ALGORITHMS By Christopher Fajardo

What is algorithm ?■ Algorithms have been around since the beginning of

time and existed well before a special word had been coined to describe them

■ Algorithms are simply a set of step by step instructions , to be carried out quite mechanically , so as to achieve some desired result .

■ Algorithms are not confined to mathematics , the Babylonians used them for deciding points of law, Latin teachers used them to get the grammar right, and they have been used in all cultures for predicting the future , for deciding medical treatment , or for preparing food.

■ Everybody today uses algorithms of one sort or another, often unconsciously, when following a recipe , using a knitting pattern, or operating household gadgets .

Where the word algorithm came from ?■Algos is the Greek word for pain. Algor is

Latin, to be cold. Neither is the root for algorithm. The word algorithm derives directly from al-Khwarizmi, the author of the oldest know work of algebra.

■His full name is Muhammad ibn musa al-Khwarizmi means literally, Muhammad son of musa from khwarezm, a region of central Asia, south of the Aral Sea.

■ He was a mathematician of the first half of the 9th century and his book Al-kitāb al-mukhtaṣar fī ḥisāb al-ğabr wa’l-muqābala (The Compendious Book on Calculation by Completion and Balancing) gave us the word “algebra” from ‘al-jabr”.

■ In the 12th century ,his work and others were translated from Arabic into Latin and began to spread throughout medieval Europe.

■ In the end the term algorithm has come to mean any process of systematic calculation that is a process that could be carried automatically

Where the word algorithm came from ?(continued)

Algorithms before our time■ Sumerian Division: Sumerian division is one of

the earliest pieces of evidence of algorithm of this type. This evidence was found on a clay tablet near Baghdad which concerns a problem of sharing. This engraves were done by Sumerian at about 2500 BC.

■ A Babylonian algorithm for calculating inverses: At the beginning of the second century BC, the Babylonians developed a numeration system , traces of which remain with us today in our use of minutes and seconds for time and angle measurements.

■ Egyptian algorithms for arithmetic: Throughout the four thousand years of their civilization, the Egyptians used a number system that was additive and denary, they also used fractions (Chinese civilization also did).

■ The tableau multiplication: There are numerous multiplication algorithms, for the most part they are nor completely general but were devised in order to deal with special cases. Some of these algorithms are Wu Jing from the Chinese , the napier’s rods , Gelosia multiplication and Lucas-Genaille multiplication rods .

■ Division on the Chinese Abacus: The Chinese abacus has only been commonly used in china since the second half of the 16th century .

■ Numbers written as decimals: The idea of decimal fractions is very old but for a long time it existed alongside other non-decimal fractional use, like that of the Egyptians' unit fractions and the ever popular use of sexagesimal fractions (which is based 60)

Algorithms before our time …

Algorithms before our time …■ Binary arithmetic: The modern binary number

system was devised by the German Gottfried Leibniz. In 1703 he wrote “The Explanation of Binary Arithmetic ” in which he explain that it uses only the character 0 and 1 , and that this language relates to a Chinese legend “King Fohy” which introduced “the figure of eight cova”. Leibniz been interested in this system of numeration for years , he had called this a Universal Characteristic

■ Computer arithmetic: Leibniz’s ambition with binary arithmetic, led him to dream of the possibility of reducing logic to mechanical operations , he made several practical advances in this direction in 1673 by inventing a machine for the four operations of arithmetic . He also invented in 1674 a machine capable of solving equations. With the birth of the computer Leibniz’s dream has been ,to a certain extent realized today.

Algorithms of the 20th century Here are some of the most important algorithms in the 20 century that had the greatest influence on the development and practice of science and engineering. (this is according to a article of the Computing in Science & Engineering magazine)■ 1946: John von Neumann, Stan Ulam, and Nick Metropolis, all at the Los

Alamos Scientific Laboratory, cook up the Metropolis algorithm, also known as the Monte Carlo method.

■ 1947: George Dantzig, at the RAND Corporation, creates the simplex method for linear programming.

■ 1950: Magnus Hestenes, Eduard Stiefel, and Cornelius Lanczos, all from the Institute for Numerical Analysis at the National Bureau of Standards, initiate the development of Krylov subspace iteration methods.

■ 1951: Alston Householder of Oak Ridge National Laboratory formalizes the decompositional approach to matrix computations

Algorithms of the 20th century ■ 1957: John Backus leads a team at IBM in developing the

Fortran optimizing compiler.■ 1959–61: J.G.F. Francis of Ferranti Ltd., London, finds a

stable method for computing eigenvalues, known as the QR algorithm.

■ 1962: Tony Hoare of Elliott Brothers, Ltd., London, presents Quicksort

■ 1965: James Cooley of the IBM T.J. Watson Research Center and John Tukey of Princeton University and AT&T Bell Laboratories unveil the fast Fourier transform.

■ 1977: Helaman Ferguson and Rodney Forcade of Brigham Young University advance an integer relation detection algorithm.

■ 1987: Leslie Greengard and Vladimir Rokhlin of Yale University invent the fast multipole algorithm

Algorithms that dominate our world The importance of algorithms in our lives today cannot

be overstated. They are used almost everywhere, from financial institutions to dating sites. But some algorithms run our world more than others for example :■ Google Search: There was a time not too long ago

when search engines battled for Internet supremacy. But along came Google and its innovative PageRank algorithm.

■ Facebook's News Feed: Facebook News Feed show the activities and updates of all your friends in chronological order or in relevance order ,you're viewing a predetermined selection of items that Facebook's algorithms have chosen just for you.

■ Dating sites: Sites such as Okcupid (co-founded by Harvard mathematician Christian Rudder) does their matching with the help of algorithms.

■NSA Data Collection, Interpretation, and Encryption: We are increasingly being watched not by people, but by algorithms. They been monitoring our phone calls, emails, webcam images, and geographical locations. And by "they" I mean their algorithms, there is far too much data for humans to collect and interpret.

■Google AdWords Similar to the previous item, Google, Facebook, and other sites track your behavior, word usage, and search queries to deliver contextual advertising. 

■ High frequency stocks trading The financial sector has long used algorithms to predict market fluctuations, but they're also being used in the increasing practice of high-frequency stock trading. This is a form of rapid-fire trading that involves algorithms (also called bots) that can make decisions on the order of milliseconds.

■ IBM's CRUSH in 2010, it was announced that, by using IBM's predictive analysis software (called CRUSH, or Criminal Reduction Utilizing Statistical History), Memphis's police department reduced serious crime by more than 30%, including a 15% reduction in violent crimes since 2006.

The Future of algorithms

■ Researchers are working on a new version of an algorithm that will power better search, autonomous cars, smarter smartphones and the Internet.

■ Deep-learning algorithms, which are based on loose simulations of the brain, have been used to advance technologies like speech recognition, natural language processing and robotic autonomy.

■ Now, researchers are working on the next generation of these algorithms, which are heavily used in machine learning and artificial intelligence and may become the foundation that critical technological advances are built on.

Conclusion

■ With the introduction of the concept of an algorithm , the history of algorithms changes into the history of a new field of science. Here we are not trying to seek to an algorithm that solves a particular problem but we seeking the solution of problems posed by the general study of algorithms. The research of algorithm has been developed along with the construction of more powerful computers and the inventions of more programing languages.

References

■ A history of Algorithms from The Pebble to the Microchip by Jean-luc Chabert

■ The Best of the 20th Century: Editors Name Top 10 Algorithms by Barry A. Cipra

■ Smarter algorithm will power our future digital lives by Sharon gaudin■ The 10 Algorithms That Dominate Our World by George Dvorsky■ http://www.leibniz-translations.com/binary.htm■ Pictures were provided from google images