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 Arithmetic:     more books (100)

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1. 4th Using Win32Forth For Graphics And Parallel Arithmetic.
http://home.wxs.nl/~josv/

2. Things Of Interest To Number Theorists
two groups. arithmetic and geometry of the curve 1+y^3 = x^4 (with MJ Klassen), Acta arithmetica, (74), 1996, 241257. This paper
http://math.scu.edu/~eschaefe/nt.html

Extractions: Here is a list of my papers followed by postscript files of eight lectures. 2-descent on the Jacobians of hyperelliptic curves, Journal of Number Theory, (51), 1995, 219-232. Class groups and Selmer groups, Journal of Number Theory, (56), 1996, 79-114. This paper gives bounds on the index of the intersection of a Selmer group and a quotient of the dual of part of a class group in each of the two groups. Arithmetic and geometry of the curve 1+y^3 = x^4 (with M.J. Klassen), Acta Arithmetica, (74), 1996, 241-257. This paper shows that the set of Weierstrass points (the flexes) is the same as the set of rational points over the field Q(zeta_12) and is a torsion packet. It also finds the bitangents to this curve and bases for the 2- and 3-torsion of the Jacobian. A simplified Data Encryption Standard algorithm, Cryptologia, (20), 1996, 77-84. This paper gives a method of explaining the DES algorithm to a cryptography class. Computing a Selmer group of a Jacobian using functions on the curve, Mathematische Annalen, (310), 1998, 447-471. This paper gives a general algorithm for finding Selmer groups for the Jacobians of curves. It includes discussions of the assumptions such algorithms seem to be based on. The Selmer group is for an isogeny, over a number field, from an abelian variety to the Jacobian of a curve where the kernel of the isogeny is killed by a power of a prime. Explicit descent for Jacobians of cyclic covers of the projective line (with B. Poonen), Journal fuer die Reine und Angewandte Mathematik, (488), 1997, 141-188. This paper gives an algorithm for finding the 1-zeta_p Selmer group for the Jacobian of a curve y^p = f(x).

3. Welcome To U C MAS
Offers courses using the ancient device of China namely Abacus physically as well as an imaginary abacus in the children , aged 4 12 years, to calculate the answer in Addition, Subtraction, Multiplication Division problems very accurately and speedily.
http://www.ucmasindia.com/

4. Surfing The Net With Kids: Arithmetic-24 Game
Surfing the Net with Kids educational website reviews for families and teachers Click for Menu ~~ Home ~~ Light a Fire Quotations
http://www.surfnetkids.com/games/math-24.htm

Extractions: ...Click for Menu... ~~ Home ~~ Light a Fire Quotations How to Add Games Email Book Clubs Book Store Calendar Blog Free Web Content Games Jokes Newsletters Postcards Printables Screensavers Suggest a Site Tell a Friend Top Ten Pages Topic Directory ~~ Search this Site Arts, Crafts, Music Computers, Internet Hobbies, Sports Geography Holidays, History Language Arts Math Parents, Teachers Pre-K and K Science, Animals Link to Us From my Mailbox My Bio Ad Rates Write Me Visit My Office Email this game to a friend with a personal message

5. Randomness In Arithmetic
Randomness in arithmetic. Scientific American 259, No. 1 (July 1988), pp. 8085. by Gregory J. Chaitin. It is impossible to prove whether
http://www.cs.auckland.ac.nz/CDMTCS/chaitin/sciamer2.html

Extractions: It is impossible to prove whether each member of a family of algebraic equations has a finite or an infinite number of solutions: the answers vary randomly and therefore elude mathematical reasoning. What could be more certain than the fact that 2 plus 2 equals 4? Since the time of the ancient Greeks mathematicians have believed there is little-if anything-as unequivocal as a proved theorem. In fact, mathematical statements that can be proved true have often been regarded as a more solid foundation for a system of thought than any maxim about morals or even physical objects. The 17th-century German mathematician and philosopher Gottfried Wilhelm Leibniz even envisioned a ``calculus'' of reasoning such that all disputes could one day be settled with the words ``Gentlemen, let us compute!'' By the beginning of this century symbolic logic had progressed to such an extent that the German mathematician David Hilbert declared that all mathematical questions are in principle decidable, and he confidently set out to codify once and for all the methods of mathematical reasoning. This result, which is part of a body of work called algorithmic information theory, is not a cause for pessimism; it does not portend anarchy or lawlessness in mathematics. (Indeed, most mathematicians continue working on problems as before.) What it means is that mathematical laws of a different kind might have to apply in certain situations: statistical laws. In the same way that it is impossible to predict the exact moment at which an individual atom undergoes radioactive decay, mathematics is sometimes powerless to answer particular questions. Nevertheless, physicists can still make reliable predictions about averages over large ensembles of atoms. Mathematicians may in some cases be limited to a similar approach.

Palladio. The arithmetic Mean. let the room to be vaulted be twelve feet long and six broad; add six to twelve and it will make

Extractions: "....let the room to be vaulted be twelve feet long and six broad; add six to twelve and it will make eighteen, the half of which is nine; the vault ought therefor to be nine feet." In an Arithmetic Mean, the second amount exeeds the first by the same amount as the third exeeds the second, as in 2:3:4. Three exeeds two by the same amount that four exeeds three. Or, in Palladio's example:

7. Chisenbop Tutorial
A method of doing basic arithmetic using the fingers that is attributed to the Korean tradition.
http://klingon.cs.iupui.edu/~aharris/chis/chis.html

Extractions: Chisenbop is a method of doing basic arithmetic using your fingers. It is attributed to the Korean tradition, but it is probably extrememly old, as the soroban and abacus use very similar methods. Probably these other devices were derived from finger counting. The key to finger math is understanding how to count. The right hand stands for the values zero through nine. Each digit counts as one, and the thumb counts as five. Here's an illustration: As you can see, digits through four are pretty self explanatory. The thumb counts as five, so here's how to represent five through nine: The left hand represents multiples of ten, with the right thumb representing 50. Here's how the left hand works: Below is a place to practice your counting techniques. You can use it in a number of ways. Press the add 1, add 10, subtract 1, and subtract 10 buttons to see the various combinations. You can also enter in any two-digit value into the text box, hit the tab key, and the fingers will show that combination. left (tens) right (ones) Note that I showed the fingers either fully extended or completely hidden. Usually, finger counting is done against a table or other surface, and the finger is pressed against the surface to indicate it is 'on', or lifted to indicate 'off.' I have chosen this other representation just because it is more clear than looking carefully at pictures to determine if the fingers are touching the surface or not.

8. Affine Arithmetic Project
Affine arithmetic A CorrelationSensitive Variant of Interval arithmetic. Affine arithmetic (AA) is a self-validated model for numerical computation.
http://www.dcc.unicamp.br/~stolfi/EXPORT/projects/affine-arith/Welcome.html

Extractions: Affine arithmetic (AA) is a self-validated model for numerical computation. Like standard interval arithmetic (IA), it can provide guaranteed bounds for the computed results, taking into account input, truncation, and rounding errors. Unlike interval arithmetic, it keeps track of correlations between computed and input quantities, and is therefore resistant to the catastrophic loss of precision often observed in long interval computations. In affine arithmetic, a quantity x is represented as a first-degree ("affine") polynomial x0 + x1 e1 + x2 e2 + ··· + xk ek where x0, x1,... xk are known real numbers, and e1, e2,... ek are dummy variables, whose value is only known to be in [-1 .. +1]. Each dummy variable ei represents some source of uncertainty or error in the quantity x - which may come from input data uncertainty, formula truncation, arithmetic rounding, etc. A dummy variable that appears in two variables x, y

9. Source Codes Of N.Tajima's Fortran Benchmark Tests (ver.2)
Codes to time floating point and integer arithmetic, intrinsic functions, and random access to memory.
http://serv.apphy.fukui-u.ac.jp/~tajima/bench/source_e.html

Extractions: Japanese page matvec.f #lines : 58 , Arrays : real*8 h(1023,1023) (8.0MB) This program repeats 6,000 times a multiplication of a double-precision real matrix of dimension 1023 x 1023 to a double-precision real vector of dimension 1023. The number of repetitions of 6,000 is determined as 6000 = NSOL x ITER, where NSOL is defined to be 3 in line No. 9 and ITER is defined to be 2000 in line No. 10 of the source code. If you find the CPU time to be too long or too short for measurement purpose, change the value of ITER. The CPU time changed in proportion to ITER. The matrix is symmetric. The program shows the largest three eigenvalues of the matrix. The precision is not guaranteed because this is a program for a bench-mark test. matvecz.f #lines : 66 , Arrays : complex*16 h(723,723) (8.0MB) This program is a Complex*16 version of matvec.f. The dimension of the matrix is reduced to 723 x 723 so that the size of array is roughly unchanged. The number of multiplications of a matrix to a vector is also reduced to 3000. The matrix is hermite. The program shows the largest three eigenvalues of the matrix. The precision is not guaranteed.

10. Arithmetic
arithmetic. This is a draft version of a text on arithmetic at undergraduate/early graduate level. Chapter 5. arithmetic functions. 5.1.
http://www.mth.uea.ac.uk/arithmetic/

11. ARIBAS By O. Forster
An interactive interpreter for big integer and multiprecision floating point arithmetic with a Pascal/Modula like syntax. It has several builtin functions for algorithmic number theory.
http://www.mathematik.uni-muenchen.de/~forster/sw/aribas.html

Extractions: ARIBAS is an interactive interpreter for big integer arithmetic and multi-precision floating point arithmetic with a Pascal/Modula like syntax. It has several builtin functions for algorithmic number theory like gcd, Jacobi symbol, Rabin probabilistic prime test, factorization algorithms (Pollard rho, continued fraction, quadratic sieve), etc. NEW in Version 1.45: Elliptic curve factorization (function ec_factorize),

12. University Of Michigan And Michigan State University Arithmetic Seminar
The University of Michigan and Michigan State University arithmetic Seminar 200304 Monday 300pm-430pm, 4096 East Hall, U of M.
http://www.math.lsa.umich.edu/seminars/arithmetic/

Extractions: 2003-04: Monday 3:00pm-4:30pm, 4096 East Hall, U of M The seminar is run jointly by Brian Conrad, George Pappas, Chris Skinner, and Kannan Soundararajan. For more information contact us at bdconrad@umich.edu pappas@math.msu.edu cskinner@umich.edu , and ksound@umich.edu respectively. [Note: the technology for this page was shamelessly stolen from the Algebraic Geometry page, which was designed by Pasha Belorousski and subsequently stolen by every algebraic geometry web page in the country.] DATE and TIME SPEAKER TITLE Sept 8

13. Number Theory At The University Of Georgia
Number Theory and arithmetic Geometry Group. Members, seminars.
http://www.math.uga.edu/~lorenz/Number_Theory_Group.html

Extractions: Number Theory and Arithmetic Geometry Group William Alford Associate Professor, Ph.D. Tulane, 1963. Factoring and other number theory problems by computer. Matthew Baker Assistant Professor, Ph.D. U.C. Berkeley, 1999. Galois actions on torsion points. Modular curves and their Jacobians. Discreteness problems for arithmetic heights. Linear series and vector bundles in characteristic p. Arithmetic of curves and their Jacobians. Sybilla Beckmann Associate Professor, Ph.D. U. Penn., 1986. Galois theory. The inverse galois problem, that is, to determine whether every finite group is the galois group of some extension of the rational numbers. Arithmetic information on branched coverings, such as fields of definition. Tilings of the plane. Mathematics education. Andrew Granville Barrow Professor, Ph.D. Queens,1987. Distribution of primes. Sieving intervals. Distribution of `smooth' numbers. Properties of binomial coefficients. Cyclotomic fields. Carmichael numbers. Exponential sums. Integer solutions to Diophantine equations. Binary quadratic forms and the elementary theory of elliptic curves. Questions related to factoring and primality testing. Symbolic computation and `computing by homomorphisms'. Computational complexity, particularly lower bounds. Power series and the combinatorics of coefficients. Counting lattice points.

14. GALOIS THEORY And ARITHMETIC, Bonn, 1-4 June 2004
Galois Theory and arithmetic Bonn, 1 4 June 2004. home. organizers, contact. registration. program. GALOIS THEORY and arithmetic. Bonn 2004, June 1 - June 4.
http://www.math.uni-bonn.de/people/gata/

15. Arithmetic Calculator
When in doubt, punch it out! Other Calculators. Recommend This Calculator! Lessons, Forums, Homework, Puzzles, Newsletter, Advertise, Search.
http://www.mathgoodies.com/calculators/calculator.htm

16. Math Worksheets, Puzzles, Printables, Problems, Test Prep
Over 5000 free printable worksheets categorized by grades. Includes practice sheets for algebra, arithmetic, fractions, decimals, and sequences.
http://www.edhelper.com/math.htm

Extractions: Place Value Whole Numbers Addition Subtraction Multiplication Division by 1-Digit Division by 2-Digits Order of Operations (positive whole numbers) Understand Decimals (Part 1) Understand Decimals (Part 2) Add and Subtract Decimals Multiply Decimals Divide Decimals Beginning Algebra Number Theory Fractions Measurement Integers Ratios and Proportional Reasoning Percents Perimeter, Circumference, and Area Volume and Surface Area Decimals Inequalities Probability

17. VHDL Library Of Arithmetic Units
VHDL Library of arithmetic Units. MICROSWISS Project TREZ-001 Reto Zimmermann Lecture on Computer arithmetic. Abstract. A lecture
http://www.iis.ee.ethz.ch/~zimmi/arith_lib.html

Extractions: VHDL Library of Arithmetic Units A comprehensive library of arithmetic units written in synthesizable VHDL code has been developed. The library contains components for a variety of arithmetic operations and for different speed requirements. The library components are implemented as circuit generators in parameterized structural VHDL code. Their modular and well-documented source code allows for simple usage and easy customization. Highly efficient circuit architectures are used, which are optimized for synthesis and cell-based design. The VHDL library is platform independent, and it provides circuits with comparable performance, but higher flexibility and a larger diversity of arithmetic operations compared to commercial data path libraries.

18. Calculator-in-the-URL: Help
Web application that evaluates arithmetic expressions embedded in a URL.
http://x42.com/help_urlcalc/

Extractions: The urlcalculator demonstrates the weirdest URL-tricks. YOU change the hostname to the function and arguments you want; and you get the result on the homepage of the site. Basic function implemented: sum adds arguments; example: http://\$sum(1,2,-33,4).x42.com will sum 1,2,-33,4 and print the result. (alias: add) diff subtracts arguments example: http://\$diff(1,2.3).x42.com will subtract 2.3 from 1 and print the result. (alias: sub) mul multiplies arguments example: http://\$mul(2,17,4711).x42.com will multiply 2 by 17 by 4711 and print the result. div divides arguments example: http://\$div(1,7).x42.com will divide 1 by 7. mod moduloates(?) arguments example: http://\$mod(11147,42).x42.com will divide 11147 by 42 and print the remainder. mean computes the mean value of the arguments example: http://\$mean(1,2,3,4,17).x42.com max returns the largest value example: http://\$max(1,-2,3,17).x42.com min returns the smallest value example: http://\$min(1,-2,3,17).x42.com

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

Extractions: 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 :- [Wallis] occupied himself in finding (mentally) the integral part of the square root of ; 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.

20. Math Forum: 2002 Mathematics Game
A contest where the contestants have to write all integers from 1 to 100 using only the digits 2,0,0,2 and arithmetic operations.
http://mathforum.org/~judyann/2002/

Extractions: For many years mathematicians, scientists, engineers and others interested in mathematics have played "year games" via e-mail and in newsgroups. We don't always know whether it is possible to write expressions for all the numbers from 1 to 100 using only the digits in the current year, but it is fun to try to see how many you can find. This year may prove to be a challenge. As with many games, the rules for the Year Game can vary slightly. Teachers may wish to use different rules in their own classrooms. This Web page is intended for students in grades three through twelve with a general knowledge of mathematics. ^ (raised to a power), sqrt (square root), and ! (factorial), along with grouping symbols, to write expressions for the counting numbers 1 through 100. This year we will also allow the use of decimal points and double-digit numbers. Please read and follow the rules carefully if you wish to have your solutions posted on this site. Teachers may print out worksheets for students to record their findings, or may print sheets of

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