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Grundzüge Der Mengenlehre
''Grundzüge der Mengenlehre'' (German for "Basics of Set Theory") is a book on set theory written by Felix Hausdorff. First published in April 1914, ''Grundzüge der Mengenlehre'' was the first comprehensive introduction to set theory. Besides the systematic treatment of known results in set theory, the book also contains chapters on measure theory and topology, which were then still considered parts of set theory. Hausdorff presented and developed original material which was later to become the basis for those areas. In 1927 Hausdorff published an extensively revised second edition under the title ''Mengenlehre'' (German for "Set Theory"), with many of the topics of the first edition omitted. In 1935 there was a third German edition, which in 1957 was translated by John R. Aumann ''et al.'' into English under the title ''Set Theory''. The author, Felix Hausdorff, committed suicide on 26 January 1942, along with his wife and his sister-in-law, to avoid the Nazi holocaust, after b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set Theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory. The non-formalized systems investigated during this early stage go under the name of '' naive set theory''. After the discovery of paradoxes within naive set theory (such as Russell's paradox, Cantor's paradox and the Burali-Forti paradox) various axiomatic systems were proposed in the early twentieth century, of which Zermelo–Fraenkel set theory (with or without the axiom of choice) is still the best-known and most studied. Set theory is commonly employed as a foundational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Felix Hausdorff
Felix Hausdorff ( , ; November 8, 1868 – January 26, 1942) was a German mathematician who is considered to be one of the founders of modern topology and who contributed significantly to set theory, descriptive set theory, measure theory, and functional analysis. Life became difficult for Hausdorff and his family after Kristallnacht in 1938. The next year he initiated efforts to emigrate to the United States, but was unable to make arrangements to receive a research fellowship. On 26 January 1942, Felix Hausdorff, along with his wife and his sister-in-law, died by suicide by taking an overdose of veronal, rather than comply with German orders to move to the Endenich camp, and there suffer the likely implications, about which he held no illusions. Life Childhood and youth Hausdorff's father, the Jewish merchant Louis Hausdorff (1843–1896), moved with his young family to Leipzig in the autumn of 1870, and over time worked at various companies, including a linen-and cotton goo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Measure Theory
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures ( length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many similarities and can often be treated together in a single mathematical context. Measures are foundational in probability theory, integration theory, and can be generalized to assume negative values, as with electrical charge. Far-reaching generalizations (such as spectral measures and projection-valued measures) of measure are widely used in quantum physics and physics in general. The intuition behind this concept dates back to ancient Greece, when Archimedes tried to calculate the area of a circle. But it was not until the late 19th and early 20th centuries that measure theory became a branch of mathematics. The foundations of modern measure theory were laid in the works of Émile Borel, Henri Lebesgue, Nikolai Luzin, Johann Radon, Const ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such as Stretch factor, stretching, Twist (mathematics), twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set (mathematics), set endowed with a structure, called a ''Topology (structure), topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity (mathematics), continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopy, homotopies. A property that is invariant under such deformations is a topological property. Basic exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chelsea Publishing Company
The Chelsea Publishing Company was a publisher of mathematical books, based in New York City New York, often called New York City or NYC, is the most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the most densely populated major city in the Un ..., founded in 1944 by Aaron Galuten while he was still a graduate student at Columbia. Its initial focus was to republish important European works that were unavailable in the United States because of wartime restrictions, such as Hausdorff's Mengenlehre, or because the works were out of print. This soon expanded to include translations of such works into English, as well as original works by American authors. As of 1985, the company's catalog included more than 200 titles. After Galuten's death in 1994, the company was acquired in 1997 by the AMS, which continues to publish a portion of the company's original catalog under the ''AMS Chelse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bulletin Of The American Mathematical Society
The ''Bulletin of the American Mathematical Society'' is a quarterly mathematical journal published by the American Mathematical Society. Scope It publishes surveys on contemporary research topics, written at a level accessible to non-experts. It also publishes, by invitation only, book reviews and short ''Mathematical Perspectives'' articles. History It began as the ''Bulletin of the New York Mathematical Society'' and underwent a name change when the society became national. The Bulletin's function has changed over the years; its original function was to serve as a research journal for its members. Indexing The Bulletin is indexed in Mathematical Reviews, Science Citation Index, ISI Alerting Services, CompuMath Citation Index, and Current Contents/Physical, Chemical & Earth Sciences. See also *'' Journal of the American Mathematical Society'' *''Memoirs of the American Mathematical Society'' *''Notices of the American Mathematical Society'' *'' Proceedings of the American M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Princeton Companion To Mathematics
''The Princeton Companion to Mathematics'' is a book providing an extensive overview of mathematics that was published in 2008 by Princeton University Press. Edited by Timothy Gowers with associate editors June Barrow-Green and Imre Leader, it has been noted for the high caliber of its contributors. The book was the 2011 winner of the Euler Book Prize of the Mathematical Association of America, given annually to "an outstanding book about mathematics".......... Topics and organization The book concentrates primarily on modern pure mathematics rather than applied mathematics, although it does also cover both applications of mathematics and the mathematics that relates to those applications; it provides a broad overview of the significant ideas and developments in research mathematics. It is organized into eight parts: *An introduction to mathematics, outlining the major areas of study, key definitions, and the goals and purposes of mathematical research. *An overview of the history ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1914 Non-fiction Books
This year saw the beginning of what became known as World War I, after Archduke Franz Ferdinand of Austria, heir to the Austrian throne was assassinated by Serbian nationalist Gavrilo Princip. It also saw the first airline to provide scheduled regular commercial passenger services with heavier-than-air aircraft, with the St. Petersburg–Tampa Airboat Line. Events January * January 1 – The St. Petersburg–Tampa Airboat Line in the United States starts services between St. Petersburg and Tampa, Florida, becoming the first airline to provide scheduled regular commercial passenger services with heavier-than-air aircraft, with Tony Jannus (the first federally-licensed pilot) conveying passengers in a Benoist XIV flying boat. Abram C. Pheil, mayor of St. Petersburg, is the first airline passenger, and over 3,000 people witness the first departure. * January 11 – The Sakurajima volcano in Japan begins to erupt, becoming effusive after a very large earthquake ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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