161. The Arithmetic Properties Of Binomial Coefficients The arithmetic Properties of Binomial Coefficients. Andrew Granville Department 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.

162. Vectors Explanations notations, arithmetic operations, rules and the relationship to Cartesian graphs. http://www.physics.uoguelph.ca/tutorials/vectors/vectors.html

Vectors In this tutorial we will examine some of the elementary ideas concerning vectors. The reason for this introduction to vectors is that many concepts in science, for example, displacement, velocity, force, acceleration, have a size or magnitude, but also they have associated with them the idea of a direction. And it is obviously more convenient to represent both quantities by just one symbol. That is the vector Graphically, a vector is represented by an arrow, defining the direction, and the length of the arrow defines the vector's magnitude. This is shown in Panel 1. . If we denote one end of the arrow by the origin O and the tip of the arrow by Q. Then the vector may be represented algebraically by OQ. Panel 1 This is often simplified to just . The line and arrow above the Q are there to indicate that the symbol represents a vector. Another notation is boldface type as: Q Note, that since a direction is implied, . Even though their lengths are identical, their directions are exactly opposite, in fact OQ = -QO The magnitude of a vector is denoted by absolute value signs around the vector symbol: magnitude of The operation of addition, subtraction and multiplication of ordinary algebra can be extended to vectors with some new definitions and a few new rules. There are two fundamental definitions.

163. Software Implementing Arithmetic Coding Software Implementing arithmetic Coding. This page points to software written in C that implements various versions of arithmetic coding. http://www.cs.toronto.edu/~radford/ac.software.html

Software Implementing Arithmetic Coding This page points to software written in C that implements various versions of arithmetic coding. The most recent version that I have been involved with is described in the following paper: Moffat, A., Neal, R. M., and Witten, I. H. (1995) ``Arithmetic coding revisited'', ACM Transactions on Information Systems , vol. 16, pp. 256-294: abstract associated reference You can get software implementing the method described in this paper from this web page The old ``CACM'' arithmetic coding software, as published in the following tutorial: Witten, I. H., Neal, R. M., and Cleary, J. G. (1987) ``Arithmetic coding for data compression'', Communications of the ACM , vol. 30, pp. 520-540. is available as a tar archive An adaptation of the CACM software to low-precision arithmetic (as described in ``Arithmetic coding revisted'') is also available [first released 8 July 1991, last updated 19 May 1993]: documentation tar archive Back to Radford Neal's home page

164. Open-Source Software Codes by Richard Brent for multiple precision arithmetic, uniform and normal random number generators, irreducible/primitive trinomials, and parallel sorting. http://web.comlab.ox.ac.uk/oucl/work/richard.brent/software.html

Open-Source Software Here are some links to software which is available (free, but with absolutely no warranty), in most cases as open-source software under the GNU General Public License The multiple precision arithmetic package MP Uniform and normal random number generators Programs related to irreducible/primitive trinomials A program for parallel sorting Some other software which I wrote a long time ago (e.g. for zero-finding and minimization) is available from Netlib (just search for Brent). Return to Richard Brent's index page

165. Larry's Ramblings Paint Shop Pro Image arithmetic. Many of the things that you can do with image arithmetic can be done more easily using layer capabilities. http://wolves.dreamhost.com/web/arith/ar.html

Home Web Top Bottom ... Next Paint Shop Pro Image Arithmetic The "Image Arithmetic" capability of Paint Shop Pro lets you combine two images into one using various arithmetic computations on the colors between the two images. This tutorial explains how image arithmetic works, and gives some examples of how you might use it. I put this tutorial together back in the days of PSP 4, and many of the examples I have here can be done more easily using newer feature of PSP. Table of Contents Introduction Addition and Average Description Effect of divisor Effect of bias Example 1: Clashing images Part 1 Part 2 (Clipped, bias) Part 3 (Unclipped, bias) Example 2: Reflection ... Example 4: Planet Subtraction and Difference Subtraction and Difference Example - Capitol Multiplication Multiplication Example - Mt. Rushmore Lightest and Darkest Lightest and Darkest Example - Polar Bears Example - A Change of Scenery AND and OR AND and OR Example Example Final Exam Your Final Exam Home Web Top ... Next

166. Shamus Software Ltd - MIRACL Multiprecision Integer and Rational arithmetic C/C++ Library. http://indigo.ie/~mscott/

Shamus Software Ltd M ultiprecision I nteger and R ational A rithmetic C /C++ L ibrary Latest version 4.82 - Itanium fully supported MIRACL is a Big Number Library which implements all of the primitives necessary to design Big Number Cryptography into your real-world application. It is primarily a tool for cryptographic system implementors. RSA public key cryptography, Diffie-Hellman Key exchange, DSA digital signature, they are all just a few procedure calls away. Support is also included for even more esoteric Elliptic Curves and Lucas function based schemes. The latest version offers full support for Elliptic Curve Cryptography over GF( p ) and GF(2 m ) - see the link below for more details. Less well-known techniques can also be implemented as MIRACL allows you to work directly and efficiently with the big numbers that are the building blocks of number-theoretic cryptography. Although implemented as a C library, a well-thought out C++ wrapper is provided, which greatly simplifies program development. Most example programs (25+ of them) are provided in both C and C++ versions. MIRACL now provides more support for conventional cryptography. The latest version implement the new Advanced Encryption Standard (AES), Modes of Operation, and the new hashing standards SHA-160/256/384/512.

167. Offers FREE Affordable Auto Insurance Policy To Consumers. Free Auto Quote; Free Life Quote; Free Home Quote; Free Health Quote; Other Insurance We want to help you find the best deal on affordable http://www.arithmeticstudios.com/

Free Auto Quote Free Life Quote Free Home Quote Free Health Quote ... Other Insurance We want to help you find the best deal on affordable auto insurance policy available. We have your affordable auto insurance policy and information. Global Insurance Guide is designed to deliver the best available affordable auto insurance policy from todays best affordable auto insurance policy carriers. By checking the affordable auto insurance policy of multiple insurers - you will have the best available selection and be in the position ot choose the best affordable auto insurance policy for you and your family. Welcome to Insurance-Guide! You have come to the webs most advanced affordable auto insurance policy system available. We are proud our developement team and our affordable auto insurance policy partners. We are confident you will find great benefit using our site for free affordable auto insurance policy while you shop for a new carrier.

168. Pure Maths At Durham Geometry and arithmetic Group. Members, meetings, preprints. http://fourier.dur.ac.uk:8000/pure/home.html

169. Early Algebra, Early Arithmetic : It includes many topics in arithmetic, such as the four operations, but it does so in novel ways. Consider the operation of addition. http://earlyalgebra.terc.edu/

Home Our Project Publications Class Materials Lesson Materials Available There are now lesson plans and student work sheets posted. Take a look. goto Posted by David Carraher on 10/10/02; 10:01:28 AM from the Planning dept. Discuss What Is Early Algebra ? Early Algebra is an approach to early mathematics teaching and learning. It includes many topics in arithmetic, such as the four operations, but it does so in novel ways. Consider the operation of addition. By second grade most students know how to add 3 to another number. But they probably have not been asked to consider expressions such as "n n +3", where n might refer to any number . As surprising as it may seem, we are finding that young learners from typical public schools can understand such expressions and use them to describe relations among numbers and quantities. In doing so they go beyond computational fluency: they begin to develop the ability to make mathematical generalizations using algebraic notation. Early algebra does not aim to increase the amount of mathematics students must learn. Rather, it is about teaching time-honored topics of early mathematics in deeper, more challenging ways. We have good reason to suspect that children who become familiar with algebraic concepts and tools from an early age and in meaningful contexts will do better in mathematics, regardless of the criteria used. Early Algebra is also an area of research. The research from our project and others should help to clarify what works and what does not work. But more importantly, it should help to clarify the issues young learners inevitably face when they attempt to apply their present modes of representation and reasoning to new circumstancesand to reconcile their prior knowledge and experience with new ideas and concepts being introduced in Mathematics classes. And it should help to identify fruitful types of learning activities for educators and curriculum developers.

170. Talking Arithmetic Tutor Free demo download shows students step by step solutions to addition, subtraction, multiplication and division problems. http://www.sssoftware.com/TalkingArithmeticTutor/index.html

Math Skill Builders: Talking Arithmetic Tutor Shortcuts to: Home Products Documentation Free Demos ... E-Mail Support Learn whole number arithmetic by watching step by step animated, spoken and visual tutorial instructions. Available for Windows, Macintosh 68k, and Power Macintosh. Description System Requirements Online Documentation Free Download! Registration $14.95 (US) Order Now! Boxed version $19.95 (US) Last Updated on February 4, 2002 by Chuck at SSSoftware.com

171. Clock Arithmetic Clock arithmetic Demonstration Set the number of hours on the clock with the slider control, then type in the number you want to http://www.wou.edu/~burtonl/arithclock.html

Clock Arithmetic Demonstration Set the number of hours on the clock with the slider control, then type in the number you want to add, subtract or multiply and press the appropriate button. The standard clock has the greatest hour on top. The zero clock has a zero on top. The tables in the upper right show addition and multiplication of the hours on the clock. The zero clock's tables are different from the standard clock's tables. Can you find any similarities? (Hint - Does zero on the zero clock behave like the top number on a standard clock?) You can use clock arithmetic to make quilt-like art. Click here to see how. Applet - enable java

172. Turn A Math Formula Into A Calculator With CalcExpress(tm) Includes arithmetic, mortgage and currency exchange processing features. Uses a dialog box and icons for input. http://www.calcexpress.com/

the math formula to calculate the monthly mortgage payment into a mortgage calculator The calculator pops up when you click on a tray icon, or press a key combination. The calculator gives you the monthly payment when you specify the exact amount, interest and duration of the loan. a payment graph when you specify a range of values for one parameter, e.g. interest rate between 6% and 7%. a two dim grid when you specify two ranges, e.g the interest rate between 6% and 7% and the duration 10 to 30 years. skins for details. create your own calculators on Windows platforms $39.95 (US) or $19.95 (US) All my products have a 30 day money back guarantee! by SoftwareMeister Gerberstr. 3, D78050 VS-Villingen, Germany, Voice: +49 (7721) 90107 Fax: +49 (7721) 90109 (central european time) If you work as a financial consultant you might be interested in other calculators as well: a savings calculator How much money to save each month to built up a treasure. a financing calculator How long does your treasure last if you need each month a certain amount. Compare with other tools For example the formula to calculate monthly payment for a loan (you see it in the screenshot above): Formulas like this are next to impossible to calculate with a common calculator. At least I can't imagine doing it.

173. The XR Exact Real Homepage This is an implementation of exact (or constructive) real arithmetic, including python and C++ versions. All internal arithmetic uses python s builtin longs. http://more.btexact.com/people/briggsk2/XR.html

2002 Jan 25 (Friday) 14:07 by Keith Briggs Current version: 2.0 Overview This is an implementation of exact (or constructive) real arithmetic, including python and C++ versions. It is an alternative to multiple-precision floating-point codes. An important distinction is that in multiple-precision floating-point one sets the precision before starting a computation, and then one cannot be sure of the final result. Interval arithmetic is an improvement on this, but still not an ideal solution because if the final interval is larger than desired, there is no simple way to restart the computation at higher precision. By constrast, in XR no precision level is set in advance, and no computation takes place until a final request takes place for some output. Python version Included in the package is python version with many transcendental functions. These could easily be translated and added to the C++ version. This code is intended to demonstrate ideas and algorithms for exact real arithmetic in python. All internal arithmetic uses python's built-in longs. Usage Just running the file XR.py will run some self-tests. For normal usage: "from XR import *".

174. PYTHABACUS.COM and instruction of using the ancient Pythagorean Abacus to do arithmetic....... http://www.pythabacus.com/

This pages includes animated demonstrations of arithmetic and fractions on the Pythagorean Abacus It uses frames if your Browser supports them.

175. Room 108 Arithmetic Cards Room 108 arithmetic Cards. This takes 1525 secs to load on slow modems. Click No solution to find the answer and I got the solution http://www.netrover.com/~3384mary/arithcard/arithcard.htm

Room 108 Arithmetic Cards By Huahai Yang and Jun Zheng This takes 15-25 secs to load on slow modems. Click: 'No solution' to find the answer and 'I got the solution' when you have an answer.Click card deck to try again. Watch the loading timer before you press a button. Return to Room 108

176. Wen-Chen Chi National Taiwan Normal University. Number theory, arithmetic algebraic geometry. http://math.ntnu.edu.tw/~wchi/EnglishPage.html

Wen-Chen Chi (Wenchen Chi) Professor of Mathematics National Taiwan Normal University Department of Mathematics 88, Sec.4, Ting-Chou Road, Taipei, Taiwan 117 Phone: (886)2-2931-2611 ext.315 Fax: (886)2-2933-2342 e-mail: wchi@math.ntnu.edu.tw wchi@cc.ntnu.edu.tw Brief CV Professor, 1996/8 - Present, National Taiwan Normal University Head, 1994/3 - 1996/7, Department of Mathematics, National Tsing Hua University Professor, 1991/8 - 1996/7, National Tsing Hua University Associate Professor, 1988/8 - 1991/7, National Tsing Hua university Lecturer, 1986/7 - 1988/6, University of Pennsylvania Ph.D., 1986/5, University of California, Berkeley B. Sc., 1977/7, National Taiwan Normal University Research Interests Number Theory, Arithmetical Algebraic Geometry Current Courses Abstract Algebra (undergraduate course) Algebra and Number Theory(senior-graduate course) Topics in Algebraic Curves (graduate course) Current Sponsered Project On Some Computations in Number Theory (NSC 89-2115-M-003-010, 2000/8 ~ 2001/7) Some Selected Publications Twists of Central Simple Algebras and Endomorphism Algebras of Some Abelian Varieties "

177. Distributed Arithmetic Distributed arithmetic isn t magic. Distributed arithmetic is a bit level rearrangement of a multiply accumulate to hide the multiplications. http://www.andraka.com/distribu.htm

Distributed Arithmetic isn't magic. Let's demystify it: Distributed arithmetic is a bit level rearrangement of a multiply accumulate to hide the multiplications. It is a powerful technique for reducing the size of a parallel hardware multiply-accumulate that is well suited to FPGA designs. It can also be extended to other sum functions such as complex multiplies, fourier transforms and so on. Look at my Radar on a chip paper for an application example of distributed arithmetic. The Derivation: In most of the multiply accumulate applications in signal processing, one of the multiplicands for each product is a constant. Usually each multiplication uses a different constant. Using our most compact multiplier, the scaling accumulator , we can construct a multiple product term parallel multiply-accumulate function in a relatively small space if we are willing to accept a serial input. In this case, we feed four parallel scaling accumulators with unique serialized data. Each multiplies that data by a possibly unique constant, and the resulting products are summed in an adder tree as shown below. If we stop to consider that the scaling accumulator multiplier is really just a sum of vectors, then it becomes obvious that we can rearrange the circuit.

178. The Largest Known CPAP's The top 10 k consecutive primes in arithmetic progression for each k. http://hjem.get2net.dk/jka/math/cpap.htm

The Largest Known CPAP's This page keeps the 10 largest and the smallest known CPAP-k for each k. CPAP-k is short for k Consecutive Primes in Arithmetic Progression. Introduction Submissions The largest known CPAP-10 The largest known CPAP-9 ... Other pages Introduction Example: 41 + 6n for n = 0, 1, 2, 3 gives the AP-4 41, 47, 53, 59. A CPAP-k is an AP-k where the k primes are consecutive, i.e. there are no other primes between them (CPAP can mean many other things). 41, 47, 53, 59 is not CPAP-4 because 43 is also prime. However 47, 53, 59 is CPAP-3. A CPAP-k search often has two parts: Find an AP-k and then test whether the k primes are consecutive. If the difference between the primes is small then it is sometimes possible to make sure in advance that all intermediate numbers will be composite. Avoiding intermediate primes in a CPAP-k becomes harder when the prime difference is big, so many searches only tries for difference k#. A CPAP-6 has minimal difference 6# = 30 which is low in this context. CPAP-7 to -10 all have minimal difference 10# = 7# = 210 which makes it harder.

179. Www.nsa.gov8080/programs/mepp/esarith.html activeThe arithmetic of Active Management. William F. Sharpe. This proves assertion number 1. Note that only simple principles of arithmetic were used in the process. http://www.nsa.gov:8080/programs/mepp/esarith.html

180. V. Vatsal's Homepage University of British Columbia. arithmetic of elliptic curves, Lfunctions. Papers and preprints. http://www.math.ubc.ca/~vatsal/

Vinayak Vatsal University of British Columbia Department of Mathematics Vancouver, BC V6T 1Z2 CANADA office: Room 234, Mathematics Building phone: fax: Office Hours: Wednesday 1-3. Math 313 Homepage A few links: Some of my papers and preprints The Langlands Project (edited by Bill Casselman The NUMDAM project Gary Gray's Macintosh TeX/LaTeX page Some reasons why I like Vancouver

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