Hardback (ISBN-13: 9780521868754)
8 line diagrams 45 half-tones
Page extent: 570 pages
Size: 247 x 174 mm
The standard cosmological picture of our Universe emerging from a 'big bang' leaves open many fundamental questions which string theory, a unified theory of all forces of nature, should be able to answer. The first book dedicated to string cosmology, it contains a pedagogical introduction to the basic notions of the subject. It describes the new possible scenarios suggested by string theory for the primordial evolution of our Universe. It discusses the main phenomenological consequences of these scenarios, stresses their differences from each other, and compares them to the more conventional models of inflation. The book summarizes over 15 years of research in this field and introduces current advances. It is self-contained, so it can be read by astrophysicists with no knowledge of string theory, and high-energy physicists with little understanding of cosmology. Detailed and explicit derivations of all the results presented provide a deeper appreciation of the subject.
* First book fully devoted to string cosmology, summarizing the results of 15 years of work ? Includes self-contained introductions to cosmology and string theory ? Contains detailed derivations of all presented results allowing for a deeper understanding and aiding preparation for independent research
Contents
Preface; Acknowledgements; Notation, units and conventions; 1. A short review of standard and inflationary cosmology; 2. The basic string cosmology equations; 3. Conformal invariance and string effective action; 4. Duality symmetries and cosmological solutions; 5. Inflationary kinematics; 6. The string phase; 7. The cosmic background of relic gravitational waves; 8. Scalar perturbations and the anisotropy of the CMB radiation; 9. Dilaton phenomenology; 10. Elements of brane cosmology; Index.
Paperback (ISBN-13: 9780521708777)
Hardback (ISBN-13: 9780521882194)
4 line diagrams 141 exercises 50 worked examples
Page extent: 206 pages
Size: 228 x 152 mm
Weight: 0.304 kg
Weight: 0.418 kg
This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with Konig's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theory and nonstandard analysis.
* Lively mathematical examples and some unusual formal systems stimulate the reader from the very beginning ? Suitable as an introduction to logic for students without any background in formal set theory ? Supported by companion web-pages containing further material and exercises
Contents
Preface; How to read this book; 1. Konig’s lemma; 2. Posets and maximal elements; 3. Formal systems; 4. Deductions in posets; 5. Boolean algebras; 6. Propositional logic; 7. Valuations; 8. Filters and ideals; 9. First-order logic; 10. Completeness and compactness; 11. Model theory; 12. Nonstandard analysis; Bibliography; Index.
Series: London Mathematical Society Student Texts (No. 71)
Hardback (ISBN-13: 9780521836104)
Paperback (ISBN-13: 9780521544207)
52 exercises
Page extent: 320 pages
Size: 228 x 152 mm
The second of a three-volume set providing a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The subject is presented from the perspective of linear representations of quivers, geometry of tubes of indecomposable modules, and homological algebra. This volume provides an up-to-date introduction to the representation theory of the representation-infinite hereditary algebras of Euclidean type, as well as to concealed algebras of Euclidean type. The book is primarily addressed to a graduate student starting research in the representation theory of algebras, but it will also be of interest to mathematicians in other fields. The text includes many illustrative examples and a large number of exercises at the end of each of the chapters. Proofs are presented in complete detail, making the book suitable for courses, seminars, and self-study.
? Self contained, only knowledge from volume one is required for volume two ? Introduces the reader to representation theory by applying tilting theory ? Class tested in courses given by the authors
Contents
Introduction; 10. Tubes; 11. Module categories over concealed algebras of Euclidean type; 12. Regular modules and tubes over concealed algebras of Euclidean type; 13. Indecomposable modules and tubes over hereditary algebras of Euclidean type; 14. Minimal representation-infinite algebras; Bibliography; Index; List of symbols.
Series: Cambridge Studies in Advanced Mathematics (No. 107)
Hardback (ISBN-13: 9780521809375)
160 line diagrams 44 exercises 160 figures
Page extent: 400 pages
Size: 228 x 152 mm
Written by a master of the subject, this text will be appreciated by students and experts for the way it develops the classical theory of functions of a complex variable in a clear and straightforward manner. In general, the approach taken here emphasises geometrical aspects of the theory in order to avoid some of the topological pitfalls associated with this subject. Thus, Cauchy’s integral formula is first proved in a topologically simple case from which the author deduces the basic properties of holomorphic functions. Starting from the basics, students are led on to the study of conformal mappings, Riemann’s mapping theorem, analytic functions on a Riemann surface, and ultimately the Riemann-Roch and Abel theorems. Profusely illustrated, and with plenty of examples, and problems (solutions to many of which are included), this book should be a stimulating text for advanced courses in complex analysis.
* Written by a master of the subject ? Straightforward presentation avoids topological diffculties ? Goes from basics to advanced topics such as Riemann surfaces and Riemann-Roch theorem
Contents
1. Holomorphic functions; 2. Cauchy’s theorem; 3. Conformal mappings; 4. Analytic continuation; 5. Riemann’s mapping theorem; 6. Riemann surfaces; 7. The structure of Riemann surfaces; 8. Analytic functions on a closed Riemann surface.