|
Bolza
Oskar Bolza (12 May 1857 – 5 July 1942) was a German mathematician, and student of Felix Klein. He was born in Bad Bergzabern, Palatinate, then a district of Bavaria, known for his research in the calculus of variations, particularly influenced by Karl Weierstrass' 1879 lectures on the subject. Life Bolza entered the University of Berlin in 1875. His first interest was in linguistics, then he studied physics with Kirchhoff and Helmholtz, but experimental work did not attract him, so he decided on mathematics in 1878. The years 1878–1881 were spent studying under Elwin Christoffel and Theodor Reye at Strasbourg, Hermann Schwarz at Göttingen, and particularly Karl Weierstrass in Berlin. In the spring of 1888 he landed in Hoboken, NJ, searching for a job in the United States: he succeeded in finding a position in 1889 at Johns Hopkins University and then at the then newly founded Clark University.According to . In 1892 Bolza joined the University of Chicago and wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bolza Surface
In mathematics, the Bolza surface, alternatively, complex algebraic Bolza curve (introduced by ), is a compact Riemann surface of genus 2 with the highest possible order of the conformal automorphism group in this genus, namely GL_2(3) of order 48 (the general linear group of 2\times 2 matrices over the finite field \mathbb_3). The full automorphism group (including reflections) is the semi-direct product GL_(3)\rtimes\mathbb_ of order 96. An affine model for the Bolza surface can be obtained as the locus of the equation :y^2=x^5-x in \mathbb C^2. The Bolza surface is the smooth completion of the affine curve. Of all genus 2 hyperbolic surfaces, the Bolza surface maximizes the length of the systole . As a hyperelliptic Riemann surface, it arises as the ramified double cover of the Riemann sphere, with ramification locus at the six vertices of a regular octahedron inscribed in the sphere, as can be readily seen from the equation above. The Bolza surface has attracted the attent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gilbert Ames Bliss
Gilbert Ames Bliss, (9 May 1876 – 8 May 1951), was an American mathematician, known for his work on the calculus of variations. Life Bliss grew up in a Chicago family that eventually became affluent; in 1907, his father became president of the company supplying all of Chicago's electricity. The family was not affluent, however, when Bliss entered the University of Chicago in 1893 (its second year of operation). Hence he had to support himself while a student by winning a scholarship, and by playing in a student professional mandolin quartet. After obtaining the B.Sc. in 1897, he began graduate studies at Chicago in mathematical astronomy (his first publication was in that field), switching in 1898 to mathematics. He discovered his life's work, the calculus of variations, via the lecture notes of Weierstrass's 1879 course, and Bolza's teaching. Bolza went on to supervise Bliss's Ph.D. thesis, ''The Geodesic Lines on the Anchor Ring'', completed in 1900 and published in the ''An ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl Weierstrass
Karl Theodor Wilhelm Weierstrass (german: link=no, Weierstraß ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis". Despite leaving university without a degree, he studied mathematics and trained as a school teacher, eventually teaching mathematics, physics, botany and gymnastics. He later received an honorary doctorate and became professor of mathematics in Berlin. Among many other contributions, Weierstrass formalized the definition of the continuity of a function, proved the intermediate value theorem and the Bolzano–Weierstrass theorem, and used the latter to study the properties of continuous functions on closed bounded intervals. Biography Weierstrass was born into a Roman Catholic family in Ostenfelde, a village near Ennigerloh, in the Province of Westphalia. Weierstrass was the son of Wilhelm Weierstrass, a government official, and Theodora Vonderforst both of whom were catholic Rhinelanders. His int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus Of Variations
The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist. Such solutions are known as ''geodesics''. A related problem is posed by Fermat's principle: light follows the path of shortest optical length connecting two points, which depends up ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bad Bergzabern
Bad Bergzabern () is a municipality in the Südliche Weinstraße district, on the German Wine Route in Rhineland-Palatinate, Germany. It is situated near the border with France, on the south-eastern edge of the Palatinate forest, approximately southwest of Landau. Bad Bergzabern is the seat of the ''Verbandsgemeinde'' ("collective municipality") Bad Bergzabern. Bad Bergzabern has a tradition as a holiday destination and contains various half-timbered houses from the seventeenth and eighteenth centuries. Of particular note from an earlier century is the Gasthaus Zum Engel (1579), which has been described as the most beautiful renaissance building in the entire region. History In the sixteenth century local scholars were keen to assert that the town had been founded under the Romans, and sources from this period refer to the medieval Latin name as ''Tabernae Montanae'' (trans. "taverns of the mountains"). Although the area was indeed under the control of the Roman empire a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anne Bosworth
Anne Lucy Bosworth Focke (September 29, 1868 – May 15, 1907) was an American mathematician who became the first mathematics professor at what is now the University of Rhode Island, and later became the first female doctoral student of David Hilbert. Early life Bosworth was originally from Woonsocket, Rhode Island. When she was four, her father and a younger sister died, and she grew up in a family of women: her mother (a librarian), her grandmother (also widowed), and her aunt. Undergraduate education and academic work Bosworth attended Woonsocket High School, and graduated from Wellesley College in 1890. At Wellesley, her classmates included mathematicians Grace Andrews (mathematician), Grace Andrews and Clara Latimer Bacon. She worked for two years as a teacher at Amesbury High School in Massachusetts, and was appointed as an instructor of mathematics at the Rhode Island College of Agriculture and Mechanic Arts (later to become the University of Rhode Island) in early 1892, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mary Emily Sinclair
Mary Emily Sinclair (September 27, 1878 – June 3, 1955) was an American mathematician whose research concerned algebraic surfaces and the calculus of variations. She was the first woman to earn a doctorate in mathematics at the University of Chicago, and became Clark Professor of Mathematics at Oberlin College. Early life and education Sinclair was born on September 27, 1878, in Worcester, Massachusetts; she was the fourth of five children of John Elbridge Sinclair and Marietta S. Fletcher Sinclair. Her father was a mathematics professor at the Worcester Polytechnic Institute, and also had two daughters from an earlier marriage. Her mother, originally from Worcester, taught English and modern languages at the Worcester Polytechnic Institute but stopped when her children were born. After graduating in 1896 from the Worcester Classical High School, Mary Emily Sinclair became a student at Oberlin, and as a student served as president of the Oberlin branch of the YWCA. She gradu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arnold Dresden
Arnold Dresden (1882–1954) was a Dutch-American mathematician, known for his work in the calculus of variations and collegiate mathematics education. He was a president of the Mathematical Association of America. Background Dresden was born in Amsterdam on November 23, 1882, into a wealthy banking family. After matriculating for three years at the University of Amsterdam he used tuition money in 1903 to book passage on a ship to New York City. He then traveled to Chicago to help a friend, arriving there on his 21st birthday. Two years later, after saving money from working at various jobs, he enrolled in the graduate program at the University of Chicago, where he earned his Ph.D. in 1909 under the direction of Oskar Bolza with thesis ''The Second Derivatives of the Extremal Integral''. Research and teaching Dresden taught at the University of Wisconsin 1909–1927. During this time he wrote several papers on the calculus of variations and systems of linear differential equation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Felix Klein
Christian Felix Klein (; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group theory. His 1872 Erlangen program, classifying geometries by their basic symmetry groups, was an influential synthesis of much of the mathematics of the time. Life Felix Klein was born on 25 April 1849 in Düsseldorf, to Prussian parents. His father, Caspar Klein (1809–1889), was a Prussian government official's secretary stationed in the Rhine Province. His mother was Sophie Elise Klein (1819–1890, née Kayser). He attended the Gymnasium in Düsseldorf, then studied mathematics and physics at the University of Bonn, 1865–1866, intending to become a physicist. At that time, Julius Plücker had Bonn's professorship of mathematics and experimental physics, but by the time Klein became his assistant, in 1866, Plücker's interest wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gustav Kirchhoff
Gustav Robert Kirchhoff (; 12 March 1824 – 17 October 1887) was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects. He coined the term black-body radiation in 1862. Several different sets of concepts are named "Kirchhoff's laws" after him, concerning such diverse subjects as black-body radiation and spectroscopy, electrical circuits, and thermochemistry. The Bunsen–Kirchhoff Award for spectroscopy is named after him and his colleague, Robert Bunsen. Life and work Gustav Kirchhoff was born on 12 March 1824 in Königsberg, Prussia, the son of Friedrich Kirchhoff, a lawyer, and Johanna Henriette Wittke. His family were Lutherans in the Evangelical Church of Prussia. He graduated from the Albertus University of Königsberg in 1847 where he attended the mathematico-physical seminar directed by Carl Gustav Jacob Jacobi, Franz Ernst Neumann and Friedrich Julius Ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helmholtz
Hermann Ludwig Ferdinand von Helmholtz (31 August 1821 – 8 September 1894) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The Helmholtz Association, the largest German association of research institutions, is named in his honor. In the fields of physiology and psychology, Helmholtz is known for his mathematics concerning the eye, theories of vision, ideas on the visual perception of space, color vision research, the sensation of tone, perceptions of sound, and empiricism in the physiology of perception. In physics, he is known for his theories on the conservation of energy, work in electrodynamics, chemical thermodynamics, and on a mechanical foundation of thermodynamics. As a philosopher, he is known for his philosophy of science, ideas on the relation between the laws of perception and the laws of nature, the science of aesthetics, and ideas on the civilizing power of science. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elwin Christoffel
Elwin Bruno Christoffel (; 10 November 1829 – 15 March 1900) was a German mathematician and physicist. He introduced fundamental concepts of differential geometry, opening the way for the development of tensor calculus, which would later provide the mathematical basis for general relativity. Life Christoffel was born on 10 November 1829 in Montjoie (now Monschau) in Prussia in a family of cloth merchants. He was initially educated at home in languages and mathematics, then attended the Jesuit Gymnasium and the Friedrich-Wilhelms Gymnasium in Cologne. In 1850 he went to the University of Berlin, where he studied mathematics with Gustav Dirichlet (which had a strong influence over him) among others, as well as attending courses in physics and chemistry. He received his doctorate in Berlin in 1856 for a thesis on the motion of electricity in homogeneous bodies written under the supervision of Martin Ohm, Ernst Kummer and Heinrich Gustav Magnus. After receiving his doctorate, Ch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
