Subject Area: Chemistry - Mathematics
ISBN-13: 9780128044896
Pub Date: 06/01/2016
Pages: Approx 272 Pages
Product Type: Hardcover
Focuses on core geometry rather than proofs, paving the way to fast and efficient insight into an extremely complex topic in geometric structures
Enables further study of more advanced topics and texts
Demonstrates in the simplest possible way how to relate concepts of geometric analysis by way of algebraic or topological techniques
Contains full topical coverage of The Log-Convex Density Conjecture
Comprehensively updated throughout
Part of Dolciani Mathematical Expositions
Date Published: February 2016
availability: Available
format: Hardback
isbn: 9780883853597
By the first year of graduate school, a young mathematician will have encountered at least three separate definitions of the integral. The associated integrals are typically studied in isolation, with little attention paid to the relationships between them or to the historical issues that motivated their definitions. This book redresses this situation by introducing the Riemann, Darboux, Lebesgue, and gauge integrals using a common set of examples. This allows the reader to see how the definitions influence proof techniques and computational strategies. Then the properties of the integrals are compared in three major areas: the class of integrable functions, the convergence properties of the integral, and the best form of the Fundamental Theorems of Calculus. With a thorough set of appendices and exercises, and interesting historical context, this book is equally useful as a reference for mathematicians or as a text for a second undergraduate course in real analysis.
An historically motivated, cohesive survey of the most common types of integration
Unifies some seemingly disparate frameworks for integration using a common set of examples
Pedagogy is a clear priority, and the different types of integration are compared in multiple enlightening ways
Preface
1. A historical introduction
2. The Riemann integral
3. The Darboux integral
4. A functional zoo
5. Another approach: measure theory
6. The Lebesgue integral
7. The gauge integral
8. Stieltjes-type integrals and extensions
9. A look back
10. Afterword: L2 spaces and Fourier series
Appendices: a compendium of definitions and results
Index.
Part of Spectrum
Publication planned for: April 2016
availability: Not yet published - available from April 2016
format: Hardback
isbn: 9781107135550
format: Paperback
isbn: 9781107594647
G. H. Hardy (1877?1947) ranks among the great mathematicians of the twentieth century. He did essential research in number theory and analysis, held professorships at Cambridge and Oxford, wrote important textbooks as well as the classic A Mathematician's Apology, and famously collaborated with J. E. Littlewood and Srinivasa Ramanujan. Hardy was a colorful character with remarkable expository skills. This book is a feast of G. H. Hardy's writing. There are selections of his mathematical papers, his book reviews, his tributes to departed colleagues. Some articles are serious, whereas others display a wry sense of humor. And there are recollections by those who knew Hardy, along with biographical and mathematical pieces written explicitly for this collection. Fans of Hardy should find much here to like. And for those unfamiliar with his work, The G. H. Hardy Reader provides an introduction to this extraordinary individual.
Introduces the extraordinary life of G. H. Hardy
Provides samples of his essays, book reviews, and personal stories of his colleagues
A treat for anyone from amateurs to serious mathematicians
Part of Anneli Lax New Mathematical Library
Publication planned for: April 2016
availability: Not yet published - available from April 2016
format: Paperback
isbn: 9780883856505
Baffling the greatest minds for over one hundred and fifty years, the Riemann hypothesis is generally considered one of the most important and intriguing open problems in mathematics. In addition, it was chosen as one of the seven Millennium Prize Problems by the Clay Mathematics Institute, so proving the Riemann hypothesis will not only make you world famous, but will earn you a one million dollar prize. This book introduces interested readers to the mathematical universe of prime numbers, infinite sequences, infinite products and complex functions that lies behind the hypothesis. It originated from an online course for talented secondary school students, organized by the authors at the University of Amsterdam. Its aim was to bring the students into contact with challenging university-level mathematics and show them why the Riemann hypothesis is such an important problem in mathematics.
Explains the Riemann hypothesis and its importance in mathematics
Originating from an online course for talented secondary school students, this book is accessible to a broad audience
Sure to inspire further interest in number theory and complex analysis
Preface
1. Prime numbers
2. The zeta function
3. The Riemann hypothesis
4. Primes and the Riemann hypothesis
Appendix A. Why big primes are useful
Appendix B. Computer support
Appendix C. Further reading and internet surfing
Appendix D. Solutions to the exercises
Index.
Part of Cambridge Texts in Applied Mathematics
Publication planned for: July 2016
availability: Not yet published - available from July 2016
format: Hardback
isbn: 9781107042728
format: Paperback
isbn: 9781107669482
This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Backlund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Pade approximants and convergence algorithms singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painleve equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thorough list of references will benefit upper-level undergraduate, and beginning graduate students as well as researchers from other disciplines.
A generous and up-to-date bibliography allows the reader to use the text as a source for branching out into more specialized directions, according to their own interests
Readers will more easily absorb the ideas and techniques by working through explicit computations built up on the basis of key examples while at the same time being presented with the general theory
Based on tried and tested lecture notes - the material has been used for teaching undergraduate courses and is tailored for student use
Preface
1. Introduction to difference equations
2. Discrete equations from transformations of continuous equations
3. Integrability of P?Es
4. Interlude: lattice equations and numerical algorithms
5. Continuum limits of lattice P?Es
6. One-dimensional lattices and maps
7. Identifying integrable difference equations
8. Hirota's bilinear method
9. Multi-soliton solutions and the Cauchy matrix scheme
10. Similarity reductions of integrable P?Es
11. Discrete Painleve equations
12. Lagrangian multiform theory
Appendix A. Elementary difference calculus and difference equations
Appendix B. Theta functions and elliptic functions
Appendix C. The continuous Painleve equations and the Garnier system
Appendix D. Some determinantal identities
References
Index.