distance in the square to the nearest of the two points? Computer calculations by Al Zimmermann yield configurations of 211 points
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 The Better File Cabinet  Eric Hsu
A database of nonroutine calculus problems used in college workshops for Uri Treisman's Emerging Scholars Programs. It was originally a highly searchable database of calculus problems, comments and solutions. It will eventually will be a database crossreferencing
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 Between Arithmetic and Algebra  Cut the Knot!, Alexander Bogomolny
What is the difference between the arithmetic 3+5 = 5+3 and the algebraic a+b = b+c? One is a specific fact, another is a pattern valid in a multitude of situations. While arithmetic may hint at some regularities, algebra, as a language, gives expression
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 Between Arithmetic and Algebra  Cut the Knot!, Alexander Bogomolny
What is the difference between the arithmetic 3 + 5 = 5 + 3 and the algebraic a + b = b + c? One is a specific fact, another is a pattern valid in a multitude of situations. While arithmetic may hint at some regularities, algebra, as a language, gives
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 Beyond Extra Large (and Ultra Small)  Ivars Peterson (MathTrek)
Metric prefixes come in handy for expressing both large and small quantities. So we have megawatt power systems and gigabyte hard drives at the high end, and we have nanoscale electronics and femtosecond lasers at the low end. Advances in scientific research
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 Beyond the Block: Tessellating Patterns  Linda Hampton Schiffer
An article about using tessellations in quilt design.
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 Beyond the Ellipse  Ivars Peterson (MathLand)
There's a simple trick one can use to draw an ellipse. Tie the ends of a length of string to two pins (or thumbtacks) stuck in a sheet of paper on a drawing board. Then, keeping the string taut with the point of a pencil, allow the pencil to trace a path
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 Beyond the IndividualSocial Antimony in Discussions of Piaget and Vygotsky  Cole, Wertsch
A discussion of the ongoing debate about the relation between the ideas of Vygotsky and Piaget, emphasizing a cardinal difference between them: their views concerning the importance of culture, in particular, the role of mediation of action through artifacts,
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 The Bible Code That Wasn't  Keith Devlin (Devlin's Angle)
Just over a year ago, journalist Michael Dronin's book The Bible Code hit the bookstores  and soon after that the television screens and review pages of national newspapers  and quickly became an international bestseller. Both author and publisher made
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 Bibliographies on Typesetting  AlfChristian Achilles
Searchable bibliographies of scientific literature on typesetting (SGML, TeX, fonts, PostScript, electronic publishing, typography, font readability, etc.). The bibliographies are updated monthly from their original locations.
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 Big Picture: What Does 'Numeracy' Mean?  Iddo Gal
Numeracy is a term increasingly used in publications aimed at adult educators, yet its meaning and purpose may be unclear. This article briefly examines the importance of numeracy and the implications for those working with the GED Tests.
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 The Big Six Skills: Information Skills Instruction  Eisenberg, Berkowitz
Information and technology literacy programs. Big6 is a systematic approach to information problemsolving, useful whenever an individual has an informationoriented problem. Six skills are listed, with examples for potential uses, a store, a bibliography,
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 Billiards in the Round  Ivars Peterson (MathLand)
On a level, rectangular table, a practiced billiard player can return the balls to their original positions, repeat a shot, and obtain an identical result. The geometry of the table, however, can greatly influence the types of motion possible in a game.
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 Binary Cubic Forms and Cubic Number Fields (Organic Mathematics Proceedings)  Henri Cohen
A paper presenting a small part of the theory of binary cubic forms, in particular its application to cubic number fields. Most of the results are due to DavenportHeilbronn, but the algorithmic applications seem to be new.
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 A biographical sketch of Ada Byron, Lady Lovelace  Dr. Betty Toole
A brief biography and book reference of Ada Byron, Lady Lovelace, one of the most picturesque characters in computer history, who suggested to Babbage a plan that is now regarded as the first "computer program." Also Ada Lovelace's Notes on her translation
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 Biographical Studies  Clark Kimberling; Dept. of Mathematics, Univ. of Evansville, Evansville, IN
Biographies of: Emmy Noether (18821935) mathematician; David Dale Owen (18071860) geologist; Joseph Granville Norwood (18071895) geologist; Margaret Chappellsmith (18061883) lecturer and writer; John Chappellsmith (18061895) artist and writer; Eduardo
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 Biographies Index  MacTutor Math History Archives
An index of pages on famous mathematicians throughout history, arranged alphabetically or chronologically and searchable by keyword. There is also an index of female mathematicians, and a full alphabetical index.
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 Biographies of Women Mathematicians  Agnes Scott College
Biographies in alphabetical and chronological order, and related resources on the Web. An ongoing project by students in math classes at Agnes Scott College in Atlanta, Georgia, to illustrate the numerous contributions by women to the field of mathematics.
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 Biography of M. C. Escher  Thames and Hudson's Escher Interactive
A biography of the wellknown, early 20th century artist. Escher's work is famous today for the imaginary worlds he created. He combined bizarre creatures and spatial illusions with craftsmanship and love of detail. Born in Holland in 1898, the son of
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 BioTech: Life Sciences Resources and Reference Tools  Indiana University
A searchable site that assists in the location and use of biotechnology resources, including the biotechnology aspects of agriculture, medicine, veterinary science, and molecular biology/biochemistry (pure sciences). An illustrated Dictionary provides
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 Birthday Surprises  Ivars Peterson (MathTrek)
It's rather unlikely that you and I share the same birthday (month and date). The more people you pull into the group, however, the more likely it is that at least two people will have matching dates. Ignoring the minor technicality of leap years, it's
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