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Arnold's Problems
''Arnold's Problems'' is a book edited by Soviet mathematician Vladimir Arnold, containing 861 mathematical problems from many different Mathematics#Areas_of_mathematics, areas of mathematics. The book was based on Arnold's seminars at Moscow State University. The problems were created over his decades-long career, and are sorted chronologically (from the period 1956–2003). It was published in Russian as ''Задачи Арнольда'' in 2000, and in a translated and revised English edition in 2004 (printed by Springer-Verlag). The book is divided into two parts: formulations of the problems, and comments upon them by 59 mathematicians. This is the largest part of the book. There are also long outlines for programs of research. Notable problems The problems in ''Arnold's Problems'' are each numbered with a year and a sequence number within the year. They include: *1956–1, the napkin folding problem, on whether a paper rectangle can be folded to a shape with larger perimeter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilbert–Arnold Problem
In mathematics, particularly in dynamical systems, the Hilbert–Arnold problem is an list of unsolved problems in mathematics, unsolved problem concerning the estimation of limit cycles. It asks whether in a generic property, generic finite-parameter family of smooth function, smooth vector fields on a sphere with a Compact space, compact parameter base, the number of limit cycles is uniformly bounded across all parameter values. The problem is historically related to Hilbert's sixteenth problem and was first formulated by Russians, Russian mathematicians Vladimir Arnold and Yulij Ilyashenko in the 1980s.Ilyashenko, Yu. (1994). "Normal forms for local families and nonlocal bifurcations". ''Astérisque'', Vol. 222, 233-258. It is closely related to the "infinitesimal Hilbert's sixteenth problem", although they are not synonyms. In ''Arnold's Problems'' there are many questions related to the Hilbert–Arnold problem: 1978–6, 1979–16, 1980–1, 1983–11, 1989–17, 1990–24, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vladimir Arnold
Vladimir Igorevich Arnold (or Arnol'd; , ; 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician. He is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, and contributed to several areas, including geometrical theory of dynamical systems, algebra, catastrophe theory, topology, real algebraic geometry, symplectic geometry, differential equations, classical mechanics, differential-geometric approach to hydrodynamics, geometric analysis and singularity theory, including posing the ADE classification problem. His first main result was the solution of Hilbert's thirteenth problem in 1957 when he was 19. He co-founded three new branches of mathematics: topological Galois theory (with his student Askold Khovanskii), symplectic topology and KAM theory. Arnold was also a populariser of mathematics. Through his lectures, seminars, and as the author of several textbooks (such as '' Mathematical Methods of Clas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Problem
A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the Solar System, or a problem of a more abstract nature, such as Hilbert's problems. It can also be a problem referring to the nature of mathematics itself, such as Russell's Paradox. Real-world problems Informal "real-world" mathematical problems are questions related to a concrete setting, such as "Adam has five apples and gives John three. How many has he left?". Such questions are usually more difficult to solve than regular mathematical exercises like "5 − 3", even if one knows the mathematics required to solve the problem. Known as word problems, they are used in mathematics education to teach students to connect real-world situations to the abstract language of mathematics. In general, to use mathematics for solving a real-world problem, the first ste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow State University
Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, and six branches. Alumni of the university include past leaders of the Soviet Union and other governments. As of 2019, 13 List of Nobel laureates, Nobel laureates, six Fields Medal winners, and one Turing Award winner were affiliated with the university. History Imperial Moscow University Ivan Shuvalov and Mikhail Lomonosov promoted the idea of a university in Moscow, and Elizabeth of Russia, Russian Empress Elizabeth decreed its establishment on . The first lectures were given on . Saint Petersburg State University and MSU each claim to be Russia's oldest university. Though Moscow State University was founded in 1755, St. Petersburg which has had a continuous existence as a "university" since 1819 sees itself as the successor of an a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second-largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ZbMATH
zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH. Editors are the European Mathematical Society, FIZ Karlsruhe, and the Heidelberg Academy of Sciences. zbMATH is distributed by Springer Science+Business Media. It uses the Mathematics Subject Classification codes for organising reviews by topic. History Mathematicians Richard Courant, Otto Neugebauer, and Harald Bohr, together with the publisher Ferdinand Springer, took the initiative for a new mathematical reviewing journal. Harald Bohr worked in Copenhagen. Courant and Neugebauer were professors at the University of Göttingen. At that time, Göttingen was considered one of the central places for mathematical research, having appointed mathematicians like David Hilbert, Hermann Minkowski, Carl Runge, and Felix Klein, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Reviews
''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also publishes an associated online bibliographic database called MathSciNet, which contains an electronic version of ''Mathematical Reviews''. Reviews Mathematical Reviews was founded by Otto E. Neugebauer in 1940 as an alternative to the German journal '' Zentralblatt für Mathematik'', which Neugebauer had also founded a decade earlier, but which under the Nazis had begun censoring reviews by and of Jewish mathematicians. The goal of the new journal was to give reviews of every mathematical research publication. As of November 2007, the ''Mathematical Reviews'' database contained information on over 2.2 million articles. The authors of reviews are volunteers, usually chosen by the editors because of some expertise in the area of the articl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Napkin Folding Problem
The napkin folding problem is a problem in geometry and the mathematics of paper folding that explores whether folding a square or a rectangular napkin can increase its perimeter. The problem is known under several names, including the Margulis napkin problem, suggesting it is due to Grigory Margulis, and the Arnold's rouble problem referring to Vladimir Arnold and the folding of a Russian ruble bank note. It is the first problem listed by Arnold in his book ''Arnold's Problems'', where he calls it the rumpled dollar problem. Some versions of the problem were solved by Robert J. Lang, Svetlana Krat, Alexey S. Tarasov, and Ivan Yaschenko. One form of the problem remains open. Formulations There are several way to define the notion of folding, giving different interpretations. By convention, the napkin is always a unit square. Folding along a straight line Considering the folding as a reflection along a line that reflects all the layers of the napkin, the perimeter is always no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arnold Conjecture
The Arnold conjecture, named after mathematician Vladimir Arnold, is a mathematical conjecture in the field of symplectic geometry, a branch of differential geometry. Strong Arnold conjecture Let (M, \omega) be a closed (compact without boundary) symplectic manifold. For any smooth function H: M \to , the symplectic form \omega induces a Hamiltonian vector field X_H on M defined by the formula :\omega( X_H, \cdot) = dH. The function H is called a Hamiltonian function. Suppose there is a smooth 1-parameter family of Hamiltonian functions H_t \in C^\infty(M), t \in [0,1]. This family induces a 1-parameter family of Hamiltonian vector fields X_ on M. The family of vector fields integrates to a 1-parameter family of diffeomorphisms \varphi_t: M \to M. Each individual \varphi_t is a called a Hamiltonian diffeomorphism of M. The strong Arnold conjecture states that the number of fixed points of a Hamiltonian diffeomorphism of M is greater than or equal to the number of critical point ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Books
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of abstract objects that consist of either abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to prove properties of objects, a ''proof'' consisting of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstractio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
