Hairer M. Ergodic Theory for Stochastic PDEs

Springer, 2000. - 538 pages. The (mathematical) heroes of this book are "perfect proofs": brilliant ideas, clever connections and wonderful observations that bring new insight and surprising perspectives on basic and challenging problems from number theory, geometry, analysis, combinatorics, and graph theory. Thirty beautiful examples are presented here. They are candidates for THE BOOK in which God records the perfect proofs - according to the...

Birkhauser Boston, 2003. - 234 pages. Mathematical Olympiad Treasures contains a stimulating collection of problems in geometry and trigonometry, algebra, number theory, and combinatorics. It encourages readers to think creatively about techniques and strategies for problem solving in the real world. The problems are clustered by topic into self-contained chapters. The book begins with elementary facts, followed by carefully selected problems a...

Springer, 1st edition, 215 pages, 2006, ISBN-10: 9781402042478 This monograph presents the basic theorems of differential geometry in three-dimensional space, including a thorough coverage of surface theory. By means of a series of carefully selected and representative mathematical models this monograph also explains at length how these theorems are used in three-dimensional elasticity and in shell theory. The presentation is essentially selfcon...

Springer, 2011. - 400 pages. It is commonly believed that chaos is linked to non-linearity, however many (even quite natural) linear dynamical systems exhibit chaotic behavior. The study of these systems is a young and remarkably active field of research, which has seen many landmark results over the past two decades. Linear dynamics lies at the crossroads of several areas of mathematics including operator theory, complex analysis, ergodic theor...

Springer, 2009. - 697 pages. Since his death in 1996, many scientific meetings have been dedicated to the memory of Paul Erd?s. From July 4 to 11, 1999, the conference "Paul Erd?s and his Mathematics" was held in Budapest, with the ambitious goal of showing the whole range of Erd?s' work - a difficult task in view of Erd?s' versatility and his broad scope of interest in mathematics. According to this goal, the topics of plenary lectures and para...

Издательство Springer, 2002, -734 pp. Since his death in 1996, many scientific meetings have been dedicated to the memory of Paul Erdos. All of them were focusing on a particular part of his vast work, a necessity due to his versatility and his broad scope of interest in mathematics. Andras Hajnal (in a paper written on the occasion of Erdos's 80th birthday) compared his work to a rain forest, where one can only see a part of one of the magnific...

Princeton University Press, 1992. - 247 pages. ISBN: 0816058539. ISBN; 9780816058532. Based on a well-received course designed for philosophy students, this book is an informal introduction to mathematical thinking. The work will be rewarding not only for philosophers concerned with mathematical questions but also for serious amateur mathematicians with an interest in the "frontiers" as well as the foundations of mathematics. In what might be te...

John Wiley & Sons, 1988. - 156 pages. Nonstandard analysis represents a fundamental change of perspective in mathematics (and sciences), comparable to the introduction of Cantor's set theory in the nineteenth century. This book is a short, readable introduction to the subject, based on the axiomatic or IST approach. The first part gives a clear, rigorous exposition of the theory; the second part consists of a number of self-contained chapter...

This book was written as lecture notes for classes that I taught to undergraduate students majoring in physics. I wrote this book in a do-it-yourself style so that I give only a draft of tensor theory, which includes formulating de?nitions and theorems and giving basic ideas and formulas. All other work such as proving consistence of de?nitions, deriving formulas, proving theorems or completing details to proofs is left to the reader in the form...

Springer, 2009. - 668 pages. This inaugural book in the new series Advances in Mathematics Education is the most up to date, comprehensive and avant garde treatment of Theories of Mathematics Education which use two highly acclaimed ZDM special issues on theories of mathematics education (issue 6/2005 and issue 1/2006), as a point of departure. Historically grounded in the Theories of Mathematics Education (TME group) revived by the book editors...