Publication planned for: October 2015
available from October 2015
format: Hardback
isbn: 9781939512079
Hardback
Using the Daniell-Riesz approach, this text presents the Lebesgue integral at a level accessible to an audience familiar only with limits, derivatives and series. Employing such minimal prerequisites allows for greatly increased curricular flexibility for course instructors, as well as providing undergraduates with a gateway to the powerful modern mathematics of functions at a very early stage. The book's topics include: the definition and properties of the Lebesgue integral; Banach and Hilbert spaces; integration with respect to Borel measures, along with their associated L2(ƒÊ) spaces; bounded linear operators; and the spectral theorem. The text also describes several applications of the theory, such as Fourier series, quantum mechanics, and probability.
Preface
Introduction
1. Lebesgue integrable functions
2. Lebesgue's integral compared to Riemann's
3. Functions spaces
4. Measure theory
5. Hilbert space operators
Solutions to selected problems
Bibliography.
available from February 2016
format: Paperback
isbn: 9781107536517
Originally published in 1927, this book presents the collected papers of the renowned Indian mathematician Srinivasa Ramanujan (1887?1920), with editorial contributions from G. H. Hardy (1877?1947). Detailed notes are incorporated throughout and appendices are also included. This book will be of value to anyone with an interest in the works of Ramanujan and the history of mathematics.
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Preface
Notice P. V. Seshu and R. Bamachaundra Rao
Notice G. H. Hardy
Part I. Papers:
1. Some properties of Bernoulli's numbers
2. On question 330 of Prof. Sanjana
3. Note on a set of simultaneous equations
4. Irregular numbers
5. Squaring the circle
6. Modular equations and approximations to ƒÎ
7. On the integral [...]
8. On the number of divisors of a number
9. On the sum of the square roots of the first n natural numbers
10. On the product [...]
11. Some definite integrals
12. Some definite integrals connected with Gauss's sums
13. Summation of a certain series
14. New expression for Riemann's functions [...]
15. Highly composite numbers
16. On certain infinite series
17. Some formulae in the analytic theory of numbers
18. On certain arithmetical functions
19. A series of Euler's constant y
20. On the expression of a number in the form of ax2+by2+cz2+du2
21. On certain trigonometrical sums and their applications in the theory of numbers
22. Some definite integrals
23. Some definite integrals
24. A proof of Bertrand's postulate
25. Some properties of p (n), the number of partitions of n
26. Proof of certain identities in combinatory analysis
27. A class of definite integrals
28. Congruence properties of partitions
29. Algebraic relations between certain infinite products
30. Congruence properties of partitions
29. Algebraic relations between certain infinite products
30. Congruence properties of partitions
Part II. Papers Written in Collaboration with G. H. Hardy:
31. Une formule asymptotique pour le nombre des partitions de n
32. Proof that almost all numbers n are composed of about log log n prime factors
33. Asymptotic formulae in combinatory analysis
34. Asymptotic formulae for the distribution of integers of various types
35. The normal number of prime factors of a number n
36. Asymptotic formulae in combinatory analysis
37. On the coefficients in the expansions of certain modular functions
Questions and solutions
Appendix 1. Notes on the papers
Appendix 2. Further extracts from Ramanujan's letters to G. H. Hardy.
available from December 2015
format: Paperback
isbn: 9781611973938
Bose-Einstein condensation is a phase transition in which a fraction of particles of a boson gas condenses into the same quantum state known as the Bose?Einstein condensate (BEC). This book, a broad study of nonlinear excitations in self-defocusing nonlinear media, presents a wide array of findings in the realm of BECs and on the nonlinear Schrodinger-type models that arise therein. It summarizes state-of-the-art knowledge on the defocusing nonlinear Schrodinger-type models in a single volume and contains a wealth of resources, including over 800 references to relevant articles and monographs and a meticulous index for ease of navigation. This book is intended for atomic and condensed-matter physicists, nonlinear scientists, and applied mathematicians. It will be equally valuable to beginners and experienced researchers in these fields.
Preface
Acknowledgments
1. Introduction
2. The one-dimensional case
3. The two-dimensional case
4. The three-dimensional case
Bibliography
Index.
Part of London Mathematical Society Lecture Note Series
available from January 2016
format: Paperback
isbn: 9781316601952
Many geometrical features of manifolds and fibre bundles modelled on Frechet spaces either cannot be defined or are difficult to handle directly. This is due to the inherent deficiencies of Frechet spaces; for example, the lack of a general solvability theory for differential equations, the non-existence of a reasonable Lie group structure on the general linear group of a Frechet space, and the non-existence of an exponential map in a Frechet?Lie group. In this book, the authors describe in detail a new approach that overcomes many of these limitations by using projective limits of geometrical objects modelled on Banach spaces. It will appeal to researchers and graduate students from a variety of backgrounds with an interest in infinite-dimensional geometry. The book concludes with an appendix outlining potential applications and motivating future research.
Preface
1. Banach manifolds and bundles
2. Frechet spaces
3. Frechet manifolds
4. Projective systems of principal bundles
5. Projective systems of vector bundles
6. Examples of projective systems of bundles
7. Connections on plb-vector bundles
8. Geometry of second order tangent bundles
Appendix. Further study.
Part of London Mathematical Society Lecture Note Series
available from March 2016
format: Paperback
isbn: 9781107565562
In the summer of 2014 leading experts in the theory of water waves gathered at the Newton Institute for Mathematical Sciences in Cambridge for four weeks of research interaction. A cross-section of those experts was invited to give introductory-level talks on active topics. This book is a compilation of those talks and illustrates the diversity, intensity, and progress of current research in this area. The key themes that emerge are numerical methods for analysis, stability and simulation of water waves, transform methods, rigorous analysis of model equations, three-dimensionality of water waves, variational principles, shallow water hydrodynamics, the role of deterministic and random bottom topography, and modulation equations. This book is an ideal introduction for PhD students and researchers looking for a research project. It may also be used as a supplementary text for advanced courses in mathematics or fluid dynamics.
Preface Thomas J. Bridges, Mark D. Groves and David P. Nicholls
1. High-Order Perturbation of Surfaces (HOPS) Short Course ? boundary value problems David P. Nicholls
2. HOPS Short Course ? traveling water waves Benjamin F. Akers
3. High-Order Perturbation of Surfaces (HOPS) Short Course ? analyticity theory David P. Nicholls
4. HOPS Short Course ? stability of travelling water waves Benjamin F. Akers
5. A novel non-local formulation of water waves Athanassios S. Fokas and Konstantinos Kalimeris
6. The dimension-breaking route to three-dimensional solitary gravity-capillary water waves Mark D. Groves
7. Validity and non-validity of the nonlinear Schrodinger equation as a model for water waves Guido Schneider
8. Vortex sheet formulations and initial value problems: analysis and computing David M. Ambrose
9. Wellposedness and singularities of the water wave equations Sijue Wu
10. Conformal mapping and complex topographies Andre Nachbin
11. Variational water wave modelling: from continuum to experiment Onno Bokhove and Anna Kalogirou
12. Symmetry, modulation and nonlinear waves Thomas J. Bridges.