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Exponentiation
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 n-th power", "b raised to the power of n", or "the n-th 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
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Algebraic Function
In mathematics, an algebraic function is a function that can be defined as the root of a polynomial equation. Quite often algebraic functions are algebraic expressions using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power
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Mathematical Notation
Mathematical notation is a system of symbolic representations of mathematical objects and ideas
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Population Growth
In biology or human geography, population growth is the increase in the number of individuals in a population. Global human population growth amounts to around 83 million annually[1], or 1.1% per year. The global population has grown from 1 billion in 1800 to 7.6 billion[2] in 2017. It is expected to keep growing, and estimates have put the total population at 8.6 billion by mid-2030, 9.8 billion by mid-2050 and 11.2 billion by 2100[3]
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Public-key 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, where the public key verifies that a holder of the paired private key sent the message, and encryption, where only the paired private key holder can decrypt the message encrypted with the public key. In a public key encryption system, any person can encrypt a message using the receiver's public key. That encrypted message can only be decrypted with the receiver's private key. To be practical, the generation of a public and private key -pair must be computationally economical. The strength of a public key cryptography system relies on the computational effort (work factor in cryptography) required to find the private key from its paired public key
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Greek Mathematics
Greek mathematics
Greek mathematics
refers to mathematics texts and advances 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 from Italy to North Africa but were united by culture and language. Greek mathematics of the period following Alexander the Great
Alexander the Great
is sometimes called Hellenistic mathematics
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Euclid
Euclid
Euclid
(/ˈjuːklɪd/; Greek: Εὐκλείδης Eukleidēs [eu̯.klěː.dɛːs]; fl. 300 BC), sometimes given the name Euclid
Euclid
of Alexandria[1] to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry"[1] or the "father of geometry". He was active in Alexandria
Alexandria
during the reign of Ptolemy I (323–283 BC). 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.[2][3][4] In the Elements, Euclid
Euclid
deduced the theorems of what is now called Euclidean geometry
Euclidean geometry
from a small set of axioms
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Muhammad Ibn Mūsā Al-Khwārizmī
Muḥammad ibn Mūsā al-Khwārizmī[note 1] (Persian: محمد بن موسى خوارزمی‎; c. 780 – c. 850), formerly Latinized as Algoritmi,[note 2] was a Persian[3][4] scholar who produced works in mathematics, astronomy, and geography under the patronage of the Caliph Al-Ma'mun
Al-Ma'mun
of the Abbasid Caliphate.[5]:668 Around 820 AD he was appointed as the astronomer and head of the library of the House of Wisdom
House of Wisdom
in Baghdad.[6]:14 Al-Khwarizmi's popularizing treatise on algebra (The Compendious Book on Calculation by Completion and Balancing, ca. 813-833 CE[7]:171) presented the first systematic solution of linear and quadratic equations in Arabic
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Mathematics In Medieval Islam
Mathematics
Mathematics
during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics
Greek mathematics
(Euclid, Archimedes, Apollonius) and Indian mathematics
Indian mathematics
(Aryabhata, Brahmagupta)
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Abū Al-Hasan Ibn Alī Al-Qalasādī
Abū al-Ḥasan ibn ʿAlī ibn Muḥammad ibn ʿAlī al-Qalaṣādī (1412–1486) was a Muslim
Muslim
Arab[1] mathematician from Al-Andalus specializing in Islamic inheritance jurisprudence. Al-Qalaṣādī is known for being one of the most influential voices in algebraic notation since antiquity and for taking "the first steps toward the introduction of algebraic symbolism''. He wrote numerous books on arithmetic and algebra, including al-Tabsira fi'lm al-hisab (Arabic: التبصير في علم الحساب‎ "Clarification of the science of arithmetic").[2]Contents1 Early life 2 Symbolic algebra 3 See also 4 Notes 5 References 6 External linksEarly life[edit] Al-Qalaṣādī was born in Baza, an outpost of the Emirate of Granada. He received education in Granada, but continued to support his family in Baza. He published many works and eventually retired to his native Baza
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Computer Science
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.[1] Its fields can be divided into a variety of theoretical and practical disciplines
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Joost Burgi
Jost Bürgi
Jost Bürgi
(also Joost, Jobst; Latinized
Latinized
surname Burgius or Byrgius; 28 February 1552 – 31 January 1632[1]), active primarily at the courts in Kassel
Kassel
and Prague, was a Swiss clockmaker, a maker of astronomical instruments and a mathematician.Contents1 Life 2 Bürgi as a clockmaker 3 Works 4 Bürgi as a mathematician4.1 Bürgi's work on trigonometry 4.2 Bürgi's work on logarithms5 Honors 6 Notes 7 External linksLife[edit] Bürgi was born in 1552 Lichtensteig, Toggenburg, at the time a subject territory of the Abbey of St. Gall
Abbey of St. Gall
(now part of the canton of St. Gallen, Switzerland)
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Rene Descartes
René Descartes
René Descartes
(/ˈdeɪˌkɑːrt/;[9] French: [ʁəne dekaʁt]; Latinized: Renatus Cartesius; adjectival form: "Cartesian";[10] 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist. Dubbed the father of modern western philosophy, much of subsequent Western philosophy
Western philosophy
is a response to his writings,[11][12] which are studied closely to this day. A native of the Kingdom of France, he spent about 20 years (1629–49) of his life in the Dutch Republic
Dutch Republic
after serving for a while in the Dutch States Army of Maurice of Nassau, Prince of Orange
Prince of Orange
and the Stadtholder
Stadtholder
of the United Provinces
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La Géométrie
La Géométrie
La Géométrie
was published in 1637 as an appendix to Discours de la méthode (Discourse on the Method), written by René Descartes. In the Discourse, he presents his method for obtaining clarity on any subject. La Géométrie
La Géométrie
and two other appendices, also by Descartes, La Dioptrique (Optics) and Les Météores (Meteorology), were published with the Discourse to give examples of the kinds of successes he had achieved following his method[1] (as well as, perhaps, considering the contemporary European social climate of intellectual competitiveness, to show off a bit to a wider audience).La GéométrieThe work was the first to propose the idea of uniting algebra and geometry into a single subject[2] and invented an algebraic geometry called analytic geometry, which involves reducing geometry to a form of arithmetic and algebra and translating geometric shapes into algebraic equations
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Henricus Grammateus
Henricus Grammateus (also known as Henricus Scriptor, Heinrich Schreyber or Heinrich Schreiber; 1495 – 1525 or 1526[1]) was a German mathematician. He was born in Erfurt. In 1507 he started to study at the University of Vienna, where he subsequently taught. Christoph Rudolff was one of his students. From 1514 to 1517 he studied in Cracow
Cracow
and then returned to Vienna. But when the plague affected Vienna
Vienna
Schreiber left the city and went to Nuremberg. In 1518 he published details of a new musical temperament,[2] which is now named after him, for the harpsichord. It was a precursor of the equal temperament. In 1525 Schreiber was back in Vienna, where he is listed as "Examinator", i.e. eligible to work holding exams. Works[edit]Algorithmus proportionum una cum monochordi generalis dyatonici compositione, pub
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