- 0 to 0 power - Math Forum, Ask Dr. Math FAQ
According to some Calculus textbooks, 0^0 is an "indeterminate form"; in some cases we think about it as having one value, and in other cases as having another...
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- 1991 Mathematics Subject Classification (MSC) - Chris Eilbeck; Heriot-Watt University, Edinburgh
A hypertext version of the 1991 MSC. The main purpose of the classification is to help readers to find the items of present or potential interest to them as readily as possible - in MR, in Zbl, or anywhere else where this classification system is used.
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- 1997 Linear Analysis Pages - Jonathan Borwein
Mathematics 419, Linear Analysis (Simon Fraser University). Course information, assignments, extras for enrichment. Classical and applied analysis, special function theory, general analytic knowledge (cardinality, irrationality, complex analysis, continued
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- The 3x+1 problem and its generalizations (Organic Mathematics Proceedings) - Jeff Lagarias
The 3x+1 problem, also known as the Collatz problem, the Syracuse problem, Kakutani's problem, Hasse's algorithm, and Ulam's problem, concerns the behavior of the iterates of the function which takes odd integers n to 3n+1 and even integers n to n/2.
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- 5 Numbers - Simon Singh and Marcus du Sautoy, BBC Radio 4
Web pages and Real Audio Music downloads of fifteen minute-long radio broadcasts that take a "quirky look" at zero, pi, the golden ratio, i, and infinity. "Hear about the stark reality behind the imaginary number, try a slice of pi, find out about the
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- The ABC Conjecture Home Page - Abderrahmane Nitaj
A statement of the abc conjecture, first formulated by Joseph Oesterlé and David Masser in 1985, with generalizations, consequences, tables, and a bibliography. Also abc theses, and relevant links.
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- Active Elementary Number Theory: n2 + 1 and coprime increasing pairs of different parity - H. B. Meyer
An interactive study of coprime increasing number-pairs of different parity and their relations to divisors of n2 + 1. Requires JavaScript.
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- Addition and Multiplication Tables in Various Bases - Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
An applet that combines addition and multiplication tables for bases from 2 through 36. In every base N, there are N digits. In the decimal system, for example, we have 10 of them: 0,1,2,3,4,5,6,7,8,9. In base 7, there are seven digits: 0,1,2,3,4,5,6.
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- Advanced Topics in Mathematics - Anthony Beckwith
Page for a high school course exploring fractals, the Global Positioning System, number theory, topology, chaos theory, and the history of mathematics. Syllabus and brief description of each topic.
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- aeyoung.mathematician - Andrew E. Young
Papers from a Mathematics graduate from The University Of Sussex at Brighton: Number Theory: GCD and Prime Factorisation; Molien's Theorem, Invariant Theory and Gregor Kemper; A History of Equality.
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- Algebraic Algorithms - Susan Landau; Univ. of Massachusetts at Amherst
The study of optimal algorithms for algebraic problems. Questions range from number theoretic issues (how hard is integer factorization?) to problems about polynomials and complex algebraic structures. Applications of this work include cryptography, symbolic
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- Algebraic Number Theory and Elliptic Curves - Ghitza, Osserman; Massachusetts Institute of Technology
A semester-long seminar giving a rapid introduction to algebraic number theory and elliptic curves. Topics: Dedekind domains, rings of integers, scheme-theoretic curves, finite morphisms thereof, splitting and ramification, the Tchebotarov density theorem
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- Algebra (MathPages) - Kevin Brown
More than 50 "informal notes" by Kevin Brown on algebra. Kummer's Objection; irreducibility criteria, multiple linear regression, string algebra, characteristic polynomial of a matrix, iterated means, sums of powers, polynomials from Pascal's Triangle,
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- Algorithmic Number Theory - Bibliography - Bach and Shallit
BibTeX files for the book Algorithmic Number Theory by Eric Bach and Jeffrey Shallit: a database of over 3100 papers.
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- alt.math.undergrad - Math Forum
An unmoderated discussion forum for issues and problems pertaining to college undergraduate mathematics. Read and search archived messages; and register to post to the 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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- The American Mathematical Monthly (MAA Online) - Roger A. Horn, Ed., Mathematical Association of America (MAA)
The Monthly publishes articles, notes, and other features about mathematics and the profession. Its readers include professional mathematicians as well as students of mathematics at all collegiate levels. Authors are invited to submit articles and notes
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- Andrew Granville
Andrew Granville researches number theory, combinatorics, and arithmetic geometry. His papers on these subjects are available for download in PostScript format. Granville also maintains a survey of results on the arithmetic properties of binomial coefficients.
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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 Shapira
Includes An image from the Collatz problem, including the Fractint code; the intensity of a point denotes the time taken to terminate. By a member of the faculty of Rensselaer Polytechnic.
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- Archives of NMBRTHRY@LISTSERV.NODAK.EDU (Number Theory List) - North Dakota Higher Education Computer Network (NODAK)
Searchable archives of postings, September 1987 - present.
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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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- 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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- arXiv.org e-Print archive - Los Alamos National Laboratory (LANL)
A major site for mathematics preprints that has incorporated many formerly independent specialist archives including alg-geom, funct-an, dg-ga, q-alg, auto-fms, cd-hg, MAGNUS, Several Complex Variables, Logic E-prints, Commutative Algebra, Dynamical Systems,
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- The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue - Koekoek, Swarttouw; Delft University of Technology
A 1998 report: definition, orthogonality relation, three-term recurrence relation, second order differential or difference equation, forward and backward shift operator, Rodrigues-type formula and generating functions of all classes of orthogonal polynomials;
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- AwesomeTutors.com
Las Vegas-based one-on-one tutoring service, with email, webcam and phone tutoring available for most tutoring subjects. Prepayment required.
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- Base 10, Base 2, and Base 16 - Walter Davis
Examples of different bases. There are several ways to represent a value using symbols. Roman numerals are an example. Position valued representation (PVR) is another example, the one with which we are the most familiar. With PVR, a limited number of
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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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- Base Converter -
Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A fairly high-level introduction to binary and other base systems, with a Java converter and links to related pages including: arithmetic operations in various bases, algorithmic conversion procedure, linguistic fun with base 36, Napier bones, abacus,
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- Basics of Computational Number Theory - Robert Campbell
An introduction to computational number theory, beginning with a quick overview of arithmetic in the modular integers. Throughout, the paper emphasizes computation and practical results rather than delving into the why. Simple programs, generally in JavaScript,
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- The Beal Conjecture
About Beal's conjecture and the prize offered for the proof or disproof of this important number theory relation.
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- The Beal Conjecture and Prize - R. Daniel Mauldin; Department of Mathematics, University of North Texas
An announcement of a prize for the solution to a problem pertaining to the Diophantine equation of the form A^x + B^y = C^z where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common factor.
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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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- A Bibliography of Bernoulli Numbers - Karl Dilcher
A bibliography of Bernoulli numbers by Karl Dilcher and Ilja Sh. Slavutskii. The Bernoulli numbers are among the most interesting and important number sequences in mathematics. They are particularly important in number theory, especially in
connection
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- Bibliography on Hilbert's Tenth Problem - Alf-Christian Achilles; Computer Science Bibliography Collection
Browse or search almost 400 references in this bibliography by Maxim Vsemirnov and Yuri Matiyasevich. Its ultimate goal is to contain references to all publications connected with the undecidability of Hilbert's Tenth Problem.
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- Binary Number System - Ken Dunham, A-Z Cryptology
Introduction to the base 2 system for those interested in computers and cryptology. Includes a review of base 10. See also other Cryptology Lessons.
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- The Binary System - Norfleet, Singleton; Wayne State University, Detroit MI
A short history of the binary system; binary to decimal and decimal to binary conversion; binary addition and multiplication; logic gates, and a glossary.
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- Binomial Coefficients - Bill Hammel
A collection of identities and formulas involving binomial coefficients: defined by factorials, appearing in Pascal's Triangle, derived with choose notation and summation formulas, approximated by Stirling's Formula, and more.
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- The Birch and Swinnerton-Dyer Conjecture - Clay Mathematics Institute
A Clay Mathematics Institute Prize problem, with a description in pdf format by Andrew Wiles. The conjecture addresses the problem of enumerating rational points, such as on elliptic curves.
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- Blog on the history of Fermat's Last Theorem and Wiles' Proof - Larry Freeman
The purpose of this blog is survey the developments of number theory in relation to Fermat's Last Theorem. I try to focus on the people, ideas, and mathematical details. It is meant to be interesting, accessible, and accurate in its mathematical details.
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- Books: Professional & Technical: Professional Science: Mathematics - Amazon.com
Browse bestselling math books from the Professional and Technical Bookstore at Amazon.com, in such categories as Applied; Chaos & Systems; Geometry & Topology; Mathematical Analysis; Mathematical Physics; Number Systems; Pure Mathematics; Transformations;
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- Brief Course Materials for Various Courses - E. Lee Lady; University of Hawaii
A collection of short handouts: files are in PDF and DVI formats. Contents include: The Fundamental Theorem of Arithmetic, the division algorithm, solutions of linear congruences, solving the Chinese Remainder problem, an example of a continued fraction,
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- A Brief History of Mechanical Calculators - James Redin
An essay on the historical evolution of calculating machines, from the abacus to Babbage's differential machine to today's computers. Contents include: the abacus; the Antikythera calculator; Napier's Bones; Leonardo da Vinci's design; Schickard’s machine;
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- Calculation and the Chess Master - Ivars Peterson (MathLand)
In 1912, J. B. Shaw wrote in the Bulletin of the American Mathematical Society: "The game of chess has always fascinated mathematicians, and there is reason to suppose that the possession of great powers of playing that game is in many features very much
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- Calculators On-Line Center: Part II - Mathematics - Martindale's Reference Desk
Over 7,420 calculators for: Unit Conversion (Time, Distance, Length, Speed, Weight, etc.); Abacus; Basic Math; Complex Mathematics; Complex Math Education; Complex Math Calculators by Specialty: Algebra and Linear Algebra; Algorithms; Calculus; Central
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- The Canadian Number Theory Association - Gary Walsh
A loosely defined group of individuals in Canada and abroad who are actively doing research in number theory and related areas of mathematics.
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- Carousel Numbers. A Lead-in to Number Theory - Gary Klatt; Univ. of Wisconsin - Whitewater; The Math Forum
A connected series of four problems in elementary number theory that are ideal for discovery learning at several levels. Each problem generates interesting questions and conjectures, and their surprising connections add interest and allow each to shed
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- Cascade Visuelle - Daniel Lemire
Java applet: génération de la fonction fondamentale associée au filtre donné en base 2. In French, with source code available. Also a link to a page of math resources in Quebec: Les sciences mathématiques au Québec.
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- A Catalog of Random Bits - Ivars Peterson (MathLand)
Researchers use random numbers for tackling a wide range of problems, from modeling molecular behavior and sampling opinion to solving certain equations and testing the efficiency of algorithms. Such numbers also play crucial roles in a wide variety of
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- Challenging mathematical problems - Naoki Sato
Some of the author's favorite and most challenging mathematical problems in algebra, geometry, number theory, inequalities, combinatorics and probability, and analysis.
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