 Algebra  University of Wales, Bangor
A paper describing research interests in algebra at Bangor, which have to a large extent been motivated by problems in algebraic topology and homological algebra. The recent spate of new and exciting concepts (crossed modules, crossed ncubes, nonabelian
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 Algorithms, Problems, Empirical Studies (APES)  Leeds and Strathclyde Universities, U.K.
An informal group of researchers interested in the understanding of algorithms and problems through empirical studies. Brian Hayes' article Can't Get No Satisfaction, introduces phase transition research in satisfiability, outlining a problem near the
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 Aligning and Articulating Standards Across the Curriculum (NCREL)  Cathy Cook; Pathways to School Improvement
Critical Issues in Mathematics. Students often do not see any connection between the mathematics they learn in school and the other subjects they study. As a result, many students do not see or understand the connection between mathematics and their daily
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 All About LaTeX2HTML  Nikos Drakos, Computer Based Learning Unit, Univ. of Leeds
LaTeX2HTML: What it is, how it works, where to get it, how to install it, how to use it and how to diagnose and fix problems. Also the LaTeX2HTML manual. Mailing list; sample converted documents; publications about LaTeX2HTML; searchable archives. Last
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 All Numbers Are Less Than A Million  Jim Loy
A "proof" that is "very close to what often passes as proof in the nonmathematical world."
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 Alternative Assessment Techniques  ERIC
An introductory bibliography of available information on alternative assessment. Provides an extensive list of resources, with abstracts and directions for obtaining fulltext copies of ERIC Journal and ERIC document citations.
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 Alternative Instruction and Alternative, PerformanceBased Assessment  Jane Ehrenfeld; Math Forum
Two annotated bibliographies designed to present ways in which assessment can be altered without drastic restructuring of class and curriculum. Some of the articles and books referenced have links to portfoliobased instruction and assessment, and can
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 Alternative or Block Scheduling  Mathematics Education at The Math Forum
The Math Forum's suggested sites on block scheduling, including Web resources, articles and reports, and discussions.
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 The Amazing ABC Conjecture  Ivars Peterson (MathTrek)
In number theory, straightforward, reasonable questions are remarkably easy to ask, yet many of these questions are surprisingly difficult or even impossible to answer. Fermat's last theorem, for instance, involves an equation of the form x^n + y^n =
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 Amazing Applications of Probability and Statistics  Kelly Rogers; Intuitor.com
Intuitor.com's Prob. and Stat. page provides clear and concise information
on a variety of topics covered in AP Statistics, including: Probability,
binomial coefficients, data analysis, random numbers, skewness, hypothesis
testing, and power. This
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 America's Favorite Number (Math Chat)  Frank Morgan, MAA Online
Math Chat invited each reader to send in a number. The most commonly submitted number, with the best explanation of why, wins. Answer: In a tight race between 7 and pi, pi wins by a single vote...
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 The Americas  Mathematics and the Liberal Arts  Todd Hammond
Notes on published articles: a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and on the connections between mathematics and other disciplines.
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 Analysis of Algorithms  Flajolet, Prodinger
A research site with papers to download, links to researchers, a newsletter, etc. Analysis of Algorithms (AofA) is a field in computer science whose overall goal is an understanding of the complexity of algorithms. While much research is devoted to worstcase
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 The Analytical Engine  John Walker
The mathematician Charles Babbage designed an Analytical Engine, a mechanical precursor to the computer, in the late 1800s. Read historical documents related to the Engine, including Blaise Pascal's account of his mechanical adding machine (in French),
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 Analytic and Descriptive Geometry  Dave Rusin; The Mathematical Atlas
An introduction to ordinary analytic geometry as studied in secondary school. (Also included here is a rather lengthy analysis of a result known as Poncelet's Porism.) History; applications and related fields and subfields; textbooks, reference works,
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 Analytic Geometry  Jim Loy
This is a quick introduction to analytic geometry, graphing functions in a coordinate system, that foreshadows the derivative.
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 Andrei Nikolaevich Kolmogorov  Alexander Adamchuk
Curriculum vitae, biography, conference announcement, memorial readings, and links about Andrei Nikolaevich Kolmogorov.
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 Andrew Odlyzko
Home page of the Head of the Mathematics and Cryptography Research Department at AT&T Labs. The site contains a comprehensive list of his papers, most of which may be downloaded in LaTex, PDF, or PostScript form if they are not available as plain
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 Andrew Ranicki's Homepage  Andrew Ranicki
Articles, video clips, bibliographies, and other assorted resources from the Scottish topologist and knot theorist who practices algebraic surgery, a classification method in topology for cutting up manifolds: the Jordan Curve Theorem and the classification
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 Annenberg Institute for School Reform (AISR)  Brown University
The Annenberg Institute develops, shares and acts on knowledge that improves outcomes of schooling in America, especially in urban communities and in schools serving disadvantaged children. Institute Projects: Rethinking Accountability; Building Capacity;
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 Another Record Prime  Ivars Peterson (MathLand)
This time, it didn't take a supercomputer. The new record for the largest known prime number goes to someone using a Pentiumpowered desktop machine. Joel Armengaud, a computer programmer working for Apsylog in Paris, made the discovery on Nov. 13 and
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 anthropicprinciple.com  Nick Bostrom
A site on 'Anthropic reasoning', which involves concepts such as probability, objective chance, rationality, and observers. See problems like the Doomsday argument.
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 Ant Math (MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
Imagine stepping into a pitchblack room. How might you figure out the room's size in the dark? You could, for example, carefully follow the walls and count how many steps you took going from one corner to the next all the way around. That would give
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 Appealing Numbers  Ivars Peterson (MathTrek)
A short history of amicable numbers  pairs in which each number is the sum of the proper divisors of the other. The smallest such pair is 220 and 284. The number 220 is evenly divisible by 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110, which add up to
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 Application of Rayleigh's ShortCut Method to Polya's Recurrence Problem [PDF]  Peter Doyle
Doyle's Ph.D. thesis at Dartmouth College, June 1982. The goals of the presentation are to explain why Polya's theorem is true and to develop techniques for applying Rayleigh's method. The main results make sense of the notion that if two graphs look
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 Applications and Misapplications of Cognitive Psychology to Math Education  Anderson, Reder, Simon
A critical view of constructivism by three leading cognitive psychologists at Carnegie Mellon University. Decomposition and decontextualization; situated learning; constructivism; recommendations for research and instruction; overall conclusions; references.
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 Applied Algebra Group  Dept. of Mathematics, Johannes Kepler Universität Linz, Austria.
This group has formed around Prof. Günter Pilz. One of its main research interests lies in nearrings: generalised rings that might generally be described as rings (N,+,*) where the addition is not necessarily abelian and only one
distributive law
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 Applied Chaos Lab (ACL)  Dr. W. Ditto; Georgia Tech University
The ACL covers a broad range of analysis and application of chaotic behavior and related phenomena. Much of the research is done in conjunction with researchers at other universities and extends into biophysics and other interdisciplinary areas. Researchers
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 Applied Mathematical Sciences Summer Institute
A summer research program for undergraduate majors in mathematics and related fields of application. AMSSI targets underrepresented minorities and women. Read "Determinisitc and SmallWorld Network Models of College Drinking Patterns," "Algebraic Interleavers
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 Approximations and Expansions  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to approximations and expansions, which primarily concern the approximation of classes of real functions by functions of special types. This includes approximations by linear functions, polynomials (not
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 Approximation Theory Network (ATNET)  Hans Joachim Schmid, Hans Strauss
Resources for the approximation theory community. Subscribe to a message group or read past bulletins. Includes a list of theses and relevant class notes (some linked or available for download), tables of contents from various journals, and an alphabetical
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 AP Statistics  BB&N Upper School
A course from the Buckingham Browne & Nichols School. Advanced Placement Statistics acquaints students with the major concepts and tools for collecting, analyzing, and drawing conclusions from data, featuring work on projects involving the handson
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 APStatistics Dissertation  Kim Robinson, Clayton College & State University
A qualitative research study focused on students' learning and their performance on the Advanced Placement Exam with respect to conceptoriented instruction as recommended by the AP Statistics Test Development Committee. Organized into chapters, including
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 Arabic mathematics: forgotten brilliance?  MacTutor Math History Archives
Linked essay exploring the debt we owe to Arabic/Islamic mathematics. In many respects the mathematics studied today is far closer in style to that of the Arabic/Islamic contribution than to that of the Greeks. Certainly many of the ideas previously thought
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 The Arabic numeral system  MacTutor Math History Archives
Linked essay exploring the transmission of Indian numerals first to the Arabic/Islamic peoples and from them to Europe. The eastern and western parts of the Arabic world (North Africa and Spain) both saw separate developments of Indian numerals with relatively
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 Arbeitsgruppe Bachem/Schrader  University of Köln
A working group of the Center for Parallel Computing (ZPR) at Köln. Site includes a list of members and contact address; informative writeups on its projects, some in English. Topics include: Basic Research (meaning "pure" as opposed to "applied");
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 Are Mathematicians Turning Soft?  Keith Devlin (Devlin's Angle)
An article about 'soft mathematics'. "...In order to capture some of the abstract patterns and structures of mind and language, linguists sometimes find it convenient (perhaps necessary) to make use of mathematics, or at least mathematical notation or
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 Aristotle and the Paradoxes of Logic  Gilbert Voeten
At about the same time that set theory began to influence other branches of mathematics, various contradictions, called paradoxes, were discovered. A paradox, however, is only due to a striking violation of at least one of Aristotle's laws of logic. The
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 Arithmagic  Ivars Peterson (MathTrek)
Arthur T. Benjamin eschews the usual trappings of the magician's trade. Calling himself a mathemagician, he astonishes audiences with amazing feats of mental arithmetic. Behind the scenes, he reveals how you, too, can look like a genius without really
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 Arithmagic (MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
Prof. Arthur Benjamin amazes audiences by multiplying numbers in his head faster than someone using a calculator. Benjamin says that anyone  young or old  can learn to do the same feats of mental arithmetic. All it takes is a memory for numbers and
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 Arithmetic (Funk & Wagnalls Multimedia Encyclopedia)  Lycos Zone: Mathematics
A short article on arithmetic: fundamental definitions and laws; theory of divisors; fractions; and decimals.
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 Arithmetic is Algebra Backwards  John Hays
A series of essays, including: Deriving integers as vectors of Naturals; rationals, vectors of integers; reals as infinite vectors of rationals by adjoining transfinite operation of LIMIT to arithmetic finite operations; complex numbers as vector of reals
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 Arithmetic Properties of Binomial Coefficients (Organic Mathematics Proceedings)  Andrew Granville
Many great mathematicians of the nineteenth century considered problems involving binomial coefficients modulo a prime power (for instance Babbage, Cauchy, Cayley, Gauss, Hensel, Hermite, Kummer, Legendre, Lucas and Stickelberger). They discovered a variety
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 Arithmetic with Roman Numerals  Jim Loy
"It is fairly obvious that Roman numerals are more difficult to use than our arabic numerals. They are fine for recording a date or indicating a chapter number. But, they make arithmetic somewhat difficult....Egypian numerals are essentially Roman numerals,
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 Arnd Roth  Arnd Roth, Institute for Theoretical Physics, Heidelberg, Germany
Arnd Roth studies computational physics and neuroscience. This page provides documentation and code for related Mathematica notebooks, and a notebook for the Knight's Tour chess problem, available online. Also links to abstracts or text of many of Roth's
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 Around the Dartboard  Ivars Peterson (MathLand)
The numbers on a standard dartboard have the following order, going clockwise starting at the top: 20, 1, 18, 4, 13, 6, 10, 15, 2, 17, 3, 19, 7, 16, 8, 11, 14, 9, 15, and 5. Why this particular order? A possible criterion for designing a dartboard is
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 Articles on Mathematics  Subramaniyan Neelagandan
Articles in four formats: DVI, PDF, PS, and TEX Code. The Distribution of Prime Numbers & Integer Factorization; The Simplification of Fermat's Last Theorem; Exploration of Collatz's Conjecture.
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 Articulation in Mathematics Education  EXTEND  Perspectives in Mathematics Education
Links to articles on creating smoother transitions between education and work, between school and college and within sectors of higher education, and about preparing teachers to facilitate these transitions and students to respond to new environments.
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 An Artist's Timely Riddles  Ivars Peterson  Science News Online
The late 19th and early 20th centuries were a time of great popular interest in visualizing a fourth spatial dimension  a concept that appeared to offer painters and sculptors, in particular, an avenue of escape from conventional representation. Moreover,
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 The Art of Asking Thought Provoking Questions in the Mathematics Classroom  Carmen Bellido, Uroyoan Walker, Keith Wayland
A position paper in PDF format: a "How To" guide for developing higherlevel conceptual questions that provoke students to think. Several techniques for modifying traditional questions are illustrated with examples ranging from elementary to high school
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