|
Poul Heegaard
Poul Heegaard (; November 2, 1871, Copenhagen - February 7, 1948, Oslo) was a Danish mathematician active in the field of topology. His 1898 thesis introduced a concept now called the Heegaard splitting of a 3-manifold. Heegaard's ideas allowed him to make a careful critique of work of Henri Poincaré. Poincaré had overlooked the possibility of the appearance of torsion in the homology groups of a space. He later co-authored, with Max Dehn, a foundational article on combinatorial topology, in the form of an encyclopedia entry. Heegaard studied mathematics at the University of Copenhagen, from 1889 to 1893 and following years of travelling, and teaching mathematics, he was appointed professor at University of Copenhagen in 1910. An English translation of his 1898 thesis, which laid a rigorous topological foundation for modern knot theory, may be found at https://www.maths.ed.ac.uk/~v1ranick/papers/heegaardenglish.pdf. The section on "a visually transparent representation of the co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Copenhagen
Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan area has 2,057,142 people. Copenhagen is on the islands of Zealand and Amager, separated from Malmö, Sweden, by the Øresund strait. The Øresund Bridge connects the two cities by rail and road. Originally a Viking fishing village established in the 10th century in the vicinity of what is now Gammel Strand, Copenhagen became the capital of Denmark in the early 15th century. Beginning in the 17th century, it consolidated its position as a regional centre of power with its institutions, defences, and armed forces. During the Renaissance the city served as the de facto capital of the Kalmar Union, being the seat of monarchy, governing the majority of the present day Nordic region in a personal union with Sweden and Norway ruled by the Danis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homology (mathematics)
In mathematics, homology is a general way of associating a sequence of algebraic objects, such as abelian groups or modules, with other mathematical objects such as topological spaces. Homology groups were originally defined in algebraic topology. Similar constructions are available in a wide variety of other contexts, such as abstract algebra, groups, Lie algebras, Galois theory, and algebraic geometry. The original motivation for defining homology groups was the observation that two shapes can be distinguished by examining their holes. For instance, a circle is not a disk because the circle has a hole through it while the disk is solid, and the ordinary sphere is not a circle because the sphere encloses a two-dimensional hole while the circle encloses a one-dimensional hole. However, because a hole is "not there", it is not immediately obvious how to define a hole or how to distinguish different kinds of holes. Homology was originally a rigorous mathematical method for defi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Danish Mathematicians
Danish may refer to: * Something of, from, or related to the country of Denmark People * A national or citizen of Denmark, also called a "Dane," see Demographics of Denmark * Culture of Denmark * Danish people or Danes, people with a Danish ancestral or ethnic identity * A member of the Danes, a Germanic tribe * Danish (name), a male given name and surname Language * Danish language, a North Germanic language used mostly in Denmark and Northern Germany * Danish tongue or Old Norse, the parent language of all North Germanic languages Food * Danish cuisine * Danish pastry, often simply called a "Danish" See also * Dane (other) * * Gdańsk * List of Danes * Languages of Denmark The Kingdom of Denmark has only one official language, Danish, the national language of the Danish people, but there are several minority languages spoken, namely Faroese, German, and Greenlandic. A large majority (about 86%) of Danes also s ... {{disambiguation Language a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1948 Deaths
Events January * January 1 ** The General Agreement on Tariffs and Trade (GATT) is inaugurated. ** The Constitution of New Jersey (later subject to amendment) goes into effect. ** The railways of Britain are nationalized, to form British Railways. * January 4 – Burma gains its independence from the United Kingdom, becoming an independent republic, named the ''Union of Burma'', with Sao Shwe Thaik as its first President, and U Nu its first Prime Minister. * January 5 ** Warner Brothers shows the first color newsreel (''Tournament of Roses Parade'' and the '' Rose Bowl Game''). ** The first Kinsey Report, ''Sexual Behavior in the Human Male'', is published in the United States. * January 7 – Mantell UFO incident: Kentucky Air National Guard pilot Thomas Mantell crashes while in pursuit of an unidentified flying object. * January 12 – Mahatma Gandhi begins his fast-unto-death in Delhi, to stop communal violence during the Partition of India. * January 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1871 Births
Events January–March * January 3 – Franco-Prussian War – Battle of Bapaume: Prussians win a strategic victory. * January 18 – Proclamation of the German Empire: The member states of the North German Confederation and the south German states, aside from Austria, unite into a single nation state, known as the German Empire. The King of Prussia is declared the first German Emperor as Wilhelm I of Germany, in the Hall of Mirrors at the Palace of Versailles. Constitution of the German Confederation comes into effect. It abolishes all restrictions on Jewish marriage, choice of occupation, place of residence, and property ownership, but exclusion from government employment and discrimination in social relations remain in effect. * January 21 – Giuseppe Garibaldi's group of French and Italian volunteer troops, in support of the French Third Republic, win a battle against the Prussians in the Battle of Dijon. * February 8 – 1871 French legislative election elect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norway
Norway, officially the Kingdom of Norway, is a Nordic country in Northern Europe, the mainland territory of which comprises the western and northernmost portion of the Scandinavian Peninsula. The remote Arctic island of Jan Mayen and the archipelago of Svalbard also form part of Norway. Bouvet Island, located in the Subantarctic, is a dependency of Norway; it also lays claims to the Antarctic territories of Peter I Island and Queen Maud Land. The capital and largest city in Norway is Oslo. Norway has a total area of and had a population of 5,425,270 in January 2022. The country shares a long eastern border with Sweden at a length of . It is bordered by Finland and Russia to the northeast and the Skagerrak strait to the south, on the other side of which are Denmark and the United Kingdom. Norway has an extensive coastline, facing the North Atlantic Ocean and the Barents Sea. The maritime influence dominates Norway's climate, with mild lowland temperatures on the se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Professor
Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professors are usually experts in their field and teachers of the highest rank. In most systems of List of academic ranks, academic ranks, "professor" as an unqualified title refers only to the most senior academic position, sometimes informally known as "full professor". In some countries and institutions, the word "professor" is also used in titles of lower ranks such as associate professor and assistant professor; this is particularly the case in the United States, where the unqualified word is also used colloquially to refer to associate and assistant professors as well. This usage would be considered incorrect among other academic communities. However, the otherwise unqualified title "Professor" designated with a capital let ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harald Bohr
Harald August Bohr (22 April 1887 – 22 January 1951) was a Danish mathematician and footballer. After receiving his doctorate in 1910, Bohr became an eminent mathematician, founding the field of almost periodic functions. His brother was the Nobel Prize-winning physicist Niels Bohr. He was a member of the Danish national football team for the 1908 Summer Olympics, where he won a silver medal. Biography Bohr was born in 1887 to Christian Bohr, a professor of physiology, from a Lutheran background, and Ellen Adler Bohr, a woman from a wealthy Jewish family of local renown. Harald had a close relationship with his elder brother, which ''The Times'' likened to that between Captain Cuttle and Captain Bunsby in Charles Dickens' ''Dombey and Son''. Mathematical career Like his father and brother before him, in 1904 Bohr enrolled at the University of Copenhagen, where he studied mathematics, obtaining his master's degree in 1909 and his doctorate a year later. Among his tutors were Hie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Topology
In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions of spaces, such as decomposition into simplicial complexes. After the proof of the simplicial approximation theorem this approach provided rigour. The change of name reflected the move to organise topological classes such as cycles-modulo-boundaries explicitly into abelian groups. This point of view is often attributed to Emmy Noether, and so the change of title may reflect her influence. The transition is also attributed to the work of Heinz Hopf, who was influenced by Noether, and to Leopold Vietoris and Walther Mayer, who independently defined homology. A fairly precise date can be supplied in the internal notes of the Bourbaki group. While topology was still ''combinatorial'' in 1942, it had become ''algebraic'' by 1944. This corresponds also to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Max Dehn
Max Wilhelm Dehn (November 13, 1878 – June 27, 1952) was a German mathematician most famous for his work in geometry, topology and geometric group theory. Born to a Jewish family in Germany, Dehn's early life and career took place in Germany. However, he was forced to retire in 1935 and eventually fled Germany in 1939 and emigrated to the United States. Dehn was a student of David Hilbert, and in his habilitation in 1900 Dehn resolved Hilbert's third problem, making him the first to resolve one of Hilbert's well-known 23 problems. Dehn's students include Ott-Heinrich Keller, Ruth Moufang, Wilhelm Magnus, and the artists Dorothea Rockburne and Ruth Asawa. Biography Dehn was born to a family of Jewish origin in Hamburg, Imperial Germany. He studied the foundations of geometry with Hilbert at Göttingen in 1899, and obtained a proof of the Jordan curve theorem for polygons. In 1900 he wrote his dissertation on the role of the Legendre angle sum theorem in axiomatic geome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torsion (algebra)
In mathematics, specifically in ring theory, a torsion element is an element of a module that yields zero when multiplied by some non-zero-divisor of the ring. The torsion submodule of a module is the submodule formed by the torsion elements. A torsion module is a module that equals its torsion submodule. A module is torsion-free if its torsion submodule comprises only the zero element. This terminology is more commonly used for modules over a domain, that is, when the regular elements of the ring are all its nonzero elements. This terminology applies to abelian groups (with "module" and "submodule" replaced by "group" and "subgroup"). This is allowed by the fact that the abelian groups are the modules over the ring of integers (in fact, this is the origin of the terminology, that has been introduced for abelian groups before being generalized to modules). In the case of groups that are noncommutative, a ''torsion element'' is an element of finite order. Contrary to the commuta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oslo
Oslo ( , , or ; sma, Oslove) is the capital and most populous city of Norway. It constitutes both a county and a municipality. The municipality of Oslo had a population of in 2022, while the city's greater urban area had a population of in 2019, and the metropolitan area had an estimated population of in 2021. During the Viking Age the area was part of Viken. Oslo was founded as a city at the end of the Viking Age in 1040 under the name Ánslo, and established as a ''kaupstad'' or trading place in 1048 by Harald Hardrada. The city was elevated to a bishopric in 1070 and a capital under Haakon V of Norway around 1300. Personal unions with Denmark from 1397 to 1523 and again from 1536 to 1814 reduced its influence. After being destroyed by a fire in 1624, during the reign of King Christian IV, a new city was built closer to Akershus Fortress and named Christiania in honour of the king. It became a municipality ('' formannskapsdistrikt'') on 1 January 1838. The city fu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
_(LOC)_-_Flickr_-_The_Library_of_Congress.jpg "Click for more on -> 1871 Births")
.svg "Click for more on -> Norway")
