41. Randomness In Arithmetic Randomness in arithmetic. He showed that Gödel's incompleteness theorem is equivalentto the assertion that there can be no general method for systematically http://www.cs.auckland.ac.nz/CDMTCS/chaitin/sciamer2.html

Randomness in Arithmetic Scientific American 259, No. 1 (July 1988), pp. 80-85 by Gregory J. Chaitin 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.

42. General Arithmetic Paper.1. Question 1 For Year 1997 Leaving Cert Ordinary Level Maths. general arithmetic Paper.1. Question1 for Year 1997 . Q.1. (a) A machine broke down at 0935 hours. http://homepage.tinet.ie/~mathsireland/arith_q1_p1_y1997.html

Leaving Cert Ordinary Level Maths General Arithmetic Paper.1. Question 1 for Year 1997 Q.1. (a) A machine broke down at 0935 hours. It was repaired at 1210 hours. For how many hours and minutes was the machine out of order. Ans : From 0935 until 1210 = 2 hrs 35 mins. (b) IR£2500 was invested for three years at Compound interest. The rate of interest was 4% per annum for the 1st year and 3% for the 2nd year. (i) Calculate the amount of the investment after two years. Ans : Interest at end of year 1 = £2500 * 4/100 = £100 Amount at beginning of year 2 = £2600 Interest at end of year 2 = £2600 * 3/100 = £78 Amount at end of year 2 = £2678 (ii) If the investment amounted to IR£2744.95 after 3 years, calculate the rate of interest for the third year. Ans : Interest for 3rd year = £2744.95 - £2678 = £66.95

43. General Arithmetic Paper.1. Question 1 For Year 1998 Leaving Cert Ordinary Level Maths. general arithmetic Paper.1. Question1 for Year 1998 . Q.1. (a) When a cyclist had travelled a http://homepage.tinet.ie/~mathsireland/arith_q1_p1_y1998.html

Leaving Cert Ordinary Level Maths General Arithmetic Paper.1. Question 1 for Year 1998 Q.1. (a) When a cyclist had travelled a distance of 12.6kms he had completed 3/7 of his journey. What was the length of the journey ? Ans : If 12.6kms = 3/7 of the journey, then 4.2kms = 1/7 of the journey. => 7 * 4.2kms = 7/7 of the journey. => 29.4 kms = length of the journey. (b) (i) At what rate of interest will IR£2000 amount to IR£2065 after one year ?. Ans : Interest at end of year 1 = £65 => Interest Rate = ( 65 / 2000 ) * 100 => Interest Rate = 3.25% (ii) Divide 357 grammes in the ratio 1/2 : 1/4 : 1 . Ans : Ratios = 1/2 : 1/4 : 1 = 2 : 1 : 4 => There are 7 parts => One part = 357 / 7 = 51 => Ratios are ( 2 * 51 ) : ( 1 * 51 ) : ( 4 * 51 ) => Ratios are 102 : 51 : 204 (c) A supplier agrees to buy 300 computer parts for 1060 DM each.

44. Interval Arithmetic next up previous Next An Example Up A few plausible general PreviousA few plausible general. Interval arithmetic. Instead of the http://www.cs.berkeley.edu/~fateman/fp98/korenA/node6.html

Next: An Example Up: A few plausible general Previous: A few plausible general Interval Arithmetic Instead of the conventional representation of a real number by an approximation: the nearest exact floating-point number, represent a real number by TWO fp numbers: a lower and an upper bound. A large body of literature with many variations has emerged on numerical computing with real intervals. This describes operations on such numbers (+,*,/, and more elaborate ones such as elem. transcendental functions, Newton iteration-based root-finding, etc. are possible.) Sample rules: [a,b] + [c,d] = [a+c, b+d] [a,b] * [c,d] = [ min(a*c, a*d, b*c, b*d), max(a*c, a*d, b*c, b*d)] To do this right, in the lower bound calc. we round all ops ToNEGV, and in the upper bound calc., round all ops ToPOSV. Careful programs can produce results with guaranteed [but rarely tight] error bounds. We are in an era when a factor of 4 or even 10 in speed and a factor of 2 in memory may be a fair trade for some assurance that the result is not totally bogus. Aside: Can you simulate rounding modes without hardware support? If you assumed that all operations were accurate to within 1/2 ULP, then one could ``round directionally after the fact'' by taking the nearly correct answer and adding or subtracting 1 ULP, thereby getting a lower or upper bound for sure. This is slow and not a good idea for interval arithmetic.

45. A Few Plausible General Reasons next up previous Next Interval arithmetic Up Why bother? Previous On Principle.A few plausible general reasons. (i) investigating numerical instability (cf. http://www.cs.berkeley.edu/~fateman/fp98/korenA/node5.html

Next: Interval Arithmetic Up: Why bother? Previous: On Principle A few plausible general reasons (i) investigating numerical instability (cf. Javahurt p 57 et seq), (ii) running various programs (cf. Borneo spec. polynomial evaluation) that make sense rounding up and down. and (iii) interval arithmetic, discussed below. Interval Arithmetic An Example Richard J. Fateman Wed Aug 12 22:44:29 PDT 1998

46. Surface Evolver Documentation - General Syntax Both the datafile and user commands follow a common general syntax describedin this file, with a few differences as noted. arithmetic expressions. http://www.susqu.edu/facstaff/b/brakke/evolver/html/syntax.htm

Surface Evolver Documentation Surface Evolver syntax Both the datafile and user commands follow a common general syntax described in this file, with a few differences as noted. Lexical format Comments Line splicing Case ... Return to top of Surface Evolver documentation. Lexical format For those who know about such things, the datafile and commands are read with a lexical analyzer generated by the lex program. The specification is in datafile.lex. Commands are further parsed by a yacc-generated parser. In parsing an expression, the longest legal expression is used. This permits coordinates to be specified by several consecutive expressions with no special separators. Comments Comments may be enclosed in /* */ pairs (as in C) and may span lines. // indicates the rest of the line is a comment, as in C++. Lines and line splicing Case Case is not significant in the datafile. All letters are converted to lower case on input. In commands, case is only significant for single-letter commands Whitespace In the datafile, whitespace consists of spaces, tabs, commas, colons, and semicolons. So it's fine if you want to use commas to separate coordinate values, and colons to prettify constraint definitions. In commands, whitespace consists of spaces and tabs. CTRL-Z is also whitespace, for the benefit of files imported from DOS.

47. Forte Developer: FAQs Tools Forte Developer 6 update 2 Fortetm Developer general FAQs Forte C++ Intervalarithmetic Common questions regarding Interval arithmetic in Forte http://wwws.sun.com/software/sundev/previous/developer/faq/

sun.com How To Buy My Sun Worldwide Sites ... Forte Developer 6 update 2 Forte Developer General FAQs Product Home System Requirements Compatibility General FAQs Family Comparison Get the Software Please choose a category below to see a list of frequently asked questions for that topic. Installation and Licensing : Questions related to installation and licensing issues. Forte C++ : Questions related to Forte C++. Forte C++ Interval Arithmetic : Common questions regarding Interval Arithmetic in Forte C++. Forte Fortran/HPC : Common questions regarding Forte Fortran/HPC, including Interval Arithmetic. Forte TeamWare : Questions related to Forte TeamWare. Sun Performance Library : Questions related to the Sun Performance Library. You may also wish to consult the release notes for more information. The release notes cover a variety of issues regarding installation, licensing, the Registry Data File, and product use with the Solaris 8 Operating Environment. Contact Sun Evaluate Product Home Trial Downloads Case Studies White Papers Get Get the Software Licensing Information Find a Partner Training Use Documentation Technical FAQs Product Registration Developer Resources Maintain Current Version Company Info Contact Privacy ... Trademarks

48. General Purpose Date Math Routine a general purpose date math routine with the following usage syntax and fiunctionalityCall JSIDateM YY1 MM1 DD1 YY2 MM2 DD2 - Sets arithmetic environment http://cwashington.netreach.net/depo/view.asp?Index=511&ScriptType=command

49. TUKIDS General Math Math Skills Builder: Talking Arithmetic Tutor Ages 24 PPC general Math Math Skills Builder TalkingArithmetic Tutor. Ages 2-4, Ages 5-8, Ages 9-12, Teachers. http://tukids.raketti.net/mac/2-4/preview/51133.html

This Site All BSD BeOS Games Linux Mac OS 7.5.3 - 9.1 Mac OS X OS/2 PDA - Cybiko PDA - Epoc PDA - Newton PDA - Palm PDA - Pocket PC PDA - RIM PDA - Series 3 PDA - Siena PDA - Windows CE Themes Themes - Cursors Themes - Editors and Tools Themes - ICQ Skins Themes - Icons Themes - Screen Savers Themes - Startup Screens Themes - Wallpaper Themes - Winamp Skins Unix Themes Windows 95/98/ME Windows NT Windows 2000 Windows 3x Sponsored By Tukids Home Download Software Head of the Herd Top Picks ... General Math Ages 2-4 Ages 5-8 Ages 9-12 Teachers Win Mac Win Mac ... Mac Ages 2-4 PPC - General Math Math Skills Builder: Talking Arithmetic Tutor 1.0b License: Rating: Size: Date: Demo August 6th, 1998 Description: Talking Arithmetic Tutor is a really cool program! The electric teacher reads you the problem and points to the numbers. It even tells you how to work each problem. You can start out simple by adding single digits, or be daring and add three two-digit numbers! The choice is yours. This download is Demo Related Sites: www.sssoftware.com BACK TO General Math BACK TO Ages 2-4 PPC Partner Central ... www.tucows.com Tucows Inc. has no liability for any content or goods on the Tucows site or the Internet, except as set forth in the terms and conditions and privacy statement.

50. TUKIDS General Math Arithmetic Review Ages 58 PPC general Math arithmetic Review.Ages 2-4, Ages 5-8, Ages 9-12, Teachers. http://tukids.raketti.net/mac/5-8/preview/6332.html

This Site All BSD BeOS Games Linux Mac OS 7.5.3 - 9.1 Mac OS X OS/2 PDA - Cybiko PDA - Epoc PDA - Newton PDA - Palm PDA - Pocket PC PDA - RIM PDA - Series 3 PDA - Siena PDA - Windows CE Themes Themes - Cursors Themes - Editors and Tools Themes - ICQ Skins Themes - Icons Themes - Screen Savers Themes - Startup Screens Themes - Wallpaper Themes - Winamp Skins Unix Themes Windows 95/98/ME Windows NT Windows 2000 Windows 3x Sponsored By Tukids Home Download Software Head of the Herd Top Picks ... General Math Ages 2-4 Ages 5-8 Ages 9-12 Teachers Win Mac Win Mac ... Mac Ages 5-8 PPC - General Math Arithmetic Review 1.0 License: Rating: Size: Date: Shareware July 4th, 1998 Description: This is an excellent program designed to help teach math skills. The program features three sections: one for learning, one for practice and one for drills. Each category has three levels, and you can choose from addition, subtraction, multiplication or division. You can customize the program, too, so that each student has his or her own entry in the program. This download is Shareware If You would like to purchase this program for $32.95 please click the Related Sites link.

51. Arithmetic, Geometric And Harmonic Sequences By Stephen R. Wassell For The Nexus It may be more intuitive to consider the general form of an arithmetic sequencestart with any number, say a, and add successive terms of a second number, say http://www.nexusjournal.com/GA3-4-Wassell.html

Abstract. Stephen Wassell replies to the question posed by geometer Marcus the Marinite: If one can define arithmetic and geometric sequences, can one define a harmonic sequence? Arithmetic, Geometric and Harmonic Sequences Stephen R. Wassell Department of Mathematical Sciences Sweet Briar College Sweet Briar, Virginia USA A sking the right question is half the battle. Ever the investigative geometer, Marcus the Marinite came up with an excellent question involving the three principal means. If one can define arithmetic and geometric sequences, can one define a harmonic sequence? [ ] It turns out that the answer has some interesting nuances. Although the answer is yes, the main distinction is that the numbers in a harmonic sequence do not increase indefinitely to as they do in arithmetic and geometric sequences. In developing the answer, an easily applied general form of a harmonic sequence is obtained. a a a a a n a n a n be any three in a row; then for this to be an arithmetic sequence, it must be the case that . It may be more intuitive to consider the general form of an arithmetic sequence: start with any number, say

52. Php.smarty.general: Re: [SMARTY] Re: Arithmetic Operations Failed In Never Smart Subject Re SMARTY Re arithmetic operations failed in never Smartyversion (. References 1, Groups php.smarty.general. They are in CVS. http://lists.php.net/article.php?group=php.smarty.general&article=7526

53. Php.smarty.general: Arithmetic Operations Failed In Never Smarty Version :( From Yar3k, Date Wed Feb 5 062608 2003. Subject arithmetic operationsfailed in never Smarty version (. Groups php.smarty.general. http://lists.php.net/article.php?group=php.smarty.general&article=7521

54. Math WWW VL: General Resources [FSU Math] Mathematics general Resources. 3D Nauta Hard mind game. Spatial, 3D, topological,cryptological. Abstract Algebra On Line. Algebra is arithmetic Backwards http://web.math.fsu.edu/Science/General.html

208 Love Building Tallahassee, FL 32306-4510 Phone: (850) 644-2202 Fax: (850) 644-4053 Home Virtual Library Print Math WWW VL: General Resources Home Contact Us Graduate Program Undergrad Program ... Faculty Resources Notes about the Virtual Library: Information categorized by subject. To suggest an addition to the Mathematics Virtual Library please fill out the on-line form Overseas users may want to try our mirror in Israel , hosted by the Israel Institute of Technology This collection of Mathematics-related resources is maintained by the Florida State University Department of Mathematics as a free service to the online community. Mathematics General Resources 3D Nauta Hard mind game. Spatial, 3D, topological, cryptological. Abstract Algebra On Line Algebra is Arithmetic Backwards Inheritance, Fiduciaries, Navation, Life's Lessons, author's introduction to Clifford Algebra American Mathematical Society (AMS) e-MATH Server Applied Mathematics Center Applied Probability Group at Dublin Institute for Advanced Studies Argonne National Lab, Mathematics and Computer Science

55. Journal Of The ACM -- 1974 Richard P. Brent. The parallel evaluation of general arithmetic expressions. Journalof the ACM , 21(2)201206, April 1974. References, Citations, etc. http://theory.lcs.mit.edu/~jacm/jacm74.html

Journal of the ACM 1974 Volume 21, Number 1, January 1974 David G. Herr . On a statistical model of Strand and Westwater for the numerical solution of a Fredholm integral equation of the first kind. Journal of the ACM , 21(1):1-5, January 1974. References, etc. BibTeX entry Nai-kuan Tsao . Some a posteriori error bounds in floating-point computations. Journal of the ACM , 21(1):6-17, January 1974. References, etc. BibTeX entry L. W. Cotten and A. M. Abd-Alla . Processing times for segmented jobs with I/O compute overlap. Journal of the ACM , 21(1):18-30, January 1974. Additional information. BibTeX entry P. A. Franaszek and T. J. Wagner . Some distribution-free aspects of paging algorithm performance. Journal of the ACM , 21(1):31-39, January 1974. References, Citations, etc. BibTeX entry Giorgio Ingargiola and James F. Korsh . Finding optimal demand paging algorithms. Journal of the ACM , 21(1):40-53, January 1974. References, etc. BibTeX entry Debasis Mitra . Some aspects of hierarchical memory systems. Journal of the ACM , 21(1):54-65, January 1974.

56. Journal Of The ACM -- 1970 BibTeX entry. Dennis F. Cudia. general problems of formal grammars. Computerinterval arithmetic Definition and proof of correct implementation. http://theory.lcs.mit.edu/~jacm/jacm70.html

Journal of the ACM 1970 Volume 17, Number 1, January 1970 G. Salton . On the role of the ACM journal. Journal of the ACM , 17(1):1-2, January 1970. [ BibTeX entry Seymour Ginsburg and John Hopcroft . Two-way balloon automata and AFL. Journal of the ACM , 17(1):3-13, January 1970. References, etc. BibTeX entry Alain Colmerauer . Total precedence relations. Journal of the ACM , 17(1):14-30, January 1970. References, Citations, etc. BibTeX entry Dennis F. Cudia . General problems of formal grammars. Journal of the ACM , 17(1):31-43, January 1970. References, etc. BibTeX entry Arnold L. Rosenberg . A note on ambiguity of context-free languages and presentations of semilinear sets. Journal of the ACM , 17(1):44-50, January 1970. References, etc. BibTeX entry D. G. Corneil and C. C. Gotlieb . An efficient algorithm for graph isomorphism. Journal of the ACM , 17(1):51-64, January 1970. Citations, etc. BibTeX entry Herbert M. Gurk and Jack Minker . Storage requirements for information handling centers. Journal of the ACM , 17(1):65-77, January 1970. References, etc.

57. Wiley :: General Computer Engineering general Computer Engineering (65), Listings 125 26-50 51-65, Sort listing by Refinelisting by Advanced Computer arithmetic Design by Michael J. Flynn http://www.wiley.com/cda/sec/0,,2907,00.html

Shopping Cart My Account Help Contact Us By Keyword By Title By Author By ISBN By ISSN Wiley Engineering Computer Engineering General Computer Engineering Discrete Mathematics General Networking Computer Architecture Optical Computers ... Join an Engineering Mailing List Featured Title Advanced Computer Arithmetic Design by Michael J. Flynn, Stuart F. Oberman US $94.50 Add To Cart General Computer Engineering (65) Listings: Sort listing by: A-Z Z-A Publication Date Author Refine listing by: All Formats Books Media Journals Advanced Computer Arithmetic Design by Michael J. Flynn, Stuart F. Oberman Hardcover, March 2001 US $94.50 Add to Cart Advanced Electronic Circuit Design by David J. Comer, Donald T. Comer Paperback, December 2002 US $26.95 Add to Cart Applying Software Metrics by Paul Oman, Shari Lawrence Pfleeger Paperback, October 1996 US $39.95 Add to Cart Asynchronous Circuit Design by Chris J. Myers Hardcover, July 2001

58. Wiley :: Quick Arithmetic: A Self-Teaching Guide, Third Edition Wiley Mathematics Statistics general Mathematics Popular Interest Quick arithmetic A SelfTeaching Guide, Third Edition. Related Subjects, http://www.wiley.com/cda/product/0,,0471384941|desc|2713,00.html

Shopping Cart My Account Help Contact Us By Keyword By Title By Author By ISBN By ISSN Wiley General Mathematics Popular Interest Quick Arithmetic: A Self-Teaching Guide, Third Edition Related Subjects General Mathematics Historical Mathematics Related Titles By These Authors Study Skills: A Student's Guide to Survival, 2nd Edition (Paperback) Quick Arithmetic: A Self-Teaching Guide, Third Edition (E-Book) Popular Interest Five More Golden Rules: Knots, Codes, Chaos, and Other Great Theories of 20th-Century Mathematics (Paperback) John L. Casti Why Do Buses Come in Threes?: The Hidden Mathematics of Everyday Life (Paperback) Rob Eastaway, Jeremy Wyndham Keys to Infinity (Paperback) Clifford A. Pickover A Mathematical Mystery Tour: Discovering the Truth and Beauty of the Cosmos (Paperback) A. K. Dewdney Imaginary Numbers: An Anthology of Marvelous Mathematical Stories, Diversions, Poems, and Musings (Paperback) William Frucht (Editor) Popular Interest Quick Arithmetic: A Self-Teaching Guide, Third Edition

59. Mathematics General Education Courses Fundamental Skills in arithmetic, is designed to strengthen basic arithmetic skillsand to introduce the elements of algebra. Students, in general, are placed http://www.wcupa.edu/_academics/sch_cas.mat/math_placement.htm

60. Electronic Computers Within The Ordnance Corps, Appendix VI -- Arithmetic Operat 3001,700 - AF/CRC 93 665-865 950 ILLIAC TABLE V (CONTINUED) arithmetic OperationTime MISTIC 108 372 348 PACKARD BELL 250 120 1,520 16,200 general MILLS APSAC http://ftp.arl.mil/~mike/comphist/61ordnance/app6.html

ENIAC World Wide Web ELECTRONIC COMPUTERS WITHIN THE ORDNANCE CORPS APPENDIX VI Arithmetic Operation Time (Including Access) of Computing Systems Up Prev Next

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

Page 3     41-60 of 99    Back | 1  | 2  | 3  | 4  | 5  | Next 20