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| Edgeworth box; *daviddfriedman.com |
The most important and urgent problems of the technology of today are no longer the satisfactions of the primary needs or of archetypal wishes, but the reparation of the evils and damages by technology of yesterday.
~Dennis Gabor
The 39th day of the year; 39 is the smallest number with multiplicative persistence 3. [Multiplicative persistence is the number of times the digits must be multiplied until they produce a one digit number; 3(9)= 27; 2(7) = 14; 1(4)=4. Students might try to find the smallest number with multiplicative persistence of four, or prove that no number has multiplicative persistence greater than 11]
For the 39th day: 39 = 3¹ + 3² + 3³ *jim wilder @wilderlab
An Armstrong (or Pluperfect digital invariant) number is a number that is the sum of its own digits each raised to the power of the number of digits. For example, 371 is an Armstrong number since \(3^3+7^3+1^3 = 371\). The largest Armstrong number in decimal numbers has 39 digits. (115,132,219,018,763,992,565,095,597,973,522,401 is the largest)
(Armstrong numbers are named for Michael F. Armstrong who named them for himself as part of an assignment to his class in Fortran Programming at the University of Rochester \)
I find it interesting that 39 = 3*13, and is the sum of all the primes from 3 to 13, 39=3+5+7+11+13 (is there a name for these kinds of numbers?)
EVENTS
1587 Mary, Queen of Scots, was beheaded after Sir Francis Walsingham did a frequency count on Mary’s cipher, read her message, and uncovered her plot to assassinate Elizabeth I, Queen of England. *VFR a more complete version of the "Babington Plot" and Walsingham's work in deciphering the code is here
In 1672, Isaac Newton's first paper on optics read before Royal Society in London. He had been elected a member only the previous month, recognizing his original design of the first reflecting telescope. Newton had already spent several years investigating optics, beginning in 1665. His studies of the colors from glass prisms with their dispersion of light were recorded in his essay New Theory about Light and Colors (1672), and expanded later in Opticks (1704).*TIS (Always sensitive to criticism, the controversy over his theories and experiments in light would lead to his not publishing on the topic until 1704.) Thony Christie has a nice post about Newton's research on color and light here.
In 1865, Gregor Mendel, aged 42, who first discovered the laws of genetics, read his first scientific paper to the Brünn Society for the study of Natural Sciences in Moravia (published 1866). He described his investigations with pea plants. Although he sent 40 reprints of his article to prominent biologists throughout Europe, including Darwin, only one was interested enough to reply. Most of the reprints, including Darwin's, were discovered later with the pages uncut, meaning they were never read. Fortunately, 18 years after Mendel's death, three botanists in three different countries researching the laws of inheritance, in spring 1900, came to realize that Mendel had found them first. Mendel was finally acknowledged as a pioneer in the field which became known as genetics*TIS
1913 Hardy wrote a letter to Ramanujan, (actually Littlewood wrote the letter, but surely speaking their joint interest) expressing his interest for his work. Hardy also added that it was "essential that I should see proofs of some of your assertions". *Wik
1945 A Patent is Filed for the Harvard Mark I. C.D Lake, H.H. Aiken, F.E. Hamilton, and B.M. Durfee file a calculator patent for the Automatic Sequence Control Calculator, commonly known as the Harvard Mark I. The Mark I was a large automatic digital computer that could perform the four basic arithmetic functions and handle 23 decimal places. A multiplication took about five seconds. *CHM (We've come a long way, baby.)
In 1969, pieces of a large meteorite were recovered in Chihuahua, Mexico. It fell at 1:05 am as a huge fireball that scattering several tons of material over an area measuring 48 by 7 km. Named after the nearby village of Allende, samples of this carbonaceous chondrite stone contain an aggregated mass of particles several of which can be easily identified as chondrules. This ancient material comes from before our Solar System formed, thus over 4.6 billion years old. Since these remnants represent the most primitive geological material from which planets were formed, and carry information to help explain the evolution of the our galaxy, Allende is one of the most studied meteorites in the world.*TIS
1978 The first issue of the CSHPM (Canadian Society for History and Philosophy of Mathematics) newsletter is issued. The issue announced the establishment of a fund as a memorial to Ken May. The fund will be used to underwrite the Kenneth O. May Lecture series. May had been one of the primary agents in the creation of the CSHPM. *CSHPM newsletter
BIRTHS
411 Proclus Diadochus (8 Feb 411 in Constantinople (now Istanbul), Byzantium (now Turkey) - 17 April 485 in Athens, Greece) was a Greek philosopher who became head of Plato's Academy and is important mathematically for his commentaries on the work of other mathematicians.
A man of great learning, Proclus was regarded with great veneration by his contemporaries. He followed the neoplatonist philosophy which Plotinus founded, and Porphyry and Iamblichus developed around 300 AD. Other developers of these ideas were Plutarch and Syrianus, the teachers of Proclus. Heath writes [4]:-
He was an acute dialectician and pre-eminent among his contemporaries in the range of his learning; he was a competent mathematician; he was even a poet. At the same time he was a believer in all sorts of myths and mysteries, and a devout worshipper of divinities both Greek and Oriental. He was much more a philosopher than a mathematician.
Of course, as one might expect, his belief in many religious sayings meant that he was highly biased in his views on many issues of science. For example he mentions the hypothesis that the sun is at the centre of the planets as proposed by Aristarchus but rejects it immediately since it contradicted the views of a Chaldean whom he says that it is unlawful not to believe.
Proclus wrote Commentary on Euclid which is our principal source about the early history of Greek geometry. The book is certainly the product of his teaching at the Academy. This work is not coloured by his religious beliefs and Martin, writing in the middle of the 19th century, says :... for Proclus the "Elements of Euclid" had the good fortune not to be contradicted either by the Chaldean Oracles or by the speculations of Pythagoreans old and new.
Proclus had access to books which are now lost and others, already lost in Proclus's time, were described based on extracts in other books available to Proclus. In particular he certainly used the History of Geometry by Eudemus, which is now lost, as is the works of Geminus which he also used.
*SAU
1627 Sir Jonas Moore (8 Feb 1627 in Whitelee, Pendle Forest, Lancashire, England - 25 Aug 1679 in Godalming, England) was an English man of science important for his support of mathematics and astronomy.*SAU He seems to have been the first to use "cot" for the cotangent function. He also founded the Royal Mathematical School at Christ's Hospital with Samuel Pepys to train young men in the mathematics of navigation. *Wik He made critical contributions to the draining of the fens in England (making my daily drive from Lakenheath to Stoke Ferry much easier) and was instrumental in convincing Charles II to create the Royal Observatory and appoint Flamsteed as Astronomer Royal. *The day that Jonas died, Renaissance Mathematicus.
1630 Pierre-Daniel Huet (8 Feb 1630, 26 Jan 1721) French scholar, antiquary, scientist, and bishop whose incisive skepticism, particularly as embodied in his cogent attacks on René Descartes, greatly influenced contemporary philosophers. Huet wrote a number of philosophical works that asserted the fallibility of human reason in addition to scientific work in the fields of astronomy, anatomy, and mathematics. *TIS
1677 Jacques Cassini (8 February 1677 – 16 April 1756) was a French astronomer, son of the famous Italian astronomer Giovanni Domenico Cassini.
Cassini was born at the Paris Observatory. Admitted at the age of seventeen to membership of the French Academy of Sciences, he was elected in 1696 a fellow of the Royal Society of London, and became maître des comptes in 1706. Having succeeded to his father's position at the observatory in 1712, he measured in 1713 the arc of the meridian from Dunkirk to Perpignan, and published the results in a volume entitled Traité de la grandeur et de la figure de la terre (1720). He also wrote Eléments d'astronomie (1740), and died at Thury, near Clermont. He published the first tables of the satellites of Saturn in 1716.*Wik
Engraving of Jacques Cassini in his Paris Observatory by L. Coquin
1700 Daniel Bernoulli (29 January 1700 (8 Feb new style), 8 March 1782) was a Dutch-Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics. Bernoulli's work is still studied at length by many schools of science throughout the world. The son of Johann Bernoulli (one of the "early developers" of calculus), nephew of Jakob Bernoulli (who "was the first to discover the theory of probability"), and older brother of Johann II, He is said to have had a bad relationship with his father. Upon both of them entering and tying for first place in a scientific contest at the University of Paris, Johann, unable to bear the "shame" of being compared as Daniel's equal, banned Daniel from his house. Johann Bernoulli also plagiarized some key ideas from Daniel's book Hydrodynamica in his own book Hydraulica which he backdated to before Hydrodynamica. Despite Daniel's attempts at reconciliation, his father carried the grudge until his death.
He was a contemporary and close friend of Leonhard Euler. He went to St. Petersburg in 1724 as professor of mathematics, but was unhappy there, and a temporary illness in 1733 gave him an excuse for leaving. He returned to the University of Basel, where he successively held the chairs of medicine, metaphysics and natural philosophy until his death.
In May, 1750 he was elected a Fellow of the Royal Society. He was also the author in 1738 of Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk), in which the St. Petersburg paradox was the base of the economic theory of risk aversion, risk premium and utility.
One of the earliest attempts to analyze a statistical problem involving censored data was Bernoulli's 1766 analysis of smallpox morbidity and mortality data to demonstrate the efficacy of vaccination. He is the earliest writer who attempted to formulate a kinetic theory of gases, and he applied the idea to explain Boyle's law. He worked with Euler on elasticity and the development of the Euler-Bernoulli beam equation. *Wik
1777 Bernard Courtois,(8 February 1777 – 27 September 1838) was a French chemist. In 1811, the French government was looking for alternate ways to manufacture saltpeter, or potassium nitrate, an ingredient essential for gunpowder. Saltpeter had traditionally been made using wood ash, but France (like England) was running out of wood, and other sources were desperately needed. So Courtois, a professional salpêtrier, was working on extracting potassium nitrate from seaweed, which one can find in great abundance along the coast of Normandy. Courtois began to suspect that there was something else in seaweed ash besides sodium and potassium, something corrosive, because the copper vats in his lab were being attacked by some chemical. He found that when he added sulfuric acid to the ash residue, a purple vapor was given off, which then formed deposits of shiny purplish-black crystals on the sides of the vats. Courtois had discovered iodine. He announced the discovery in the journal Annales de Chimie in 1813. *Linda Hall Org
1834 Dmitry Ivanovich Mendeleev (8 Feb 1834; 2 Feb 1907 at age 73) (Also spelled Mendeleyev) Russian chemist who developed the periodic classification of the elements. In his final version of the periodic table (1871) he left gaps, foretelling that they would be filled by elements not then known and predicting the properties of three of those elements.*TIS
Mendeleev's 1871 periodic table
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| *Wik |
1845 Francis Ysidro Edgeworth FBA (8 February 1845, Edgeworthstown – 13 February 1926, Oxford) was an Irish philosopher and political economist who made significant contributions to the methods of statistics during the 1880s. Edgeworth was a highly influential figure in the development of neo-classical economics. He was the first to apply certain formal mathematical techniques to individual decision making in economics. He developed utility theory, introducing the indifference curve and the famous Edgeworth box, which is now familiar to undergraduate students of microeconomics. He is also known for the Edgeworth conjecture which states that the core of an economy shrinks to the set of competitive equilibria as the number of agents in the economy gets large. In statistics Edgeworth is most prominently remembered by having his name on the Edgeworth series. *Wik In 1881 he published Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences. This work, really on economics, looks at the Economical Calculus and the Utilitarian Calculus. In fact most of his work could be said to be applications of mathematical psychics which Edgeworth saw as analogous to mathematical physics. They were applied to the measure of utility, the measure of ethical value, the measure of evidence, the measure of probability, the measure of economic value, and the determination of economic equilibria. He formulated mathematically a capacity for happiness and a capacity for work. His conclusions that women have less capacity for pleasure and for work than do men would not be popular today. *SAU
1853 Alexander Ziwet (February 8, 1853 - November 18, 1928) born in Breslau. He became professor at the University of Michigan, an editor of the Bulletin of the AMS, and a collector of mathematics text who enriched the Michigan library. *VFR His early education was obtained in a German gymnasium. He afterwards studies in the universities of Warsaw and Moscow, one year at each, and then entered the Polytechnic School at Karlsruhe, where he received the degree of Civil Engineer in 1880.
He came immediately to the United States and received employment on the United States Lake Survey. Two years later he was transferred to the United States Coast and Geodetic Survey, computing division, where he remained five years.
In 1888 he was appointed Instructor in Mathematics in the University of Michigan. From this position he was advanced to Acting Assistant Professor in 1890, to Assistant Professor in 1891, to Junior Professor in 1896, and to Professor of Mathematics in 1904.
He was a member of the Council of the American Mathematical Society and an editor of the "Bulletin" of the society. In 1893-1894 he published an "Elementary Treatise on Theoretical Mechanics" in three parts, of which a revised edition appeared in 1904. He also translated from the Russian of I. Somoff "Theoretische Mechanik" (two volumes, 1878, 1879).
*Burke A. Hinsdale and Isaac Newton Demmon, History of the University of Michigan (Ann Arbor: University of Michigan Press, 1906), pp. 320-321.
While an Assistant Professor at UM, Ziwet attended and took notes, (published in 1894, and recently reprinted by the AMS), for a famous series of "colloquium" lectures of Felix Klein, featuring some of the important mathematical developments of the late 19th century, including Lie theory, function theory, algebraic geometry (of curves and surfaces), number theory, and non euclidean geometry. These lectures, held under the hospitality of Northwestern University, followed a Congress of Mathematics sponsored by the World's Fair Auxillary, 21-26 August, 1893. This occasion launched the greatly influential role that Klein played in the development of American mathematics.
1875 Thomas John l'Anson Bromwich (8 Feb 1875 in Wolverhampton, England - 26 Aug 1929 in Northampton, England) He worked on infinite series, particularly during his time in Galway. In 1908 he published his only large treatise An introduction to the theory of infinite series which was based on lectures on analysis he had given at Galway. He also made useful contributions to quadratic and bilinear forms and many consider his algebraic work to be his finest. In a series of papers he put Heaviside's calculus on a rigorous basis treating the operators as contour integrals*SAU G. H. Hardy described him as the “best pure mathematician among the applied mathematicians at Cambridge, and the best applied mathematician among the pure mathematicians.” *VFR
1996 Ennio de Giorgi (8 February 1928 – 25 October 1996) was an Italian mathematician who worked on partial differential equations and the foundations of mathematics.
De Giorgi's first work was in geometric measure theory, on the topic of the sets of finite perimeters which he called in 1958 Caccioppoli sets, after his mentor and friend. His definition applied some important analytic tools and De Giorgi's theorem for the sets established a new tool for set theory as well as his own works.[citation needed] This achievement not only brought Ennio immediate recognition but displayed his ability to attack problems using completely new and effective methods which, though conceived before, can be used with greater precision as shown in his research works.
De Giorgi solved Bernstein's problem about minimal surfaces for 8 dimensions in 1969 with Enrico Bombieri and Enrico Giusti, for which Bombieri won the Fields Medal in 1974.
De Giorgi solved 19th Hilbert problem on the regularity of solutions of elliptic partial differential equations. Before his results, mathematicians were not able to venture beyond second-order nonlinear elliptic equations in two variables. In a major breakthrough, De Giorgi proved that solutions of uniformly elliptic second-order equations of divergence form, with only measurable coefficients, were Hölder continuous. His proof was proved in 1956/57 in parallel with John Nash's, who was also working on and solved Hilbert's problem.*Wik
1930 Hans Grauert (8 February 1930 in Haren, Emsland, Germany – 4 September 2011) was a German mathematician. He is known for major works on several complex variables, complex manifolds and the application of sheaf theory in this area, which influenced later work in algebraic geometry. Together with Reinhold Remmert he established and developed the theory of complex-analytic spaces.
Grauert attended school at the Gymnasium in Meppen before studying for a semester at the University of Mainz in 1949, and then at the University of Münster, where he was awarded his doctorate in 1954.
He became professor at the University of Göttingen in 1958, as successor to C. L. Siegel. The lineage of this chair traces back through an eminent line of mathematicians: Weyl, Hilbert, Riemann, and ultimately to Gauss. Until his death, he was professor emeritus at Göttingen. *Wik
1960 Yewande Olubummo (February 8, 1960, - ) is a Nigerian-American mathematician whose research interests include functional analysis and dynamical systems. She is an associate professor of mathematics at Spelman College, where she served as chair of the mathematics department from 2006 to 2010. She is a member of the National Association of Mathematicians, as well as the Mathematical Association of America.
Olubummo is originally from Ibadan in Nigeria, and is the oldest of three children of mathematician Adegoke Olubummo and hospital administrator Edak Olubummo; her father was the second Nigerian to earn a doctorate in mathematics. As a child, she was educated at the staff school of the University of Ibadan, where her father taught, and then at the International School Ibadan on the university campus. She earned a bachelor's degree with first class honours in mathematics from the University of Ibadan in 1980, and did her compulsory national service in the National Youth Service Corps as a mathematics teacher in Keffi.
On the advice of her father Olubummo moved abroad for graduate study, choosing Yale University over the University of Oxford (to which she was also admitted) because of its financial assistance. She felt alone, isolated, and the victim of racial discrimination at Yale; she did poorly on her doctoral exams, and ended up leaving in 1983 with a master's degree.[4] At the suggestion of a visiting African-American mathematics professor, Donald F. St. Mary, she transferred to the University of Massachusetts Amherst, where she completed her doctorate eight years later in 1991. Her dissertation, Measures on Empirical Logics and the Properties of Their Associated Dual Banach Spaces, was supervised by Thurlow Cook. *Wik
DEATHS
1909 Giacinto Morera (born Novara, 18 July 1856 – died Turin, 8 February 1909), was an Italian engineer and mathematician. He is remembered for Morera's theorem in the theory of functions of a complex variables and for his work in the theory of linear elasticity. *Wik
In complex analysis, a branch of mathematics, *WikMorera's theorem, named after Giacinto Morera, gives an important criterion for proving that a function is holomorphic.The assumption of Morera's theorem is equivalent to f locally having an antiderivative on D.The converse of the theorem is not true in general. A holomorphic function need not possess an antiderivative on its domain, unless one imposes additional assumptions.
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A curve C in a domain D, as required by the
statement of Morera's theorem*Wik |
1957 John von Neumann (28 Dec 1903, 8 Feb 1957 at age 53)Hungarian-American mathematician who made important contributions in quantum physics, logic, meteorology, and computer science. He invented game theory, the branch of mathematics that analyses strategy and is now widely employed for military and economic purposes. During WW II, he studied the implosion method for bringing nuclear fuel to explosion and he participated in the development of the hydrogen bomb. He also set quantum theory upon a rigorous mathematical basis. In computer theory, von Neumann did much of the pioneering work in logical design, in the problem of obtaining reliable answers from a machine with unreliable components, the function of “memory,” and machine imitation of “randomness.”*TIS
In his classic, How to Solve It, Polya tells this story about von Neumann as his student
1974 Fritz Zwicky (14 Feb 1898, 8 Feb 1974 at age 76) Swiss-American astronomer and physicist who proposed dark matter exists in the universe, and made valuable contributions to the theory and understanding of supernovas (stars that for a short time are far brighter than normal).*TIS
He worked most of his life at the California Institute of Technology in the United States of America, where he made many important contributions in theoretical and observational astronomy. In 1933, Zwicky was the first to use the virial theorem to postulate the existence of unseen dark matter, describing it as "dunkle Materie"
Zwicky married Dorothy Vernon Gates (1904-1991), a member of a prominent local family and a daughter of California State Senator Egbert James Gates. Her money was instrumental in the funding of the Palomar Observatory during the Great Depression. Nicholas Roosevelt, cousin of President Theodore Roosevelt, was his brother-in-law by marriage to Tirzah Gates.
He is remembered as both a genius and a curmudgeon. One of his favorite insults was to refer to people whom he did not like as "spherical bastards", because, as he explained, they were bastards no matter which way one looked at them.
1979 Dennis Gabor (5 Jun 1900, 8 Feb 1979 at age 78) Hungarian-born British electrical engineer who won the Nobel Prize for Physics in 1971 for his invention of holography, a system of lensless, three-dimensional photography that has many applications. He first conceived the idea of holography in 1947 using conventional filtered-light sources. Because such sources had limitations of either too little light or too diffuse, holography was not commercially feasible until the invention of the laser (1960), which amplifies the intensity of light waves. He also did research on high-speed oscilloscopes, communication theory, physical optics, and television. Gabor held more than 100 patents. *TIS
1998 Franz Daniel Kahn FRS FRAS (1926–1998) was a mathematician and astrophysicist at the University of Manchester. He was Professor of Astronomy from 1966 to 1993, then Emeritus thereafter in the School of Physics and Astronomy.
1983 Robert (Roy) Charles Geary (April 11, 1896 – February 8, 1983) was an Irish mathematician, statistician and founder of both the Central Statistics Office and the Economic and Social Research Institute. Geary is known for his contributions to the estimation of errors-in-variables models, Geary's C, the Geary–Khamis dollar, the Stone–Geary utility function, and Geary's theorem, which has that if the sample mean is distributed independently of the sample variance, then the population is distributed normally.
Geary was born in Dublin, Ireland and received his secondary education at the O'Connell School. He went on to study mathematics and mathematical physics at the University College Dublin, where he obtained his B.Sc. and M.Sc. degrees in 1916 and 1918, respectively. He was awarded a scholarship to continue his study at the Sorbonne in Paris, where he attended lectures by Émile Borel, Élie Cartan, Édouard Goursat, Henri Lebesgue, and Paul Langevin. Geary returned to Ireland in 1921, and was offered a lecturer position in mathematics at the University of Southampton (1922–23) and in applied economics at Cambridge University (1946–47). He was a statistician in the Department of Industry and Commerce between 1923 and 1957. The National University of Ireland conferred a Doctorate of Science on him in 1938.
Geary was the founding director of the Central Statistics Office (Ireland) (in 1949). He was head of the National Accounts Branch of the United Nations in New York from 1957 to 1960. He was the founding director of the Economic and Social Research Institute (ESRI) in 1960 where he stayed till his retirement in 1966. He was an honorary fellow of the American Statistical Association and the Institute of Mathematical Statistics. In 1981, he won the Boyle Medal. To honour his contributions to social sciences, the UCD Geary Institute for Public Policy was named after him in 2005. *Wik
Franz Daniel Kahn FRS FRAS (13 May 1926–8 February 1998) was a mathematician and astrophysicist at the University of Manchester. He was Professor of Astronomy from 1966 to 1993, then Emeritus thereafter in the School of Physics and Astronomy.
Kahn was educated at St Paul's School, London from 1940 to 1944, after which he secured an open scholarship to The Queen's College, Oxford. After graduating with first-class honours in mathematics in 1947 he moved to Balliol College, Oxford in 1948 as a Skynner senior student. He was awarded a Doctor of Philosophy degree in 1950 for research supervised by Sydney Chapman on the luminosity of the upper atmosphere.
According to his certificate of election as a Fellow of the Royal Society:
Franz Kahn has made many original contributions to plasma astrophysics, cosmical gas dynamics and the physics of star formation, with significant early papers on the structure of ionisation fronts and collision-free shocks. More recently he has done important work on stellar winds and galactic fountains, on planetary nebulae and on remnants of novae and supernovae. His versatility is shown by papers on the spiral structure of the Galaxy, on the nature of the Local Group and the account (with the late Carla Kahn) of the Einstein-de Sitter correspondence. Kahn's style is especially noteworthy for his skill in building simple mathematical models which bring out the essence of the physics.
Kahn was elected a Fellow of the Royal Society (FRS) in 1993. He was also a Fellow of the Royal Astronomical Society (FRAS). In 1991 the International Astronomers Union named the asteroid Kahnia after him. *Wik
2005 Germund Dahlquist (January 16, 1925 – February 8, 2005) was a Swedish mathematician known primarily for his early contributions to the theory of numerical analysis as applied to differential equations.
Dahlquist began to study mathematics at Stockholm University in 1942 at the age of 17, where he cites the Danish mathematician Harald Bohr (who was living in exile after the occupation of Denmark during World War II) as a profound influence.[1]
He received the degree of licentiat from Stockholm University in 1949, before taking a break from his studies to work at the Swedish Board of Computer Machinery (Matematikmaskinnämnden), working on (among other things) the early computer BESK, Sweden's first. During this time, he also worked with Carl-Gustaf Rossby on early numerical weather forecasts.
Dahlquist returned to Stockholm University to complete his Ph.D., Stability and Error Bounds in the Numerical Solution of Ordinary Differential Equations, which he defended in 1958, with Fritz Carlson and Lars Hörmander as his advisors.[2] As part of this work he introduced the logarithmic norm (also introduced by Russian mathematician Sergei Lozinskii the same year).
In 1959 he moved to the Royal Institute of Technology (KTH), where he would later establish what became the Department of Numerical Analysis and Computer Science (NADA) in 1962 (now part of the School of Computer Science and Communication), and become Sweden's first Professor of Numerical Analysis in 1963.[3] He helped establish the Nordic journal of numerical analysis, BIT, in 1961. In 1965 he was elected into the Royal Swedish Academy of Engineering Sciences (IVA).
The software package COMSOL Multiphysics, for finite element analysis of partial differential equations, was started by a couple of Dahlquist's graduate students based upon codes developed for a graduate course at KTH *Wik
Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell
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