Edmund F. Robertson
|Born||1 June 1943 (age 75)|
Robertson is one of the creators of the noted MacTutor History of Mathematics Archive along with John J. O'Connor. He has written over one hundred research articles, mainly in the theory of groups and semigroups. He is the author or co-author of seventeen textbooks.
Robertson obtained a Bachelor of Science degree at the University of St Andrews in 1965. He subsequently went to the University of Warwick where he received an M.Sc. degree in 1966 and a Doctor of Philosophy degree in 1968.
In 2015 he received together with his colleague O'Connor the Hirst prize of the London Mathematical Society for his work on the MacTutor History of Mathematics archive. His thesis on "Classes of Generalised Nilpotent Groups" was done with Stewart E. Stonehewer. 
He lives at home with his wife Helena, and his son David.
Al-Ali is a group of Arab clans who are not necessarily from a common ancestor but were once rulers of their own Arab state in Southern Persia and are still influential in the United Arab Emirates as they are the ruling family in Umm al-Quwain. Many of whom are from an Arab tribe, a branch of Bani Malik from Central Arabia. Bani Malik are named after the renowned army leader, Malik Al-Ashtar Al-Nakha'i, and are a branch of Azd Mecca ( the descendants of Khuza'a Ibn Amr),. Azd Mecca are one of four branches of Azd ( or Al-Azd), a major pre-Islamic tribes, a branch of Kahlan which was one of the branches of Qahtan the other being Himyar. Most of Al-Ali tribe migrated by the end of the 16th century from what is now Saudi Arabia to different neighboring countries. Members of Al-Ali tribe live in Saudi Arabia, UAE, Qatar, Kuwait, Bahrain, Iraq and Jordan and Syria.Edmund Robertson
Edmund Robertson may refer to:
Edmund Robertson, 1st Baron Lochee (1845–1911), Scottish barrister, academic and politician
Edmund F. Robertson (born 1943), Scottish mathematicianExponential function
In mathematics, an exponential function is a function of the form
where b is a positive real number, and in which the argument x occurs as an exponent. For real numbers c and d, a function of the form is also an exponential function, as it can be rewritten as
As functions of a real variable, exponential functions are uniquely characterized by the fact that the growth rate of such a function (that is, its derivative) is directly proportional to the value of the function. The constant of proportionality of this relationship is the natural logarithm of the base b:
For b = 1 the real exponential function is a constant and the derivative is zero because for positive a and b > 1 the real exponential functions are monotonically increasing (as depicted for b = e and b = 2), because the derivative is greater than zero for all arguments, and for b < 1 they are monotonically decreasing (as depicted for b = 1/), because the derivative is less than zero for all arguments.
The constant e = 2.71828... is the unique base for which the constant of proportionality is 1, so that the function's derivative is itself:
Since changing the base of the exponential function merely results in the appearance of an additional constant factor, it is computationally convenient to reduce the study of exponential functions in mathematical analysis to the study of this particular function, conventionally called the "natural exponential function", or simply, "the exponential function" and denoted by
While both notations are common, the former notation is generally used for simpler exponents, while the latter tends to be used when the exponent is a complicated expression.
The exponential function satisfies the fundamental multiplicative identity
This identity extends to complex-valued exponents. It can be shown that every continuous, nonzero solution of the functional equation is an exponential function, with The fundamental multiplicative identity, along with the definition of the number e as e1, shows that for positive integers n and relates the exponential function to the elementary notion of exponentiation.
The argument of the exponential function can be any real or complex number or even an entirely different kind of mathematical object (for example, a matrix).
Its ubiquitous occurrence in pure and applied mathematics has led mathematician W. Rudin to opine that the exponential function is "the most important function in mathematics". In applied settings, exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change (that is, percentage increase or decrease) in the dependent variable. This occurs widely in the natural and social sciences; thus, the exponential function also appears in a variety of contexts within physics, chemistry, engineering, mathematical biology, and economics.
The graph of is upward-sloping, and increases faster as x increases. The graph always lies above the x-axis but can be arbitrarily close to it for negative x; thus, the x-axis is a horizontal asymptote. The slope of the tangent to the graph at each point is equal to its y-coordinate at that point, as implied by its derivative function (see above). Its inverse function is the natural logarithm, denoted or because of this, some old texts refer to the exponential function as the antilogarithm.
Giovanni Ceva (December 7, 1647 – June 15, 1734) was an Italian mathematician widely known for proving Ceva's theorem in elementary geometry. His brother, Tommaso Ceva was also a well-known poet and mathematician.Infinity
Infinity (symbol: ∞) is a concept describing something without any bound, or something larger than any natural number. Philosophers have speculated about the nature of the infinite, for example Zeno of Elea, who proposed many paradoxes involving infinity, and Eudoxus of Cnidus, who used the idea of infinitely small quantities in his method of exhaustion. This idea is also at the basis of infinitesimal calculus.
At the end of 19th century, Georg Cantor introduced and studied infinite sets and infinite numbers, which are now an essential part of the foundation of mathematics. For example, in modern mathematics, a line is viewed as the set of all its points, and their infinite number (the cardinality of the line) is larger than the number of integers. Thus the mathematical concept of infinity refines and extends the old philosophical concept. It is used everywhere in mathematics, even in areas, such as combinatorics and number theory that may seem to have nothing to do with it. For example, Wiles's proof of Fermat's Last Theorem uses the existence of very large infinite sets.
The concept of infinity is also used in physics and the other sciences.Ion Barbu
Ion Barbu (Romanian pronunciation: [iˈon ˈbarbu], pen name of Dan Barbilian; 18 March 1895 –11 August 1961) was a Romanian mathematician and poet.Jacques Philippe Marie Binet
Jacques Philippe Marie Binet (French: [binɛ]; 2 February 1786 – 12 May 1856) was a French mathematician, physicist and astronomer born in Rennes; he died in Paris, France, in 1856. He made significant contributions to number theory, and the mathematical foundations of matrix algebra which would later lead to important contributions by Cayley and others. In his memoir on the theory of the conjugate axis and of the moment of inertia of bodies he enumerated the principle now known as Binet's theorem. He is also recognized as the first to describe the rule for multiplying matrices in 1812, and Binet's Formula expressing Fibonacci numbers in closed form is named in his honour, although the same result was known to Abraham de Moivre a century earlier.
Binet graduated from l'École Polytechnique in 1806, and returned as a teacher in 1807. He advanced in position until 1816 when he became an inspector of studies at l'École. He held this post until 13 November 1830, when he was dismissed by the recently crowned King Louis-Philippe of France, probably because of Binet's strong support of the previous King, Charles X. In 1823 Binet succeeded Delambre in the chair of astronomy at the Collège de France. He was made a Chevalier in the Légion d'Honneur in 1821, and was elected to the Académie des Sciences in 1843.James Cockle
Sir James Cockle FRS FRAS FCPS (14 January 1819 – 27 January 1895) was an English lawyer and mathematician.
Cockle was born on 14 January 1819. He was the second son of James Cockle, a surgeon, of Great Oakley, Essex. Educated at Charterhouse and Trinity College, Cambridge, he entered the Middle Temple in 1838, practising as a special pleader in 1845 and being called in 1846. Joining the midland circuit, he acquired a good practice, and on the recommendation of Chief Justice Sir William Erle he was appointed as the first Chief Justice of the Supreme Court of Queensland in Queensland, Australia on 21 February 1863; he served until his retirement on 24 June 1879. Cockle was made a Fellow of the Royal Society (FRS) on 1 June 1865. He received the honour of knighthood on 29 July 1869. He returned to England in 1878.James Gregory (mathematician)
James Gregory FRS (November 1638 – October 1675) was a Scottish mathematician and astronomer. His surname is sometimes spelled as Gregorie, the original Scottish spelling. He described an early practical design for the reflecting telescope – the Gregorian telescope – and made advances in trigonometry, discovering infinite series representations for several trigonometric functions.
In his book Geometriae Pars Universalis (1668) Gregory gave both the first published statement and proof of the fundamental theorem of the calculus (stated from a geometric point of view, and only for a special class of the curves considered by later versions of the theorem), for which he was acknowledged by Isaac Barrow.Jean-Marie Duhamel
Jean-Marie Constant Duhamel (; French: [dy.amɛl]; 5 February 1797 – 29 April 1872) was a French mathematician and physicist.
His studies were affected by the troubles of the Napoleonic era. He went on to form his own school École Sainte-Barbe. Duhamel's principle, a method of obtaining solutions to inhomogeneous linear evolution equations, is named after him. He was primarily a mathematician but did studies on the mathematics of heat, mechanics, and acoustics. He also did work in calculus using infinitesimals. Duhamel's theorem for infinitesimals says that the sum of a series of infinitesimals is unchanged by replacing the infinitesimal with its principal part.Jean-Victor Poncelet
Jean-Victor Poncelet (1 July 1788 – 22 December 1867) was a French engineer and mathematician who served most notably as the Commanding General of the École Polytechnique. He is considered a reviver of projective geometry, and his work Traité des propriétés projectives des figures is considered the first definitive text on the subject since Gérard Desargues' work on it in the 17th century. He later wrote an introduction to it: Applications d’analyse et de géométrie.As a mathematician, his most notable work was in projective geometry, although an early collaboration with Charles Julien Brianchon provided a significant contribution to Feuerbach's theorem. He also made discoveries about projective harmonic conjugates; relating these to the poles and polar lines associated with conic sections. He developed the concept of parallel lines meeting at a point at infinity and defined the circular points at infinity that are on every circle of the plane. These discoveries led to the principle of duality, and the principle of continuity and also aided in the development of complex numbers.As a military engineer, he served in Napoleon's campaign against the Russian Empire in 1812, in which he was captured and held prisoner until 1814. Later, he served as a professor of mechanics at the École d’application in his home town of Metz, during which time he published Introduction à la mécanique industrielle, a work he is famous for, and improved the design of turbines and water wheels. In 1837, a tenured 'Chaire de mécanique physique et expérimentale' was specially created for him at the Sorbonne (the University of Paris). In 1848, he became the commanding general of his alma mater, the École Polytechnique. He is honoured by having his name listed among notable French engineers and scientists displayed around the first stage of the Eiffel tower.Lev Pontryagin
Lev Semyonovich Pontryagin (Russian: Лев Семёнович Понтрягин, also written Pontriagin or Pontrjagin) (3 September 1908 – 3 May 1988) was a Soviet mathematician. He was born in Moscow and lost his eyesight due to a primus stove explosion when he was 14. Despite his blindness he was able to become one of the greatest mathematicians of the 20th century, partially with the help of his mother Tatyana Andreevna who read mathematical books and papers (notably those of Heinz Hopf, J. H. C. Whitehead, and Hassler Whitney) to him. He made major discoveries in a number of fields of mathematics, including algebraic topology and differential topology.List of people considered father or mother of a scientific field
The following is a list of people who are considered a "father" or "mother" (or "founding father" or "founding mother") of a scientific field. Such people are generally regarded to have made the first significant contributions to and/or delineation of that field; they may also be seen as "a" rather than "the" father or mother of the field. Debate over who merits the title can be perennial. As regards science itself, the title has been bestowed on the ancient Greek philosophers Thales – who attempted to explain natural phenomena without recourse to mythology – and Democritus, the atomist..Louis Nirenberg
Louis Nirenberg (born 28 February 1925) is a Canadian-American mathematician, considered one of the most outstanding mathematicians of the 20th century.He has made fundamental contributions to linear and nonlinear partial differential equations (PDEs) and their application to complex analysis and geometry. His contributions include the Gagliardo–Nirenberg interpolation inequality, which is important in the solution of the elliptic partial differential equations that arise in many areas of mathematics, and the formalization of the bounded mean oscillation known as John–Nirenberg space, which is used to study the behavior of both elastic materials and games of chance known as martingales.Nirenberg's work on PDEs was described by the American Mathematical Society in 2002 as "about the best that's been done" towards solving the Navier–Stokes existence and smoothness problem of fluid mechanics and turbulence, which is a Millennium Prize Problem and one of the largest unsolved problems in physics.Luca Pacioli
Fra Luca Bartolomeo de Pacioli (sometimes Paccioli or Paciolo; c. 1447 – 19 June 1517) was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and an early contributor to the field now known as accounting. He is referred to as "The Father of Accounting and Bookkeeping" in Europe and he was the first person to publish a work on the double-entry system of book-keeping on the continent. He was also called Luca di Borgo after his birthplace, Borgo Sansepolcro, Tuscany.MacTutor History of Mathematics archive
The MacTutor History of Mathematics archive is a website maintained by John J. O'Connor and Edmund F. Robertson and hosted by the University of St Andrews in Scotland. It contains detailed biographies on many historical and contemporary mathematicians, as well as information on famous curves and various topics in the history of mathematics.
The History of Mathematics archive was an outgrowth of Mathematical MacTutor system, a HyperCard database by the same authors, which won them the European Academic Software award in 1994. In the same year, they founded their web site. As of 2015 it has biographies on over 2800 mathematicians and scientists.In 2015, O'Connor and Robertson won the Hirst Prize of the London Mathematical Society for their work. The citation for the Hirst Prize calls the archive "the most widely used and influential web-based resource in history of mathematics".Mathematics in medieval Islam
Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta). Important progress was made, such as the full development of the decimal place-value system to include decimal fractions, the first systematised study of algebra (named for The Compendious Book on Calculation by Completion and Balancing by scholar Al-Khwarizmi), and advances in geometry and trigonometry.Arabic works also played an important role in the transmission of mathematics to Europe during the 10th to 12th centuries.Morris Kline
Morris Kline (May 1, 1908 – June 10, 1992) was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.Stephanie van Willigenburg
Stephanie van Willigenburg is a professor of mathematics at the University of British Columbia whose research is in the field of algebraic combinatorics and concerns quasisymmetric functions. Together with James Haglund, Kurt Luoto and Sarah Mason, she introduced the quasisymmetric Schur functions, which form a basis for quasisymmetric functions.[HLM]van Willigenburg earned her Ph.D. in 1997 at the University of St. Andrews under the joint supervision of Edmund F. Robertson and Michael D. Atkinson, with a thesis titled The Descent Algebras of Coxeter Groups. She was awarded the Krieger–Nelson Prize in 2017 by the Canadian Mathematical Society.