21. The Arithmetic Coding Page By Alistair Moffat.Category Science Math Communication Theory Coding Theory......The arithmetic Coding Page. Software. Source code for the arithmeticcoding routines described by Moffat, Neal, and Witten, arithmetic http://www.cs.mu.oz.au/~alistair/arith_coder/

The Arithmetic Coding Page Software Source code for the arithmetic coding routines described by Moffat, Neal, and Witten, "Arithmetic Coding Revisited" , ACM Transactions on Information Systems, 16(3):256-294, July 1998, and the modified cumulative statistics structure described in "An Improved Data Structure for Cumulative Probability Tables" (Note that the mechanism reported by Stuiver and Moffat is not currently included.) Source code: arith_coder-3.tar.gz , February 1999. Source code: Versions 1 (March 1995) and 2 (October 1996) A suite of minimum-redundancy coding routines is also available, see http://www.cs.mu.oz.au/~alistair/mr_coder/ Books If compression programs are of interest to you, so too will be this new book: Compression and Coding Algorithms by Alistair Moffat and Andrew Turpin, Kluwer Academic Publishers , Boston, March 2002. If you desperately need a book and cannot wait until March, consider Managing Gigabytes: Compressing and Indexing Documents and Images by Ian H. Witten, Alistair Moffat, and Timothy C. Bell, Morgan Kaufmann , San Francisco, 1999.

22. Arithmetic Algebraic Geometry A European network of 12 working groups from 6 countries.Category Science Math Number Theory Research Groups...... The main themes of research of the network are A. arithmetic of algebraic varietiesover local fields. Previous network in arithmetic algebraic geometry. http://www.maths.univ-rennes1.fr/arithgeom/

A Research Training Network of the European Community Overview Partners Programme Post-docs Activities Project overview Developing powerful methods taken from geometry to study the arithmetical properties of algebraic equations Algebraic equations and their arithmetical properties have interested mankind since antiquity. One has only to think of the works of Pythagoras and Diophantus, which were a milestone in their time. For many centuries such problems have fascinated both serious mathematicians (Fermat, Gauss, ...) and amateurs alike. However, developments in recent years have transformed the subject into one of the central areas of mathematical research, which has relations with, or applications to, virtually every mathematical field, as well as an impact to contemporary everyday life (for example, the use of prime numbers and factorisation for encoding "smart" cards). The classical treatment of equations by analysis and geometry in the realm of complex numbers in this century has found a counterpart, in the similar theories over finite and p -adic fields, which have particular significance for arithmetic questions. The study of certain functions encoding arithmetic information and generalising the Riemann zeta-function (

23. Arithmetic Algebraic Geometry Since October 1, 2000, a new Research Training Network in arithmetic Algebraic Geometryis sponsored by the European Community. Its home page can be found at http://www.maths.univ-rennes1.fr/arithgeom.html

A Research Training Network of the European Community Since October 1, 2000, a new Research Training Network in Arithmetic Algebraic Geometry is sponsored by the European Community. Its home page can be found at : http://www.maths.univ-rennes1.fr/arithgeom/ For informations about the previous network (TMR programme), please look at : http://www.maths.univ-rennes1.fr/arithgeom/tmr/ P. Berthelot Last update : 29.10.00 This network is a Research Training Network of the European Community, under the programme Improving Human Potential and the Socio-Economic Knowledge Base Contract : HPRN-CT-2000-00120

24. General Decimal Arithmetic While suitable for many purposes, binary floatingpoint arithmetic should not beused for financial, commercial, and user-centric applications or web services http://www2.hursley.ibm.com/decimal/

General Decimal Arithmetic FAQ Bibliography Arithmetic specification Encoding ... Related links Most computers today support binary floating-point in hardware. While suitable for many purposes, binary floating-point arithmetic should not be used for financial, commercial, and user-centric applications or web services because the decimal data used in these applications cannot be represented exactly using binary floating-point. (See the Frequently Asked Questions pages for more explanation and examples.) The problems of binary floating-point can be avoided by using base 10 (decimal) exponents and preserving those exponents where possible. This site describes a decimal arithmetic which achieves the necessary results, is suitable for both hardware and software implementation, and conforms to the relevant ANSI, IEEE, and ECMA standards . Notably, a single data type can be used for integer, fixed-point, and floating-point decimal arithmetic. This first document describes the decimal arithmetic in a language-independent and representation-independent manner: Arithmetic Version Description Specification .html .pdf .ps Decimal floating-point arithmetic, with unrounded and integer arithmetic as a subset (IEEE 854 + ANSI X3.274 + ECMA 334).

25. Decimal Arithmetic For Java - 1.08 Improved BigDecimal class from IBM. Open sourceCategory Computers Programming Math and Calculations......Decimal arithmetic for Java TM. (Software version 1.08 – 6 Sep 2000) This makesit especially easy to add humanoriented arithmetic to your applications. http://www2.hursley.ibm.com/decimalj/

Decimal arithmetic for Java [TM] same results as the arithmetic that people learn at school (see the Decimal Arithmetic FAQ for more details). This site describes an enhanced BigDecimal class ( com.ibm.math.BigDecimal ) for Java, which is the basis for a proposed enhancement to java.math.BigDecimal . Please see the Java Specification Request (JSR) for details of the proposal. This JSR is proceeding to plan; you can find changes from this design in the Decimal Arithmetic Enhancement Public Review Draft The com.ibm.math.BigDecimal class (and its supporting class, MathContext ) is fully implemented and is available below, and is also included with IBM's Java developer kits as of version 1.1.8. The new class extends the existing class with the floating point arithmetic from ANSI X3.274, which does arithmetic the way people do. This makes it especially easy to add human-oriented arithmetic to your applications. Here, you'll find: Decimal Arithmetic for Java Frequently Asked Questions (FAQ). Detailed Acrobat format documentation for the decimal arithmetic classes (including background information and design notes). This is also available on the World Wide Web in

26. Interval Computations following page); Generalizations of Interval arithmetic and their Applications;Interval Notations (original suggestion, reaction); Open http://cs.utep.edu/interval-comp/main.html

27. Vector Arithmetic Vector arithmetic This representation of position is called a vector . Justas there is an arithmetic of numbers, there is an arithmetic of vectors. http://mcasco.com/p1va.html

Vector Arithmetic ARE THESE THE ARROWS OF OUTRAGEOUS FORTUNE, OF WHICH WE HAVE HEARD?... In measuring position by distance and direction we used a line with an arrowhead on it. This representation of position is called a "vector". Just as there is an arithmetic of numbers, there is an arithmetic of vectors. We are going to be interested in motion of particles and have already said that motion is change in position over time. To get a change in a number it is customary to subtract the initial value from the final. To get a change in position we will use the same technique, subtracting the starting position from the ending. So how would you subtract two positions? Well it is most convenient to think of the positions as vectors to do this. We have identified a line segment with direction and magnitude as a vector. If V V To add vectors there are two techniques available, geometric addition and algebraic addition. Both yield the same result. The choice of which technique to use in adding vectors depends on the application and is a matter of convenience. First we will discuss geometric vector addition. Since a vector is defined by its magnitude and direction, changing its location in our reference frame without changing its direction or magnitude leaves it the same vector. We are free to relocate a vector anywhere in our space where we find it convenient. To add vectors geometrically we just place the tail of one at the head of the other. The sum then is a vector from the tail of the first vector to the head of the last. Run the

28. Architecture & Arithmetic Group This page has moved to http//arith.stanford.eduIn one moment you'll be there . http://umunhum.stanford.edu/

This page has moved to http://arith.stanford.edu In one moment you'll be there....

29. Computer Arithmetic Algorithms Computer arithmetic Algorithms, 2nd Edition. Main features SecondEdition (pdf file). The Computer arithmetic Algorithms Simulator. http://www.ecs.umass.edu/ece/koren/arith/

Computer Arithmetic Algorithms, 2nd Edition by Israel Koren Published by: A. K. Peters , Natick, MA, 2002 ISBN 1-56881-160-8 The table of contents and main features - GIF file or PostScript file Main features - Second Edition (pdf file) The Computer Arithmetic Algorithms Simulator A review of the 1st edition of the book from IEEE Computer Magazine Solutions to selected problems (Chapters 1 - 10) (PostScript file) (PDF version) Solutions to almost all the problems (For instructors only: You should contact the publishers to get your password) Transparency masters for the book Relevant links koren@euler.ecs.umass.edu Last updated February 8, 2002

30. Computer Arithmetic Algorithms Simulator A companion website to the book Computer arithmetic Algorithms byIsrael Koren. About this site. THE ALGORITHMS Addition Ripple http://www.ecs.umass.edu/ece/koren/arith/simulator/

A companion website to the book " Computer Arithmetic Algorithms " by Israel Koren. About this site. THE ALGORITHMS: Addition Ripple-Carry Addition Manchester Adder Carry-Look-Ahead Adder Ling's Adder ... Hybrid Adder (Lynch and Swartzlander) Multiplication Sequential Booth's Algorithm Modified Booth's Algorithm Two's Complement Array Multiplier ... Fused Multiplier-Adder Division Restoring Non-Restoring SRT Radix-2 SRT Radix-4 ... By Reciprocation Square Root Restoring Non-Restoring SRT Radix-2 SRT Radix-4 ... By convergence Floating-Point Arithmetic Addition and Subtraction Multiplication and Division Division by Convergence Error Analysis Elementary Functions Exponential Logarithmic Trigonometric Inverse Tangent Unconventional Number Systems SD Addition and Subtraction Residue Addition and Multiplication Sign-Log Arithmetic Operations Miscellaneous Wallace Carry-Save Tree Overturned Stairs Carry-Save Tree Radix Conversion Last modified August 22, 2002 Send questions and comments to koren@euler.ecs.umass.edu

31. Modular Arithmetic Clock arithmetic. Clock (or modular) arithmetic is arithmetic you doon a clock instead of a number line. A useful shortcut. arithmetic. http://www.math.csusb.edu/faculty/susan/number_bracelets/mod_arith.html

Clock Arithmetic Clock (or modular ) arithmetic is arithmetic you do on a clock instead of a number line. On a 12-hour clock, there are only 12 numbers in the whole number system. However, every number has lots of different names. For example, the number before 1 is 0, so 12=0 on a 12-hour clock. If you don't have a java-enabled browser, you won't be able to see this applet. Here is a 12-hour clock showing several of the names for each number. Clock arithmetic has negative numbers, but each negative number has a positive number name. If you don't have a java-enabled browser, you won't be able to see this applet. Usually people decide on one set of standard names for the numbers on the clock, and they usually start with 0, not 1. So let's use for the standard names on the 12-hour clock. Find the standard names for these numbers on a 12-hour clock. Try to find shortcuts to save work. Answers. A useful shortcut. Arithmetic In clock arithmetic, you can add, subtract, and multiply; you can divide by some numbers. Addition and subtraction Addition and subtraction work the same as on a number line. For example, to add 9 and 7, start at 0, count 9 along the line, then count 7 more. You are at 16. If you count on a 12-hour clock, you will be at 4.

32. Modular Arithmetic Index Clock (Modular) arithmetic Pages. On these pages clock arithemtic. Otherpeople's web pages on clock arithmetic and secret codes. Chryzodes http://www.math.csusb.edu/faculty/susan/modular/modular.html

Clock (Modular) Arithmetic Pages On these pages you can learn about modular arithmetic, which is arithmetic on a circle instead of a number line. Some of these materials have been used with current and future teachers (elementary and middle school), and with actual kids as young as second grade. I hope that anyone who is interested in numbers can find something to learn from here. Explanations The short (well, medium length) version: What is clock arithmetic? [Coming soon] The long version: What is clock arithmetic? [Coming later] What is clock arithmetic good for? (Hint: just ask the National Security Agency. Also see the references below about RSA and PGP.) Tools A calculator for renaming numbers on a clock. A calculator for arithmetic (+, -, x) on a clock. [Coming soon] A calculator for dividing on a clock. [Coming soon] A calculator for exponentiation on a clock. An encoder for secret message"code.html">encoder for secret messages encoded/decoded using clock arithmetic. [Coming soon] A decoder for secret messages. Activities Number bracelets: a game/activity that is based on clock arithemtic.

33. Main Site http://www.arithmetic.com/

34. Jones On Arithmetic arithmetic Tutorials. http://www.cs.uiowa.edu/~jones/bcd/

Arithmetic Tutorials by Douglas W. Jones T HE U ... Department of Computer Science Index BCD Arithmetic on Binary Machines Division by Reciprocal Multiplication Binary to Decimal Conversion These tutorials are characterized by an interest in doing arithmetic on machines with just binary add, subtract, logical and shift operators, making no use of special hardware support for such complex operations as BCD arithmetic or multiplication and division. While some of these techniques are old, they remain relevant today. Last Modified:Wednesday, 18-Sep-2002 14:19:07 CDT.

35. Frege's Logic, Theorem, And Foundations For Arithmetic Stanford Encyclopedia article on Frege's work on the foundations of mathematics.Category Science Math History People Frege, Gottlob......Frege's Logic, Theorem, and Foundations for arithmetic. Frege formulatedtwo distinguished formal systems and used these systems http://plato.stanford.edu/entries/frege-logic/

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A B C D ... Z content revised JAN Frege's Logic, Theorem, and Foundations for Arithmetic Frege formulated two distinguished formal systems and used these systems in his attempt both to express certain basic concepts of mathematics precisely and to derive certain mathematical laws from the laws of logic. In his Begriffsschrift of 1879, he developed a second-order predicate calculus and used it both to define interesting mathematical concepts and to state and prove mathematically interesting propositions. However, in his Grundgesetze der Arithmetik of 1893/1903, Frege added (as an axiom) what he thought was a distinguished logical proposition (Basic Law V) and tried to derive the fundamental theorems of various mathematical (number) systems from this proposition. Unfortunately, not only did Basic Law V fail to be a logical proposition, but the resulting system proved to be inconsistent, for it was subject to Russell's Paradox. Although the inconsistency in Frege's Grundgesetze is widely known, it is not very well known that a deep theoretical accomplishment can be extracted from his work. The

36. Untitled arithmetic Coding + Statistical Modeling = Data Compression. Part 1 arithmeticCoding. arithmetic Coding + Statistical Modeling = Data Compression. http://dogma.net/markn/articles/arith/part1.htm

Arithmetic Coding + Statistical Modeling = Data Compression Part 1 - Arithmetic Coding by Mark Nelson Dr. Dobb's Journal February, 1991 This page contains my original text and figures for the article that appeared in the February, 1991 DDJ. The article was originally written to be a 2 part feature, but was cut down to 1 part. Links to Part 2 are here and at the end of the article. Arithmetic Coding + Statistical Modeling = Data Compression Part 1 - Arithmetic Coding by Mark Nelson Most of the data compression methods in common use today fall into one of two camps: dictionary based schemes and statistical methods. In the world of small systems, dictionary based data compression techniques seem to be more popular at this time. However, by combining arithmetic coding with powerful modeling techniques, statistical methods for data compression can actually achieve better performance. This two-part article discusses how to combine arithmetic coding with several different modeling methods to achieve some impressive compression ratios. The first part of the article details how arithmetic coding works. The second shows how to develop some effective models that can use an arithmetic coder to generate high performance compression programs. Terms of Endearment Data compression operates in general by taking "symbols" from an input "text", processing them, and writing "codes" to a compressed file. For the purposes of this article, symbols are usually bytes, but they could just as easily be pixels, 80 bit floating point numbers, or EBCDIC characters. To be effective, a data compression scheme needs to be able to transform the compressed file back into an identical copy of the input text. Needless to say, it also helps if the compressed file is smaller than the input text!

37. The Arithmetic Properties Of Binomial Coefficients Activated text by Andrew Granville.Category Science Math Number Theory......The arithmetic Properties of Binomial Coefficients. Andrew GranvilleDepartment of Mathematics University of Georgia Athens, GA. http://www.cecm.sfu.ca/organics/papers/granville/

The Arithmetic Properties of Binomial Coefficients Andrew Granville Department of Mathematics University of Georgia Athens, GA Math activated text Other available formats Related links ... Author biography Abstract: 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 see Dickson). They discovered a variety of elegant and surprising Theorems which are often easy to prove. In this article we shall exhibit most of these results, and extend them in a variety of ways.

38. Announcement - Arithmetic CD Basic K8 arithmetic lessons with explanations, interactive practice, and challenge games.Category Science Math Education Software......arithmetic CD. Order Online or use Mail Order The arithmetic CD contains over 1700basic arithmetic lessons for Kindergarten through 8th grade level students. http://www.aaamath.com/cd/

Arithmetic CD Order Online or use Mail Order The Arithmetic CD contains over 1700 basic arithmetic lessons for Kindergarten through 8th grade level students. All of the lessons have an explanation, interactive practice, and challenge games. The CD is available to be shipped worldwide. Bonus!! The CD contains a light colored version of all the pages in addition to the brighter colored pages. All of the lessons are the same, just the page backgrounds are lighter or more brightly colored. This helps greatly with some computer monitors that have an especially bright screen. Each lesson page on the CD has a "Report Totals" button that provides a summary of the number of problems completed and the scores. The CD also has a progress report form for each grade to record practice and improvements. Each of the two versions on the CD contains approximately 1700 pages of interactive math lessons. The lessons are arranged into grades (K-8) and into math topic areas (e.g. fractions). A table listing the number of lessons in each category can be found here. The lessons on the CD consist of interactive html files and require a web browser to operate. The CD and lessons are compatible with Windows 3.1, 95, 98, NT, ME and 2000

39. Algfront A personal view of algebra and its relationship to economics.Category Science Math Algebra High School......(DIGITALLY) ALGEBRA IS arithmetic BACKWARDS FOR INHERITANCE, FIDUCIARIES, MEASURES,OPTIMIZATION, TOPOLOGY, HISTORY, LIFE, ALL BACKWARD PROJECTS. http://members.fortunecity.com/jonhays/algfront.htm

web hosting domain names email addresses marketplace ... DIGITALLY ALGEBRA IS ARITHMETIC BACKWARDS FOR INHERITANCE, FIDUCIARIES, MEASURES, OPTIMIZATION Life can only be understood backwards, but must be lived forward Kierkegaard. (Algebra trains us in Math without cheating or weirdness! ONLY this thesis connects the dots: ARITHMETIC ALGEBRA LIFE. Prove otherwise!) Y'ALL.COM [Today] production workers must know math", L. Thurow, MIT Economist READ ME HEED ME BESTMATH ... domain names Powered by Ampira

40. Mental Arithmetic Memory, mental arithmetic and mathematics. Other mathematicians who have exhibitedgreat powers in mental arithmetic include Ampere, Hamilton and Gauss. http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Mental_arithmetic.html

Memory, mental arithmetic and mathematics Alphabetical list of History Topics History Topics Index All the mathematicians whose biographies are given in our archive exhibited extraordinary mental powers. In this article we look at a few mathematicians who have shown extraordinary powers of memory and calculating. We also look at a number of people who had no mathematical skills, usually no education, yet were able to display feats of mental arithmetical skills which astounded their contemporaries and today still astound us. First we mention John Wallis whose calculating powers are described in [2]:- [Wallis] occupied himself in finding (mentally) the integral part of the square root of 3 x 10 ; and several hours afterwards wrote down the result from memory. This fact having attracted notice, two months later he was challenged to extract the square root of a number of digits; this he performed mentally, and a month later he dictated the answer which he had not meantime committed to writing. This, although quite remarkable, is rather typical of the feats we shall describe in this article. It is the combination of exceptional memory and calculating ability which seems to combine in many of those we consider. However, in one respect Wallis is very different from others we describe in that he was 53 years old when he performed the above feats. Most of the others we describe were at the height of their powers when young children, often around 10 years of age.

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