Branches of Mathematics

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• Algebra
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• Dynamical systems and differential equations
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• Electromagnetic Spectrum
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• 
  

• 
  India
  India (ⁱ/ˈɪndiə/), officially the Republic of India (Bhārat Gaṇarājya), is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world. Bounded by the Indian Ocean on the south, the Arabian Sea on the south-west, and the Bay of Bengal on the south-east, it shares land borders with Pakistan to the west;China, Nepal, and Bhutan to the north-east; and Burma and Bangladesh to the east. In the Indian Ocean, India is in the vicinity of Sri Lanka and the Maldives; in addition, India's Andaman and Nicobar Islands share a maritime border with Thailand and Indonesia.
  Home to the ancient Indus Valley Civilisation and a region of historic trade routes and vast empires, the Indian subcontinent was identified with its commercial and cultural wealth for much of its long history. Four of the world's major religions—Hinduism, Buddhism, Jainism, and Sikhism—originated here, whereas Zoroastrianism, Christianity, and Islam arrived in the 1st millennium CE and also helped shape the region's diverse culture. Gradually annexed by and brought under the administration of the British East India Company from the early 18th century and administered directly by the United Kingdom from the mid-19th century, India became an independent nation in 1947 after a struggle for independence that was marked by non-violent resistance led by Mahatma Gandhi.
  
  wn.com/India

• 
  Abraham ibn Ezra
  Rabbi Abraham Ben Meir Ibn Ezra (Hebrew: אברהם אבן עזרא or ראב"ע, Arabic ابن عزرا; also known as Abenezra) (1089 — 1164) was born at Tudela, Navarre Tudela, Navarre (now in Spain) in 1089, and died c. 1167, apparently in Calahorra. He was one of the most distinguished Jewish men of letters and writers of the Middle Ages. Ibn Ezra excelled in philosophy, astronomy/astrology, mathematics, poetry, linguistics, and exegesis; he was called The Wise, The Great and The Admirable Doctor.
  He was born at Tudela^{[citation needed]}, (current day province of Navarre) when the town was under the Muslim rule of the emirs of Zaragoza. Later he lived in Córdoba. In Granada, it is said, he met his future friend (and perhaps his father-in-law) Yehuda Halevi. He left Spain before 1140 to escape persecution of the Jews by the new fanatical regime of the Almohads. He led a life of restless wandering, which took him to North Africa, Egypt (in 1109, maybe in the company of Yehuda Halevi), the Land of Israel, Italy (Rome in 1140-1143, Lucca, Mantua, Verona), Southern France (Rodez, Narbonne, Béziers), Northern France (Dreux), England (London, and Oxford in 1158), and back again to Narbonne in 1161, until his death on January 23 or 28, 1167, the exact location unknown: maybe at Calahorra at the border of Navarre and Aragon, or maybe in Rome or in the Holy Land.
  
  wn.com/Abraham_ibn_Ezra
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  Archimedes
  Archimedes of Syracuse (Ancient Greek: Ἀρχιμήδης; c. 287 BC – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an explanation of the principle of the lever. He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors.
  Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi. He also defined the spiral bearing his name, formulae for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers.
  
  wn.com/Archimedes
• 
  Blaise Pascal
  Blaise Pascal (French pronunciation: [blɛz paskal]; 19 June 1623 – 19 August 1662), was a French mathematician, physicist, inventor, writer and Catholic philosopher. He was a child prodigy who was educated by his father, a tax collector in Rouen. Pascal's earliest work was in the natural and applied sciences where he made important contributions to the study of fluids, and clarified the concepts of pressure and vacuum by generalizing the work of Evangelista Torricelli. Pascal also wrote in defense of the scientific method.
  In 1642, while still a teenager, he started some pioneering work on calculating machines, and after three years of effort and 50 prototypes he invented the mechanical calculator. He built twenty of these machines (called the Pascaline) in the following ten years. Pascal was an important mathematician, helping create two major new areas of research: he wrote a significant treatise on the subject of projective geometry at the age of sixteen, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science. Following Galileo and Torricelli, in 1646 he refuted Aristotle's followers who insisted that nature abhors a vacuum. Pascal's results caused many disputes before being accepted.
  
  wn.com/Blaise_Pascal
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  Chrysippus
  Chrysippus of Soli (Ancient Greek: Χρύσιππος ὁ Σολεύς, Chrysippos ho Soleus; c. 279 BC – c. 206 BC) was a Greek Stoic philosopher. He was a native of Soli, Cilicia, but moved to Athens as a young man, where he became a pupil of Cleanthes in the Stoic school. When Cleanthes died, around 230 BC, Chrysippus became the third head of the school. A prolific writer, Chrysippus expanded the fundamental doctrines of Zeno of Citium, the founder of the school, which earned him the title of Second Founder of Stoicism.
  Chrysippus excelled in logic, the theory of knowledge, ethics and physics. He created an original system of propositional logic in order to better understand the workings of the universe and role of humanity within it. He adhered to a deterministic view of fate, but nevertheless sought a role for personal freedom in thought and action. Ethics, he taught, depended on understanding the nature of the universe, and he taught a therapy of extirpating the unruly passions which depress and crush the soul. He initiated the success of Stoicism as one of the most influential philosophical movements for centuries in the Greek and Roman world.
  
  wn.com/Chrysippus
• 
  Gian-Carlo Rota
  Gian-Carlo Rota (April 27, 1932 – April 18, 1999, known as Juan Carlos Rota to Spanish-speakers) was an Italian-born American mathematician and philosopher.
  Rota was born in Vigevano, Italy. Gian-Carlo's family left Italy when he was 13 years old, initially going to Switzerland.
  Rota attended the Colegio Americano de Quito in Ecuador, and earned degrees at Princeton University and Yale University. Much of his career was spent as a professor at the Massachusetts Institute of Technology, where he was and remains the only person ever to be appointed Professor of Applied Mathematics and Philosophy. Rota was also the Norbert Wiener Professor of Applied Mathematics.
  He taught a difficult but very popular course in probability, 18.313, which MIT has not offered again. He also taught 18.001 (Applications of Calculus), 18.03 (Differential Equations), and 18.315 (Combinatorial Theory). His philosophy course in phenomenology was offered on Friday nights to keep the enrollment manageable. Among his many eccentricities, he would not teach without a can of Coca-Cola, and handed out prizes ranging from Hershey bars to pocket knives to students who asked questions in class or did well on tests.
  
  wn.com/Gian-Carlo_Rota
• Hassler Whitney
  Hassler Whitney (March 23, 1907 – May 10, 1989) was an American mathematician. He was one of the founders of singularity theory, and did foundational work in manifolds, embeddings, immersions, and characteristic classes.
  Hassler Whitney was the son of First District New York Supreme Court judge Edward Baldwin Whitney and Josepha (Newcomb) Whitney, the grandson of Yale University Professor of Ancient Languages William Dwight Whitney, the great-grandson of Connecticut Governor and US Senator Roger Sherman Baldwin, and the great-great-great-grandson of American founding father Roger Sherman.
  Hassler Whitney's maternal grandparents were astronomer and celestial mechanician Simon Newcomb and Mary Hassler Newcomb (the granddaughter of the first superintendent of the Coast Survey Ferdinand Hassler).
  He married Margaret R. Howell, May 30, 1930; children: James Newcomb, Carol, Marian; married Mary Barnett Garfield, January 16, 1955; children: Sarah Newcomb, Emily Baldwin; and married Barbara Floyd Osterman, February 8, 1986.
  
  wn.com/Hassler_Whitney
• 
  Hipparchus
  Hipparchus/hɪˈpɑːrkəs/, or more correctly Hipparchos (Greek: Ἵππαρχος, Hipparkhos; c. 190 BC – c. 120 BC), was a Greek astronomer, geographer, and mathematician of the Hellenistic period. He is considered the founder of trigonometry.
  Hipparchus was born in Nicaea (now Iznik, Turkey), and probably died on the island of Rhodes. He is known to have been a working astronomer at least from 162 to 127 BC. Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity. He was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. For this he certainly made use of the observations and perhaps the mathematical techniques accumulated over centuries by the Chaldeans from Babylonia. He developed trigonometry and constructed trigonometric tables, and he solved several problems of spherical trigonometry. With his solar and lunar theories and his trigonometry, he may have been the first to develop a reliable method to predict solar eclipses. His other reputed achievements include the discovery of Earth's precession, the compilation of the first comprehensive star catalog of the western world, and possibly the invention of the astrolabe, also of the armillary sphere, which he used during the creation of much of the star catalogue. It would be three centuries before Claudius Ptolemaeus' synthesis of astronomy would supersede the work of Hipparchus; it is heavily dependent on it in many areas.
  
  wn.com/Hipparchus
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  Isaac Newton
  Sir Isaac Newton PRS MP (25 December 1642 – 20 March 1727 [NS: 4 January 1643 – 31 March 1727]) was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived." His monograph Philosophiæ Naturalis Principia Mathematica, published in 1687, lays the foundations for most of classical mechanics. In this work, Newton described universal gravitation and the three laws of motion, which dominated the scientific view of the physical universe for the next three centuries. Newton showed that the motions of objects on Earth and of celestial bodies are governed by the same set of natural laws, by demonstrating the consistency between Kepler's laws of planetary motion and his theory of gravitation, thus removing the last doubts about heliocentrism and advancing the Scientific Revolution.
  
  wn.com/Isaac_Newton
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  Jacob Bernoulli
  Jacob Bernoulli (also known as James or Jacques) (27 December 1654 – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family.
  Jacob Bernoulli was born in Basel, Switzerland. Following his father's wish, he studied theology and entered the ministry. But contrary to the desires of his parents, he also studied mathematics and astronomy. He traveled throughout Europe from 1676 to 1682, learning about the latest discoveries in mathematics and the sciences. This included the work of Robert Boyle and Robert Hooke.
  He became familiar with calculus through a correspondence with Gottfried Leibniz, then collaborated with his brother Johann on various applications, notably publishing papers on transcendental curves (1696) and isoperimetry (1700, 1701). In 1690, Jacob Bernoulli became the first person to develop the technique for solving separable differential equations.
  Upon returning to Basel in 1682, he founded a school for mathematics and the sciences. He was appointed professor of mathematics at the University of Basel in 1687, remaining in this position for the rest of his life.
  
  wn.com/Jacob_Bernoulli
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  Leonard Euler
  Leonhard Euler (German pronunciation: [ˈɔʏlɐ], ( Swiss German pronunciation (help·info)) ( Standard German pronunciation (help·info)) English approximation, "Oiler"; 15 April 1707 – 18 September 1783) was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. He is also renowned for his work in mechanics, fluid dynamics, optics, and astronomy.
  Euler spent most of his adult life in St. Petersburg, Russia, and in Berlin, Prussia. He is considered to be the preeminent mathematician of the 18th century, and one of the greatest of all time. He is also one of the most prolific mathematicians ever; his collected works fill 60–80 quarto volumes. A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all."
  
  wn.com/Leonard_Euler
• Levi ben Gerson
  Levi ben Gershon, better known by his Latinised name as Gersonides or the abbreviation of first letters as RaLBaG (1288–1344), philosopher, Talmudist, mathematician, astronomer/astrologer. He was born at Bagnols in Languedoc, France. According to Abraham Zacuto and others, he was the son of Gerson ben Solomon Catalan.
  As in the case of the other medieval Jewish philosophers little is known of his life. His family had been distinguished for piety and exegetical skill in Talmud, but though he was known in the Jewish community by commentaries on certain books of the Bible, he never seems to have accepted any rabbinical post. It has been suggested that the uniqueness of his opinions may have put obstacles in the way of his preferment. He is known to have been at Avignon and Orange during his life, and is believed to have died in 1344, though Zacuto asserts that he died at Perpignan in 1370.
  Part of his writings consist of commentaries on the portions of Aristotle then known, or rather of commentaries on the commentaries of Averroes. Some of these are printed in the early Latin editions of Aristotle’s works. His most important treatise, that by which he has a place in the history of philosophy, is entitled Sefer Milhamot Ha-Shem, ("The Wars of the Lord"), and occupied twelve years in composition (1317–1329). A portion of it, containing an elaborate survey of astronomy as known to the Arabs, was translated into Latin in 1342 at the request of Pope Clement VI.
  
  wn.com/Levi_ben_Gerson
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  Plutarch
  
  Plutarch (English pronunciation: /'pluːtɑːk/; Greek: Πλούταρχος, Ploútarkhos, Koine Greek: [plŭːtarkʰos]) then named, on his becoming a Roman citizen, Lucius Mestrius Plutarchus (Μέστριος Πλούταρχος),c. 46 – 120 AD, was a Greek historian, biographer, essayist, and Middle Platonist known primarily for his Parallel Lives and Moralia. He was born to a prominent family in Chaeronea, Boeotia, a town about twenty miles east of Delphi.
  Plutarch was born in 46 AD in the small town of Chaeronea, in the Greek region known as Boeotia. His family was wealthy. The name of Plutarch's father has not been preserved, but it was probably Nikarchus (Greek: Nίκαρχoς), from the common habit of Greek families to repeat a name in alternate generations. The name of Plutarch's grandfather was Lamprias, as he attested in Moralia and in his Life of Antony.
  His brothers, Timon and Lamprias, are frequently mentioned in his essays and dialogues, where Timon is spoken of in the most affectionate terms. Rualdus, in his 1624 work Life of Plutarchus, recovered the name of Plutarch's wife, Timoxena, from internal evidence afforded by his writings. A letter is still extant, addressed by Plutarch to his wife, bidding her not give way to excessive grief at the death of their two year old daughter, who was named Timoxena after her mother. Interestingly, he hinted at a belief in reincarnation in that letter of consolation.
  
  wn.com/Plutarch
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  Richard P. Stanley
  Richard Peter Stanley (born June 23, 1944 in New York City, New York) is the Norman Levinson Professor of Applied Mathematics at the Massachusetts Institute of Technology, in Cambridge, Massachusetts. He received his Ph.D. at Harvard University in 1971 under the supervision of Gian-Carlo Rota. He is universally recognized as a leading expert in the field of combinatorics and its applications to a variety of other mathematical disciplines.^{[citation needed]} He is well known for his two-volume book Enumerative Combinatorics (1986–1999), a far-reaching and authoritative treatise on enumerative methods that is widely regarded for its elegant exposition, usefulness as a reference, and creative exercises. (Perhaps the most famous exercise is in volume 2, where readers are asked to prove that 66 different definitions of the Catalan numbers are equivalent.) He is also the author of Combinatorics and Commutative Algebra (1983) and well over 100 research articles in mathematics. He has served as thesis advisor to more than 45 doctoral students, many of whom have had distinguished careers in combinatorial research. Among Stanley's many distinctions are membership in the National Academy of Sciences (elected in 1995), the 2001 Leroy P. Steele Prize for mathematical exposition, the 2003 Schock Prize, and a plenary lecture at the 2006 meeting of the ICM (in Madrid, Spain).
  
  wn.com/Richard_P._Stanley
• 
  Sushruta
  Suśruta (Sanskrit: सुश्रुत (sʊʃɾʊt̪), fl. 800 BCE) was an ancient Indian surgeon and is the author of the book Suśruta Saṃhitā, in which he describes over 300 surgical procedures, 120 surgical instruments and classifies human surgery in eight categories. He lived, taught and practiced his art on the banks of the Ganges in the area that corresponds to the present day city of Varanasi in North India.
  Because of his seminal and numerous contributions to the science and art of surgery he is also known by the title "Father of Surgery." Much of what is known about this inventive surgeon is contained in a series of volumes he authored, which are collectively known as the Sushruta Samhita.
  Sushruta was educated in Varanasi.
  
  wn.com/Sushruta

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