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Exponentiation EXPONENTIATION is a mathematical operation , written as BN, involving two numbers, the BASE b and the EXPONENT n. When n is a positive integer , exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases: b n = b b n {displaystyle b^{n}=underbrace {btimes cdots times b} _{n}} The exponent is usually shown as a superscript to the right of the base. In that case, bn is called b raised to the nth power, b raised to the power of n, or the nth power of b. When n is a positive integer and b is not zero, b−n is naturally defined as 1/bn, preserving the property bn × bm = bn + m. With exponent −1, b−1 is equal to 1/b, and is the reciprocal of b. The definition of exponentiation can be extended to allow any real or complex exponent. Exponentiation Exponentiation by integer exponents can also be defined for a wide variety of algebraic structures, including matrices [...More...]  "Exponentiation" on: Wikipedia Yahoo 

Publickey Cryptography PUBLIC KEY CRYPTOGRAPHY, or ASYMMETRICAL CRYPTOGRAPHY, is any cryptographic system that uses pairs of keys : public keys which may be disseminated widely, and private keys which are known only to the owner. This accomplishes two functions: authentication , which is when the public key is used to verify that a holder of the paired private key sent the message, and encryption , whereby only the holder of the paired private key can decrypt the message encrypted with the public key. In a public key encryption system, any person can encrypt a message using the public key of the receiver, but such a message can be decrypted only with the receiver's private key. For this to work it must be computationally easy for a user to generate a public and private keypair to be used for encryption and decryption [...More...]  "Publickey Cryptography" on: Wikipedia Yahoo 

Greek Mathematics GREEK MATHEMATICS, as the term is used in this article, is the mathematics written in Greek , developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean . Greek mathematicians lived in cities spread over the entire Eastern Mediterranean Mediterranean from Italy to North Africa but were united by culture and language . Greek mathematics Greek mathematics of the period following Alexander the Great is sometimes called Hellenistic mathematics. The word "mathematics" itself derives from the ancient Greek μάθημα (mathema), meaning "subject of instruction". The study of mathematics for its own sake and the use of generalized mathematical theories and proofs is the key difference between Greek mathematics Greek mathematics and those of preceding civilizations [...More...]  "Greek Mathematics" on: Wikipedia Yahoo 

Euclid EUCLID (/ˈjuːklᵻd/ ; Greek : Εὐκλείδης, Eukleidēs Ancient Greek: ; fl. 300 BCE), sometimes called EUCLID OF ALEXANDRIA to distinguish him from Euclides of Megara , was a Greek mathematician , often referred to as the "father of geometry". He was active in Alexandria Alexandria during the reign of Ptolemy I (323–283 BCE). His Elements is one of the most influential works in the history of mathematics , serving as the main textbook for teaching mathematics (especially geometry ) from the time of its publication until the late 19th or early 20th century. In the Elements, Euclid Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms . Euclid Euclid also wrote works on perspective , conic sections , spherical geometry , number theory , and rigor [...More...]  "Euclid" on: Wikipedia Yahoo 

Muhammad Ibn Mūsā AlKhwārizmī MUḥAMMAD IBN MūSā ALKHWāRIZMī (Persian : محمد بن موسی خوارزمی, Arabic : محمد بن موسى الخوارزمی; c. 780 – c. 850), formerly Latinized as Algoritmi, was a Persian (modern Khiva Khiva , Uzbekistan Uzbekistan ) mathematician , astronomer , and geographer during the Abbasid Caliphate , a scholar in the House of Wisdom House of Wisdom in Baghdad Baghdad . In the 12th century, Latin Latin translations of his work on the Indian numerals introduced the decimal positional number system to the Western world. AlKhwārizmī's The Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear and quadratic equations in Arabic. He is often considered one of the fathers of algebra [...More...]  "Muhammad Ibn Mūsā AlKhwārizmī" on: Wikipedia Yahoo 

Wave In physics , a WAVE is an oscillation accompanied by a transfer of energy . Frequency refers to the addition of time. Wave motion transfers energy from one point to another, which displace particles of the transmission medium–that is, with little or no associated mass transport. Waves consist, instead, of oscillations or vibrations (of a physical quantity), around almost fixed locations. A wave is a disturbance that transfers energy through matter or space. There are two main types of waves. Mechanical waves propagate through a medium, and the substance of this medium is deformed. Restoring forces then reverse the deformation. For example, sound waves propagate via air molecules colliding with their neighbors. When the molecules collide, they also bounce away from each other (a restoring force). This keeps the molecules from continuing to travel in the direction of the wave. The second main type, electromagnetic waves , do not require a medium [...More...]  "Wave" on: Wikipedia Yahoo 

Chemical Reaction Kinetics CHEMICAL KINETICS, also known as REACTION KINETICS, is the study of rates of chemical processes . Chemical kinetics Chemical kinetics includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about the reaction\'s mechanism and transition states , as well as the construction of mathematical models that can describe the characteristics of a chemical reaction [...More...]  "Chemical Reaction Kinetics" on: Wikipedia Yahoo 

Physics PHYSICS (from Ancient Greek : φυσική (ἐπιστήμη), translit. physikḗ (epistḗmē), lit. 'knowledge of nature', from φύσις phýsis "nature" ) is the natural science that studies matter and its motion and behavior through space and time and that studies the related entities of energy and force . Physics Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves. Physics Physics is one of the oldest academic disciplines and, through its inclusion of astronomy , perhaps the oldest. Over the last two millennia, physics, chemistry , biology , and certain branches of mathematics were a part of natural philosophy , but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right [...More...]  "Physics" on: Wikipedia Yahoo 

Computer Science COMPUTER SCIENCE is the study of the theory, experimentation, and engineering that form the basis for the design and use of computers. It is the scientific and practical approach to computation and its applications and the systematic study of the feasibility, structure, expression, and mechanization of the methodical procedures (or algorithms ) that underlie the acquisition, representation, processing, storage, communication of, and access to, information. An alternate, more succinct definition of computer science is the study of automating algorithmic processes that scale. A computer scientist specializes in the theory of computation and the design of computational systems. Its fields can be divided into a variety of theoretical and practical disciplines [...More...]  "Computer Science" on: Wikipedia Yahoo 

Compound Interest COMPOUND INTEREST is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previouslyaccumulated interest. Compound interest Compound interest is standard in finance and economics . Compound interest Compound interest may be contrasted with simple interest, where interest is not added to the principal, so there is no compounding. The simple annual interest rate is the interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as the NOMINAL INTEREST RATE (not to be confused with the interest rate not adjusted for inflation , which goes by the same name) [...More...]  "Compound Interest" on: Wikipedia Yahoo 

Mathematical Notation MATHEMATICAL NOTATION is a system of symbolic representations of mathematical objects and ideas. Mathematical notations are used in mathematics , the physical sciences , engineering , and economics . Mathematical notations include relatively simple symbolic representations, such as the numbers 0, 1 and 2, function symbols such as sin , operator symbols such as + ; conceptual symbols such as lim and dy/dx ; equations and variables ; and complex diagrammatic notations such as Penrose graphical notation and Coxeter–Dynkin diagrams [...More...]  "Mathematical Notation" on: Wikipedia Yahoo 

Samuel Jeake SAMUEL JEAKE (1623–1690), dubbed THE ELDER to distinguish him from his son, was an English merchant, nonconformist , antiquary and astrologer from Rye, East Sussex Rye, East Sussex , England England . CONTENTS * 1 Life * 2 Works * 3 In literature * 4 Family * 5 References * 6 Further reading LIFEBorn at Rye in Sussex, on 9 October 1623, he may have belonged to one of the French Protestant families who settled in the county at the end of the 16th century: the name Jeake, written also Jake, Jaque, Jeakes, and Jacque, does point to a French origin. Samuel's father was a baker. His mother, a pious woman, was daughter of the Rev. John Pearson of Peasmarsh Peasmarsh , Sussex; she died 20 November 1639. In 1640 Samuel severed his connection with the Church of England England , and was appointed minister of a conventicle , apparently Baptist [...More...]  "Samuel Jeake" on: Wikipedia Yahoo 

Robert Recorde ROBERT RECORDE (c. 1512–1558) was a Welsh physician and mathematician. He invented the "equals" sign (=) and also introduced the preexisting "plus" sign (+) to English speakers in 1557. CONTENTS * 1 Biography * 2 Publications * 3 See also * 4 Notes * 5 References * 6 External links BIOGRAPHYA member of a respectable family of Tenby Tenby , Wales Wales , born in 1512, Recorde entered the University of Oxford University of Oxford about 1525, and was elected a Fellow of All Souls College there in 1531. Having adopted medicine as a profession, he went to the University of Cambridge University of Cambridge to take the degree of M.D. in 1545. He afterwards returned to Oxford, where he publicly taught mathematics, as he had done prior to going to Cambridge [...More...]  "Robert Recorde" on: Wikipedia Yahoo 

Isaac Newton SIR ISAAC NEWTON PRS (/ˈnjuːtən/ ; 25 December 1642 – 20 March 1726/27 ) was an English mathematician , astronomer , and physicist (described in his own day as a "natural philosopher ") who is widely recognised as one of the most influential scientists of all time and a key figure in the scientific revolution . His book Philosophiæ Naturalis Principia Mathematica ("Mathematical Principles of Natural Philosophy"), first published in 1687, laid the foundations of classical mechanics . Newton also made seminal contributions to optics , and he shares credit with Gottfried Wilhelm Leibniz Gottfried Wilhelm Leibniz for developing the infinitesimal calculus . Newton's Principia formulated the laws of motion and universal gravitation that dominated scientists' view of the physical universe for the next three centuries [...More...]  "Isaac Newton" on: Wikipedia Yahoo 

Involution (mathematics) In mathematics , an (ANTI)INVOLUTION, or an INVOLUTORY FUNCTION, is a function f that is its own inverse , f(f(x)) = x for all x in the domain of f. CONTENTS * 1 General properties * 2 Involution throughout the fields of mathematics * 2.1 Precalculus * 2.2 Euclidean geometry * 2.3 Projective geometry * 2.4 Linear algebra * 2.5 Quaternion algebra, groups, semigroups * 2.6 Ring theory * 2.7 Group theory Group theory * 2.8 Mathematical logic * 2.9 Computer science * 3 See also * 4 References * 5 Further reading GENERAL PROPERTIESAny involution is a bijection . The identity map is a trivial example of an involution. Common examples in mathematics of nontrivial involutions include multiplication by −1 in arithmetic , the taking of reciprocals , complementation in set theory and complex conjugation [...More...]  "Involution (mathematics)" on: Wikipedia Yahoo 