Open Problems in Mathematics | Buch

Cover: 9783319321608 | Open Problems in Mathematics | Michael Th. Rassias (u. a.) | Buch

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Beschreibung

The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash¿s legendary mathematical achievements.

The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory,cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.

Über den Autor

John Forbes Nash, Jr. was Senior Research Mathematician at Princeton University. Professor Nash was the recipient of the Nobel Prize in Economics in 1994 and the Abel Prize in Mathematics in 2015 and is most widely known for the Nash equilibrium in game theory and the Nash embedding theorem in geometry and analysis. He was also the recipient of the John von Neumann Theory prize in 1978. Nash's groundbreaking works in game theory, algebraic & differential geometry, non-linear analysis and partial differential equations have provided insight into the factors that govern chance and events inside complex systems in daily life. Moreover, Nash's theories are widely used in economics, computing, evolutionary biology, artificial intelligence, accounting, politics and other disciplines.

Michael Th. Rassias during his collaboration in 2014-2015 with John Forbes Nash, Jr. for the preparation of this book was a postdoctoral researcher at the Departments of Mathematics of Princeton University and ETH-Zurich, working at Princeton. He is currently a postdoctoral researcher at the Institute of Mathematics of the University of Zurich and a visiting researcher at the Program in Interdisciplinary Studies of the Institute for Advanced Study, Princeton. His research interests lie in mathematical analysis and analytic number theory. Rassias has received several awards in national and international mathematical Olympiads. He was also awarded the 2014 Notara Prize in Mathematics from the Academy of Athens. He has also authored, co-authored and co-edited five other books with Springer.

Zusammenfassung

Self-contained presentation of methods, theory, and results related to some of the most important open problems in mathematics

Useful for advanced graduate courses and seminars as well as for researchers (pure and applied) working toward the proof of longstanding open problems in mathematical sciences

First book to treat a wide range of fields of open problems in mathematics and the status of problems' solutions to date

Includes supplementary material: [...]

Inhaltsverzeichnis

Preface (J.F. Nash, Jr., [...]. Rassias).- Introduction (M. Gromov).- 1. P Versus NP (S. Aaronson).- 2. From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond (O. Barrett, F.W.K. Firk, S.J. Miller, C. Turnage-Butterbaugh).- 3. The Generalized Fermat Equation (M. Bennett, P. Mih¿ilescu, S. Siksek).- 4. The Conjecture of Birch and Swinnerton-Dyer (J. Coates).- 5. An Essay on the Riemann Hypothesis (A. Connes).- 6. Navier Stokes Equations (P. Constantin).- 7. Plateau's Problem (J. Harrison, H. Pugh).- 8. The Unknotting Problem (L.H. Kauffman).- 9. How Can Cooperative Game Theory Be Made More Relevant to Econimics? (E. Maskin).- 10. The Erd¿s-Szekeres Problem (W. Morris, V. Soltan).- 11. Novikov's Conjecture (J. Rosenberg).- The Discrete Logarithm Problem (R. Schoof).- 13. Hadwiger's Conjecture (P. Seymour).- 14. The Hadwiger-Nelson Problem (A. Soifer).- 15. Erd¿s's Unit Distance Problem (E. Szemerédi).- 16. Goldbach's Conjectures (R.C. Vaughan).- 17. The Hodge Conjecture (C. Voisin).

Details

Erscheinungsjahr:	2016
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xiii 543 S. 71 s/w Illustr. 17 farbige Illustr. 543 p. 88 illus. 17 illus. in color.
ISBN-13:	9783319321608
ISBN-10:	3319321609
Sprache:	Englisch
Herstellernummer:	978-3-319-32160-8
Einband:	Gebunden
Autor:	Nash, John Forbes Rassias, Michael Th.
Redaktion:	Rassias, Michael Th. Nash, Jr.
Herausgeber:	John Forbes Nash Jr/Michael Th Rassias
Auflage:	1st edition 2016
Hersteller:	Springer Nature Switzerland Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 36 mm
Von/Mit:	Michael Th. Rassias (u. a.)
Erscheinungsdatum:	14.07.2016
Gewicht:	0,998 kg

Artikel-ID: 103898071