Series: Spectrum
Hardback (ISBN-13: 9780883855645)
Page extent: 440 pages
Size: 253 x 177 mm
Weight: 0.926 kg
* An extensive treatment of Euler’s lesser-known contributions outside
pure mathematics * Includes rare and detailed accounts of Euler’s family
life * Readers already familiar with Euler’s work will find here much
to enhance their appreciation of this extraordinary scientist and human
being
Introduction; Translator’s note; From the editors; 1. Opening speech of the symposium ‘Modern Developments of Euler’s Ideas’ October 24, 1983 A. P. Aleksandrov; 2. Leonhard Euler: his life and work A. P. Yushkevich; 3. Leonhard Euler, active and honored member of the Petersburg Academy of Sciences Yu. Kh. Kopelevich; 4. The part played by the Petersburg Academy of Sciences (the Academy of Sciences of the USSR) in the publication of Euler’s collected works E. P. Ozhigova; 5. Leonhard Euler and the Berlin Academy of Sciences K. Grau; 6. Was Leonhard Euler driven from Berlin by J. H. Lambert* K.-R. Biermann; 7. Euler’s mathematical notebooks E. Knobloch; 8. On Euler’s surviving manuscripts and notebooks G. P. Matvievskaya; 9. The manuscript materials of Euler on number theory G. P. Matvievskaya and E. P. Ozhigova; 10. Euler’s contribution to algebra I. G. Bashmakova; 11. Diophantine equations in Euler’s works T. A. Lavrinenko; 12. The foundations of mechanics and hydrodynamics in Euler’s works G. K. Mikha*lov and L. I. Sedov; 13. Leonhard Euler and the variational principles of mechanics V. V. Rumyantsev; 14. Leonhard Euler and the mechanics of elastic systems N. V. Banichuk and A. Yu. Ishlinski*; 15. Euler’s research in mechanics during the first Petersburg period N. N. Polyakhov; 16. The significance of Euler’s research in ballistics A. P. Mandryka; 17. Euler and the development of astronomy in Russia V. K. Abalakin and E. A. Grebenikov; 18. Euler and the evolution of celestial mechanics N. I. Nevskaya and K. V. Kholshevnikov; 19. New evidence concerning Euler’s development as an astronomer and historian of science N. I. Nevskaya; 20. Leonhard Euler in correspondence with Clairaut, d’Alembert and Lagrange A. P. Yushkevich and R. Taton; 21. Letters to a German Princess and Euler’s physics A. T. Grigor’ian and V. S. Kirsanov; 22. Euler and I. P. Kulibin N. M. Raskin; 23. Euler and the history of a certain musical-mathematical idea E. V. Gertsman; 24. Euler’s music-rheoretical manuscripts and the formation of his conception of the theory of music S. S. Tserlyuk-Askadskaya; 25. An unknown portrait of Euler by J. F. A. Darbes G. B. Andreeva and M. P. Vikturina; 26. Eulogy in memory of Leonhard Euler Nikola* Fuss; 27. Leonhard Euler’s family and descendants I. R. Gekker and A. A. Euler; Index.
Hardback (ISBN-13: 9780898716467)
Page extent: 450 pages
Size: 247 x 174 mm
A thorough and elegant treatment of the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms. Key features include a detailed treatment of the matrix sign function and matrix roots; a development of the theory of conditioning and properties of the Frechet derivative; Schur decomposition; block Parlett recurrence; a thorough analysis of the accuracy, stability, and computational cost of numerical methods; general results on convergence and stability of matrix iterations; and a chapter devoted to the f(A)b problem. Ideal for advanced courses and for self-study, its broad content, references and appendix also make this book a convenient general reference. Contains an extensive collection of problems with solutions and MATLAB implementations of key algorithms.
* Includes new and unpublished research results and improved algorithms
* Ideal for advanced courses, but also suitable for self-study and reference
purposes * Contains an extensive collection of problems with solutions
Hardback (ISBN-13: 9780898716443)
Page extent: 745 pages
Size: 247 x 174 mm
This new book from the authors of the highly successful classic, Numerical Methods (Prentice-Hall, 1974), addresses the increasingly important role of numerical methods in science and engineering. More cohesive and comprehensive than any other modern textbook in the field, it combines traditional and well-developed topics with other material that is rarely found in numerical analysis texts, such as interval arithmetic, elementary functions, operator series, convergence acceleration, and continued fractions. Although this volume is self-contained, more comprehensive treatments of matrix computations will be given in a forthcoming volume. A supplementary Website contains three appendices: an introduction to matrix computations; a description of Mulprec, a MATLABR multiple precision package; and a guide to literature, algorithms, and software in numerical analysis. Review questions, problems, and computer exercises are also included. For use in an introductory graduate course in numerical analysis and for researchers who use numerical methods in science and engineering.
* Includes review questions, problems and computer exercises drawn from
40 years of teaching * Contains over 60 short biographical notes on mathematicians
who have made significant contributions to the field * A supplementary
website provides an introduction to matrix analysis, a basic review of
the MATLABR package Mulprec, and a guide to literature in numerical analysis
List of figures; List of tables; List of conventions; Preface; 1. Principles of numerical calculations; 2. How to obtain and estimate accuracy; 3. Series, operators and continued fractions; 4. Interpolation and approximation; 5. Numerical integration; 6. Solving scalar nonlinear equations; Bibliography; Index; Online appendix A. Introduction to matrix computations; Online appendix B. A MATLAB multiple precision package; Online appendix C. Guide to literature.
Series: London Mathematical Society Lecture Note Series (No. 349)
Paperback (ISBN-13: 9780521694841)
6 line diagrams 25 worked examples
Page extent: 352 pages
Size: 228 x 152 mm
The first of a two volume set showcasing current research in model theory and its connections with number theory, algebraic geometry, real analytic geometry and differential algebra. Each volume contains a series of expository essays and research papers around the subject matter of a Newton Institute Semester on Model Theory and Applications to Algebra and Analysis. The articles convey outstanding new research on topics such as model theory and conjectures around Mordell-Lang; arithmetic of differential equations, and Galois theory of difference equations; model theory and complex analytic geometry; o-minimality; model theory and noncommutative geometry; definable groups of finite dimension; Hilbert's tenth problem; and Hrushovski constructions. With contributions from so many leaders in the field of model theory and areas with links to model theory, this book cannot fail to be of interest to model theorists, from graduate students to senior researchers, and to researchers in many other areas of mathematics.
* Includes significant new results from leading researchers in model theory
and related areas * All major recent developments in the area are discussed;
future directions in the area are proposed * Essential reading for all
model theorists and any student or researcher interested in the topic
Preface; List of contributors; 1. Model theory and stability theory, with
applications in differential algebra and algebraic geometry Anand Pillay;
2. Differential algebra and generalizations of Grothendieck’s conjecture
on the arithmetic of linear differential equations Anand Pillay; 3. Schanuel’s
conjecture for non-isoconstant elliptic curves over function fields Daniel
Bertrand; 4. An afterthought on the generalized Mordell-Lang conjecture
Damian Rossler; 5. On the definitions of Difference Galois Groups Zoe Chatzidakis,
Charlotte Hardouin and Michael F. Singer; 6. Differentially valued fields
are not differentially closed Thomas Scanlon; 7. Complex analytic geometry
in a nonstandard setting Ya’acov Peterzil and Sergei Starchenko; 8. Model
theory and Kahler geometry Rahim Moosa and Anand Pillay; 9. Some local
definability theory for holomorphic functions A. J. Wilkie; 10. Some observations
about the real and imaginary parts of complex Pfaffian functions Angus
Macintyre; 11. Fusion of structures of finite Morley rank Martin Ziegler;
12.Establishing the o-minimality for expansions of the real field Jean-Philippe
Rolin; 13. On the tomography theorem by P. Schapira Sergei Starchenko;
14. A class of quantum Zariski geometries Boris Zilber; 15. Model theory
guidance in number theory* Ivan Fesenko.
Series: London Mathematical Society Lecture Note Series (No. 350)
Paperback (ISBN-13: 9780521709088)
1 table 30 exercises 25 worked examples
Page extent: 448 pages
Size: 228 x 152 mm
The second of a two volume set showcasing current research in model theory and its connections with number theory, algebraic geometry, real analytic geometry and differential algebra. Each volume contains a series of expository essays and research papers around the subject matter of a Newton Institute Semester on Model Theory and Applications to Algebra and Analysis. The articles convey outstanding new research on topics such as model theory and conjectures around Mordell-Lang; arithmetic of differential equations, and Galois theory of difference equations; model theory and complex analytic geometry; o-minimality; model theory and noncommutative geometry; definable groups of finite dimension; Hilbert's tenth problem; and Hrushovski constructions. With contributions from so many leaders in the field of model theory and areas with links to model theory, this book cannot fail to be of interest to model theorists, from graduate students to senior researchers, and to researchers in many other areas of mathematics.
* Includes significant new results from leading researchers in model theory
and related areas * All major recent developments in the area are discussed;
future directions in the area are proposed * Essential reading for all
model theorists and any student or researcher interested in the topic
Preface; List of contributors; 1. Conjugacy in groups of finite Morley rank Olivier Frecon and Eric Jaligot; 2. Permutation groups of finite Morley rank Alexandre Borovik and Gregory Cherlin; 3. A survey of asymptotic classes and measurable structures Richard Elwes and Dugald Macpherson; 4. Counting and dimensions Ehud Hrushovski and Frank Wagner; 5. A survey on groups definable in o-minimal structures Margarita Otero; 6. Decision problems in algebra and analogues of Hilbert’s tenth problem Thanases Pheidas and Karim Zahidi; 7. Hilbert’s tenth problem for function fields of characteristic zero Kirsten Eisentrager; 8. First-order characterization of function field invariants over large fields Bjorn Poonen and Florian Pop; 9. Nonnegative solvability of linear equations in ordered Abelian groups Philip Scowcroft; 10. Model theory for metric structures IItai Ben Yaacov, Alexander Berenstein, C. Ward Henson and Alexander Usvyatsov.
Series: New Mathematical Monographs (No. 11)
Hardback (ISBN-13: 9780521887205)
4 line diagrams 2 half-tones 4 tables 125 exercises 6 figures
Page extent: 488 pages
Size: 228 x 152 mm
Property (T) is a rigidity property for topological groups, first formulated by D. Kazhdan in the mid 1960's with the aim of demonstrating that a large class of lattices are finitely generated. Later developments have shown that Property (T) plays an important role in an amazingly large variety of subjects, including discrete subgroups of Lie groups, ergodic theory, random walks, operator algebras, combinatorics, and theoretical computer science. This monograph offers a comprehensive introduction to the theory. It describes the two most important points of view on Property (T): the first uses a unitary group representation approach, and the second a fixed point property for affine isometric actions. Via these the authors discuss a range of important examples and applications to several domains of mathematics. A detailed appendix provides a systematic exposition of parts of the theory of group representations that are used to formulate and develop Property (T).
* Introduces a very active area of research with applications to topological group theory, measure theory, ergodic theory, random walks, combinatorics, and more * The Appendix acts as an introduction to numerous important subjects of mathematics, plus as a first course on representation theory on Hilbert spaces * Includes lots of examples and avoids unnecessary technicalities, ensuring it is accessible to students as well as academic researchers
Introduction; Part I. Kazhdan’s Property (T): 1. Property (T); 2. Property (FH); 3. Reduced Cohomology; 4. Bounded generation; 5. A spectral criterion for Property (T); 6. Some applications of Property (T); 7. A short list of open questions; Part II. Background on Unitary Representations: A. Unitary group representations; B. Measures on homogeneous spaces; C. Functions of positive type; D. Representations of abelian groups; E. Induced representations; F. Weak containment and Fell topology; G. Amenability; Appendix; Bibliography; List of symbols; Index.
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