3 awesome free Math programs Posted by Antonio Cangiano in Software on June 2nd, 2007 | 109 responses Mathematical software can be very expensive. Programs like Mathematica, Maple and Matlab are incredibly powerful, flexible and usually well documented and supported. Their price tags however are a big let down for many people, even if there are cheap (in some cases crippled) versions available for educational purposes (if you are a student or a teacher). 1. A general purpose CAS (Computer Algebra System) is a program that’s able to perform symbolic manipulation for the resolution of common problems. Valuable mentions are: 2. Matlab is the standard for numerical computing, but there are a few clones and valid alternatives that are entirely free. Valid alternatives are: For statistical computing and analysis in the Open Source world, it doesn’t get any better than R. As usual, please feel free to share your experiences and add your suggestions to enrich the discussion.
High School Mathematics Extensions/Discrete Probability Introduction[edit] Probability theory is one of the most widely applicable mathematical theories. It deals with uncertainty and teaches you how to manage it. It is simply one of the most useful theories you will ever learn. Please do not misunderstand: We are not learning to predict things; rather, we learn to utilise predicted chances and make them useful. Therefore, we don't care about questions like what is the probability it will rain tomorrow? As suggested above, a probability is a percentage, and it's between 0% and 100% (inclusive). Application[edit] You might ask why we are even studying probability. Consider the following gambling game: Toss a coin; if it's heads, I give you $1; if it's tails, you give me $2. Another real-life example: I observed one day that there are dark clouds outside. In real life, probability theory is heavily used in risk analysis by economists, businesses, insurance companies, governments, etc. Why discrete probability? Event and Probability[edit] 1. 2. 3.
Primal Chaos The image shows a random multiple of 6 at "6k". In order to have twin primes we cannot have any circle intersecting adjacently to 6k (obviously). Let's see how this happens: Please note that the reason I'm only using prime numbers for this is because we only need prime numbers. -Multiples of 3 can only fall on 6k. -Multiples of 5 can fall on 6k, 6k-2, 6k-3. -Multiples of 7 can fall on 6k, 6k-2, 6k-3, 6k-4, 6k-5. -Similarly Multiples of 11 can fall on 6k, 6k-2, 6k-3, 6k-4, 6k-5, 6k-6, 6k-7, 6k-8, 6k-9. Let's put this in a chart of sorts. Wieferich pair In mathematics, a Wieferich pair is a pair of prime numbers p and q that satisfy pq − 1 ≡ 1 (mod q2) and qp − 1 ≡ 1 (mod p2) Wieferich pairs are named after German mathematician Arthur Wieferich. Wieferich pairs play an important role in Preda Mihăilescu's 2002 proof[1] of Mihăilescu's theorem (formerly known as Catalan's conjecture).[2] Known Wieferich pairs[edit] There are only 7 Wieferich pairs known:[3][4] (2, 1093), (3, 1006003), (5, 1645333507), (5, 188748146801), (83, 4871), (911, 318917), and (2903, 18787). Wieferich triple[edit] A Wieferich triple is a triple of prime numbers p, q and r that satisfy pq − 1 ≡ 1 (mod q2), qr − 1 ≡ 1 (mod r2), and rp − 1 ≡ 1 (mod p2). There are 17 known Wieferich triples: Barker sequence[edit] Barker sequence or Wieferich n-tuple is a generalization of Wieferich pair and Wieferich triple. p1p2 − 1 ≡ 1 (mod p22), p2p3 − 1 ≡ 1 (mod p32), p3p4 − 1 ≡ 1 (mod p42), ..., pn−1pn − 1 ≡ 1 (mod pn2), pnp1 − 1 ≡ 1 (mod p12).[5] Wieferich sequence[edit] 3, 11, 71, 47, ?
A 10 minute tutorial for solving Math problems with Maxima Posted by Antonio Cangiano in Essential Math, Software on June 4th, 2007 | 132 responses About 50,000 people read my article 3 awesome free Math programs. Chances are that at least some of them downloaded and installed Maxima. Maxima as a calculator You can use Maxima as a fast and reliable calculator whose precision is arbitrary within the limits of your PC’s hardware. (%i1) 9+7; (%o1) (%i2) -17*19; (%o2) (%i3) 10/2; (%o3) Maxima allows you to refer to the latest result through the % character, and to any previous input or output by its respective prompted %i (input) or %o (output). (%i4) % - 10; (%o4) (%i5) %o1 * 3; (%o5) For the sake of simplicity, from now on we will omit the numbered input and output prompts produced by Maxima’s console, and indicate the output with a => sign. float(1/3); => float(26/4); => As mentioned above, big numbers are not an issue: float((7/3)^35); => Constants and common functions Here is a list of common constants in Maxima, which you should be aware of: log(%e); =>
Santé | Jeunes et minces? Les maths contre la retouche photo Des chercheurs du Dartmouth College ont mis au point un algorithme capable de déterminer quand une photo a été retouchée hors de proportion par des outils comme Photoshop, un procédé abondamment utilisé dans les photos de mode et dans les magazines de célébrités et dénoncé par les spécialistes en santé publique. Le logiciel mis au point par Hani Farid, décrit dans une publication dans les Proceedings of the National Academy of Sciences, permettrait de quantifier la retouche effectuée sur une photo, et donc de déterminer objectivement à partir de quand on exagère. Cet outil pourrait permettre de lutter plus facilement contre ces images dont on sait qu’elles nuisent à la bonne santé et à l’estime de soi de ceux et celles qui les regardent. Sur son site, le chercheur donne en exemple quelques images avant/après analysées par son logiciel. (mesdames, si vous craquez pour le beau George Clooney, vous risquez d’avoir tout un choc.
Ulam spiral Do you see any pattern in this graph? You will not believe at first glance that it is generated using prime numbers. In order to generate it, the numbers are arranged in a spiral, as follows: Then the prime numbers are marked. In the applet above you can see the spiral made up to 1014. Move the graph by clicking in the arrows or using the arrow keys. You can also see the position (x, y) in the spiral and the number n of any point of the graph by moving the cursor to that point. Move the center by typing a new number (up to 14 digits) in the left input box and press the return key. Change the starting number in the center of the spiral by typing a new number (up to 14 digits) in the right input box and press the return key. The formula that gives the numbers in the diagonal lines can be expressed using quadratic polynomials. When the quadratic polynomial cannot be factorized, then its diagonal will contain primes.
Wike's law of low odd primes From Wikipedia, the free encyclopedia Wike's law of low odd primes is a methodological principle to help design sound experiments in psychology. It is: "If the number of experimental treatments is a low odd prime number, then the experimental design is unbalanced and partially confounded" (Wike, 1973, pp. 192–193). This law was stated by Edwin Wike in a humorous article in which he also admits that the association of his name with the law is an example of Stigler's law of eponymy.
Introduction Many of the articles on this Web site are versions of the Fermi Problem described in the first section. Others are essays - some short, some long. Some are merely attempts to come to terms with basic concepts, such as the 'size' of the speed of light or the number 'one trillion'. Others discuss more advanced concepts. The energy density article was written to fill a gap, which I noted in books on Special Relativity. The earlier pieces are nowhere near so involved, and require only a little number skill and, possibly, some high school algebra. There are many cases in science, and even in everyday life, when we encounter seemingly insolvable problems such as this. And most of all, remember to have fun!
De l’inexactitude dans nos ordinateurs S’il y a bien un endroit où l’on peut être certain des informations que l’on traite, c’est dans les puces de nos ordinateurs. Mais ceci pourrait bien changer grâce aux travaux conjugués de plusieurs instituts... Les Université Rice, de Californie, de Berkeley, de Nanyang à Singapour et le Centre d’Electronique et Microtechnologie de Suisse travaillent sur le projet d’une puce informatique tolérant l’erreur depuis 2003. Les chercheurs se sont en effet aperçus que les traitements et le matériel nécessaires pour annihiler le taux d’erreur demandaient beaucoup d’énergie et faisaient baisser les performances. Attention cela dit, il ne s’agit pas ici d’annuler toutes vérifications, ces “puces inexactes” doivent garantir un taux d’erreur acceptable selon son utilisation. Ci-dessous, un exemple d’une photo, à droite, ayant 7,58% d’erreur par rapport à celle de gauche : Cette “inexactitude” est à rapprocher de la logique floue, perception qui commence à toucher la micro-informatique. [theverge]
Wilson's Theorem _ from Wolfram MathWorld Iff is a prime, then is a multiple of , that is This theorem was proposed by John Wilson and published by Waring (1770), although it was previously known to Leibniz. It was proved by Lagrange in 1773. except when A corollary to the theorem states that iff a prime is of the form , then The first few primes of the form are , 13, 17, 29, 37, 41, ... Gauss's generalization of Wilson's theorem considers the product of integers that are less than or equal to and relatively prime to an integer . , 2, ..., the first few values are 1, 1, 2, 3, 24, 5, 720, 105, 2240, 189, ... gives the congruence for an odd prime. , this reduces to which is equivalent to . are 0, Szántó (2005) notes that defining then, taking the minimal residue, For , 1, ..., the first terms are then 0,
SuperPrime From Wikipedia, the free encyclopedia Background information[edit] In August 1995, the calculation of Pi up to 4,294,960,000 decimal digits was achieved by using a supercomputer at the University of Tokyo. The program used to achieve this was ported to personal computers, for operating systems such as Windows NT and Windows 95 and called Super-PI. Landmarks[edit] On September 29, 2006, a milestone was broken when bachus_anonym of www.xtremesystems.org broke the 30 seconds barrier using a highly overclocked Core 2 Duo machine [1] See also[edit] Erodov.com, the 'home forum' for the SuperPrime benchmark. References[edit] External links[edit]
Handy Mathematics Facts for Graphics email scd@cs.brown.edu with suggested additions or corrections Eric Weisstein's world of Mathematics (which used to be called Eric's Treasure Trove of Mathematics) is an extremely comprehensive collection of math facts and definitions. Eric has other encyclopedias at www.treasure-troves.com S.O.S. Mathematics has a variety of algebra, trigonometry, calculus, and differential equations tutorial pages. Dave Eberly has a web site called Magic Software with several pages of descriptions and code that answers questions from comp.graphics.algorithms. Steve Hollasch at Microsoft has a very comprehensive page of graphics notes which he would like to turn into a graphics encyclopedia. Vector math identities and algorithms from Japan. Paul Bourke has a variety of pages with useful tidbits, many of which are linked to from Steve Hollasch's page. The graphics group at UC Davis also has notes about computer graphics. Peter H. Josh Levenberg has a page of links to yet more graphics algorithm resources. e pi