The 20th Century A Gi

Each volume of the Dictionary of World Biography contains 250 entries on the lives of the individuals who shaped their times and left their mark on world history. This is not a who's who. Instead, each entry provides an in-depth essay on the life and career of the individual concerned. Essays commence with a quick reference section that provides basic facts on the individual's life and achievements. The extended biography places the life and works of the individual within an historical context, and the summary at the end of each essay provides a synopsis of the individual's place in history. All entries conclude with a fully annotated bibliography.

Each volume of the Dictionary of World Biography contains 250 entries on the lives of the individuals who shaped their times and left their mark on world history. This is not a who's who. Instead, each entry provides an in-depth essay on the life and career of the individual concerned. Essays commence with a quick reference section that provides basic facts on the individual's life and achievements. The extended biography places the life and works of the individual within an historical context, and the summary at the end of each essay provides a synopsis of the individual's place in history. All entries conclude with a fully annotated bibliography.

The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.

Learn how 20th century history changed world geography with this social studies book that piques students’ curiosity about history through dynamic primary sources. Primary sources give students unique insights and personal connections to history. Examples of primary sources include images of Pearl Harbor, nuclear weapon testing, a pro-communism poster, and a factory assembly line. This 32-page book includes text features that help students increase reading comprehension and their understanding of the subject. Packed with interesting facts, sidebars, and essential vocabulary, this book is perfect for reports or projects.

Learn how 20th century history changed world geography with this social studies book that piques students’ curiosity about history through dynamic primary sources. Primary sources give students unique insights and personal connections to history. Examples of primary sources include images of Pearl Harbor, nuclear weapon testing, a pro-communism poster, and a factory assembly line. This 32-page book includes text features that help students increase reading comprehension and their understanding of the subject. Packed with interesting facts, sidebars, and essential vocabulary, this book is perfect for reports or projects.

In the 20th century, many mathematicians in Russia made great contributions to the field of mathematics. This invaluable book, which presents the main achievements of Russian mathematicians in that century, is the first most comprehensive book on Russian mathematicians. It has been produced as a gesture of respect and appreciation for those mathematicians and it will serve as a good reference and an inspiration for future mathematicians. It presents differences in mathematical styles and focuses on Soviet mathematicians who often discussed “what to do” rather than “how to do it”. Thus, the book will be valued beyond historical documentation. The editor, Professor Yakov Sinai, a distinguished Russian mathematician, has taken pains to select leading Russian mathematicians — such as Lyapunov, Luzin, Egorov, Kolmogorov, Pontryagin, Vinogradov, Sobolev, Petrovski and Krein — and their most important works. One can, for example, find works of Lyapunov, which parallel those of Poincaré; and works of Luzin, whose analysis plays a very important role in the history of Russian mathematics; Kolmogorov has established the foundations of probability based on analysis. The editor has tried to provide some parity and, at the same time, included papers that are of interest even today. The original works of the great mathematicians will prove to be enjoyable to readers and useful to the many researchers who are preserving the interest in how mathematics was done in the former Soviet Union. Contents:Lyapunov (A New Case of Integrability of Differential Equations of Motion of a Solid Body in Liquid)Luzin (Sur l'absolue convergence des series trigonometriques)SteklovEgorov (Mathematics and Religion in Moscow, by C E Ford)Smirnov (Sur les polynomes orthogonaux a une veriable complexe)Bernstein (Sur la meilleure approximation sur tout l'axe reel des fonctions continues par des fonctions entieres de degre fini)UrysohnChebotaryovVinogradov (Representation of an Odd Number as the Sum of Three Primes)Aleksandrov (Sur la notion de dimension des ensembles fermes)MenshovGelfond (Sur le septierie probleme de Hilbert)Khinchin (Three Pearls of Number Theory)Kolmogorov (Local Structure of Turbulence in an Incompressible Viscous Fluid at Very Large Reynolds Numbers)Pontryagin (Homotopic Classification of an (n+2)-Dimensional Spheres into an n-Dimensional Spheres)Gelfand (On Identities for Eigenvalues of a Second Order Differential Operators)Sobolev (On a Theorem of Functional Analysis)Petrovsky (On Problem of some PDE's)Krein (On Extreme Points of Regularly Convex Sets)Liusternik (Topology and Variational Problem)Rokhlin (Proof of Gudkov's Hypothesis)Novikov (Periodic Groups)Bogoliubov (Mathematical Problems of Quantum Field Theory)Aleksandrov (Neue ungleichungen fur die mischvolumen konvexer korper)Kantorovich (A New Method of Solving of Some Classes of Extremal Problems)Malcev (Free Topological Algebras)Linnik (An Application of the Theory of Matrices and of Lobatschevskian Geometry to the Theory of Dirichlet's Real Characters)Markov (The Theory of Algorithms)Lavrentev (On the Theory of Quasi-Conformal Mapping of Three-Dimensional Domains)Tikhonov (Ueber die Erweiteung von Raumen)Delone (Sur le nombre de representations d'un nombre par une forme eubique a discriminent negatif)Keldysh (On the Completeness of the Eigenfunctions of Some Classes of Non-Self Adjoint Linear Operators)Faddeevand other articles Readership: General mathematicians. Keywords:Geometry & Topology;Analysis & Differential Equations;Algebra & Number TheoryReviews:“For anyone who wants an overview of mathematics in Russia during the 20th century there is now the volume Russian Mathematicians in the 20th century … It shall remain on my book shelf as a monument over a heroic generation.”Professor Lennart Carleson Institute of Mathematics, The Royal Institute of Technology, Stockholm, Sweden “The list selected is very representative both topically and geographically. It covers research in all areas of mathematics … The 33 persons in the list worked not only in Moscow and Leningrad (now Saint Petersburg), but also in Kiev, Odessa, Kazan, and Novosibirsk. Most of the work presented in this volume was done during the Soviet era when the Russian mathematical community was artificially isolated from the international one for political reasons. Thus to develop their subjects, Soviet mathematicians needed to be self-sufficient. And this volume shows that they indeed succeeded in it. The originality of the Russian mathematical school is clearly seen when one reads the papers included in the book. Altogether this volume gives a very strong impression of the versatility, originality and strength of the Russian mathematical school.”L D Faddeev Petersburg Department of the Steklov Institute of Mathematics , Russian Academy of Sciences “This book is fascinating … It shows the greatness of Russian or Soviet mathematicians and the foundations on which younger mathematicians could build up, leading to world leadership until the end of the Soviet Union when the exodus started.”F Hirzebruch Emeritus Professor of Mathematics University of Bonn

This book is a collage of human experiences made from overlapping pieces and woven together by themes of crises, revolution, and change, aiming to raise issues that people in the twentieth-century world tried to address.

This is an examination of the crucial formative period of Chinese attitudes toward nuclear weapons, the immediate post-Hiroshima/Nagasaki period and the Korean War. It also provides an account of US actions and attitudes during this period and China's response.