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Hans Freudenthal
Hans Freudenthal (17 September 1905 – 13 October 1990) was a Jewish-German-born Dutch mathematician. He made substantial contributions to algebraic topology and also took an interest in literature, philosophy, history and mathematics education. Biography Freudenthal was born in Luckenwalde, Brandenburg, on 17 September 1905, the son of a Jewish teacher. He was interested in both mathematics and literature as a child, and studied mathematics at the University of Berlin beginning in 1923.. He met Brouwer in 1927, when Brouwer came to Berlin to give a lecture, and in the same year Freudenthal also visited the University of Paris.. He completed his thesis work with Heinz Hopf at Berlin, defended a thesis on the ends of topological groups in 1930, and was officially awarded a degree in October 1931. After defending his thesis in 1930, he moved to Amsterdam to take up a position as assistant to Brouwer. In this pre-war period in Amsterdam, he was promoted to lecturer at the Universit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Group
In mathematics, topological groups are logically the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time, such that the continuity condition for the group operations connects these two structures together and consequently they are not independent from each other. Topological groups have been studied extensively in the period of 1925 to 1940. Haar and Weil (respectively in 1933 and 1940) showed that the integrals and Fourier series are special cases of a very wide class of topological groups. Topological groups, along with continuous group actions, are used to study continuous symmetries, which have many applications, for example, in physics. In functional analysis, every topological vector space is an additive topological group with the additional property that scalar multiplication is continuous; consequently, many results from the theory of topological groups can be applied to functional analysis. Formal definition ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compact Set
In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space by making precise the idea of a space having no "punctures" or "missing endpoints", i.e. that the space not exclude any ''limiting values'' of points. For example, the open interval (0,1) would not be compact because it excludes the limiting values of 0 and 1, whereas the closed interval ,1would be compact. Similarly, the space of rational numbers \mathbb is not compact, because it has infinitely many "punctures" corresponding to the irrational numbers, and the space of real numbers \mathbb is not compact either, because it excludes the two limiting values +\infty and -\infty. However, the ''extended'' real number line ''would'' be compact, since it contains both infinities. There are many ways to make this heuristic notion precise. These ways usually agree in a metric space, but may not be equivalent in other topologic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Space
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points, along with an additional structure called a topology, which can be defined as a set of neighbourhoods for each point that satisfy some axioms formalizing the concept of closeness. There are several equivalent definitions of a topology, the most commonly used of which is the definition through open sets, which is easier than the others to manipulate. A topological space is the most general type of a mathematical space that allows for the definition of limits, continuity, and connectedness. Common types of topological spaces include Euclidean spaces, metric spaces and manifolds. Although very general, the concept of topological spaces is fundamental, and used in virtually every branch of modern mathematics. The study of topological spac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Utrecht
Utrecht ( , , ) is the List of cities in the Netherlands by province, fourth-largest city and a List of municipalities of the Netherlands, municipality of the Netherlands, capital and most populous city of the Provinces of the Netherlands, province of Utrecht (province), Utrecht. It is located in the eastern corner of the Randstad conurbation, in the very centre of mainland Netherlands, about 35 km south east of the capital Amsterdam and 45 km north east of Rotterdam. It has a population of 361,966 as of 1 December 2021. Utrecht's ancient city centre features many buildings and structures, several dating as far back as the High Middle Ages. It has been the religious centre of the Netherlands since the 8th century. It was the most important city in the Netherlands until the Dutch Golden Age, when it was surpassed by Amsterdam as the country's cultural centre and most populous city. Utrecht is home to Utrecht University, the largest university in the Netherlands, as well as seve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometriae Dedicata
''Geometriae Dedicata'' is a mathematical journal, founded in 1972, concentrating on geometry and its relationship to topology, group theory and the theory of dynamical systems. It was created on the initiative of Hans Freudenthal in Utrecht, the Netherlands.. It is published by Springer Netherlands. The Editors-in-Chief An editor-in-chief (EIC), also known as lead editor or chief editor, is a publication's editorial leader who has final responsibility for its operations and policies. The highest-ranking editor of a publication may also be titled editor, managing ... are John R. Parker and Jean-Marc Schlenker.Journal website References External links Springer site Mathematics journals Springer Science+Business Media academic journals {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Freudenthal Institute
The Freudenthal Institute (FI) is a research institute, part of the Faculty of Science of Utrecht University in the Netherlands. The FI aims to improve education in science and mathematics by means of education research and valorisation. The institute was founded in 1971 by the German/Dutch writer, pedagogue and mathematician, professor Hans Freudenthal (1905–1990), as the Institute for the Development of Mathematical Education. In 1991, the institute was renamed after its founder. Since 2003, an international institute for mathematics education, Freudenthal Institute - USA (Fi-US) was established in collaboration with the Wisconsin University in Madison, Wisconsin, USA. Since January 2006 Fi-US has been reallocated to the University of Colorado at Boulder The University of Colorado Boulder (CU Boulder, CU, or Colorado) is a public research university in Boulder, Colorado. Founded in 1876, five months before Colorado became a state, it is the flagship university of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Commission On Mathematical Instruction
The International Commission on Mathematical Instruction (ICMI) is a commission of the International Mathematical Union and is an internationally acting organization focussing on mathematics education. ICMI was founded in 1908 at the International Congress of Mathematicians (ICM) in Rome and aims to improve teaching standards around the world, through programs, workshops and initiatives and publications. It aims to work a great deal with developing countries, to increase teaching standards and education which can improve life quality and aid the country. HistoryICMIwas founded at the ICM, and mathematician Felix Klein was elected first president of the organisation. Henri Fehr and Charles Laisant created the international research journal '' L'Enseignement Mathématique'' in 1899, and from early on this journal became the official organ of ICMI. A bulletin is published twice a year by ICMI, and from December 1995 this bulletin has been available at the organisation's official websi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Utrecht University
Utrecht University (UU; nl, Universiteit Utrecht, formerly ''Rijksuniversiteit Utrecht'') is a public research university in Utrecht, Netherlands. Established , it is one of the oldest universities in the Netherlands. In 2018, it had an enrollment of 31,801 students, and employed 7,191 faculty and staff. In 2018, 525 PhD degrees were awarded and 6,948 scientific articles were published. The 2018 budget of the university was €857 million. Utrecht University counts a number of distinguished scholars among its alumni and faculty, including 12 Nobel Prize laureates and 13 Spinoza Prize laureates. Utrecht University has been placed consistently in the top 100 universities in the world by prominent international ranking tables. The university is ranked as the best university in the Netherlands by the Shanghai Ranking of World Universities 2022, ranked 14th in Europe and 54th in the world. The university's motto is "Sol Iustitiae Illustra Nos", which means ''May the Sun of Righteous ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foundations Of Mathematics
Foundations of mathematics is the study of the philosophy, philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be quite vague. Foundations of mathematics can be conceived as the study of the basic mathematical concepts (set, function, geometrical figure, number, etc.) and how they form hierarchies of more complex structures and concepts, especially the fundamentally important structures that form the language of mathematics (formulas, theories and their model theory, models giving a meaning to formulas, definitions, proofs, algorithms, etc.) also called metamathematics, metamathematical concepts, with an eye to the philosophical aspects and the unity of mathematics. The search for foundations of mathematics is a cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Havelte
Havelte ( Drèents: ''Haovelte'' or ''Haovelt'') is a village in the Northeastern Netherlands. It is located in the municipality of Westerveld, Drenthe, about 60 km (37.2 mi) south-southwest of Groningen and 120 km (74.5 mi) northeast of Amsterdam. As of 1 January 2021, it had a population of 3,825. History The village was first mentioned in 1342 as "to Hovelde". The etymology is unclear. Havelte is an ''esdorp'' on a sandy ridge. It developed in the Late Middle Ages into a little village with four triangular village squares. The ''hunebed'' (dolmen) is located in Havelterberg near Havelte and is the second largest of the Netherlands. It spans nearly , and contains 9 capstones and 21 side stones. It used to have a beautiful ring of 40 stones. There were still 24 left in 1918 when Albert Egges van Giffen researched the dolmen. Nowadays, there are only 10 left. All the stones have been put back in there place in 1918. The Dutch Reformed is located somewhat off-centre, be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Battle Of The Netherlands
The German invasion of the Netherlands ( nl, Duitse aanval op Nederland), otherwise known as the Battle of the Netherlands ( nl, Slag om Nederland), was a military campaign part of Battle of France, Case Yellow (german: Fall Gelb), the Nazi Germany, Nazi German invasion of the Low Countries (Belgium, Luxembourg, and the Netherlands) and French Third Republic, France during World War II. The battle lasted from 10 May 1940 until the surrender of the main Dutch forces on 14 May. Dutch troops in the province of Zeeland continued to resist the ''Wehrmacht'' until 17 May when Germany completed its occupation of the whole country. The invasion of the Netherlands saw some of the earliest mass paratroop drops, to occupy tactical points and assist the advance of ground troops. The German ''Luftwaffe'' used paratroopers in the capture of several airfields in the vicinity of Rotterdam and The Hague, helping to quickly overrun the country and immobilise Dutch forces. After the devastating ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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