Courant Lecture Notes, Volume: 26
2015; 249 pp; softcover
ISBN-13: 978-1-4704-1080-3
Expected publication date is July 8, 2015.
The path from relatively unstructured egg to full organism is one of the most fascinating trajectories in the biological sciences. Its complexity calls for a very high level of organization, with an array of subprocesses in constant communication with each other. These notes introduce an interleaved set of mathematical models representative of research in the last few decades, as well as the techniques that have been developed for their solution. Such models offer an effective way of incorporating reliable data in a concise form, provide an approach complementary to the techniques of molecular biology, and help to inform and direct future research.
Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
Graduate students and research mathematicians interested in mathematical biology.
Mathematical Surveys and Monographs, Volume: 205
2015; approx. 350 pp; hardcover
ISBN-13: 978-1-4704-2024-6
Expected publication date is July 16, 2015.
Is there a vector space whose dimension is the golden ratio? Of course not--the golden ratio is not an integer! But this can happen for generalizations of vector spaces--objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories.
Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
Graduate students and research mathematicians interested in category theory and Hopf algebras.
Abelian categories
Monoidal categories
Z+-rings
Tensor categories
Representation categories of Hopf algebras
Finite tensor categories
Module categories
Braided categories
Fusion categories
Bibliography
Index
Hindustan Book Agency
2015; 310 pp; softcover
ISBN-13: 978-93-80250-72-4
This book introduces the reader to the fascinating world of modular forms through a problem-solving approach. As such, it can be used by undergraduate and graduate students for self-instruction. The topics covered include q-series, the modular group, the upper half-plane, modular forms of level one and higher level, the Ramanujan Ą-function, the Petersson inner product, Hecke operators, Dirichlet series attached to modular forms, and further special topics. It can be viewed as a gentle introduction for a deeper study of the subject. Thus, it is ideal for non-experts seeking an entry into the field.
A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.
Students and research mathematicians interested in modular forms.
Part I. Problems
Jacobi's q-series
The modular group
The upper half-plane
Modular forms of level one
The Ramanujan ƒÎ-function
Modular forms of higher level
The Petersson inner product
Hecke operators of higher level
Dirichlet series and modular forms
The Petersson inner product
Hecke operators of higher level
Dirichlet series and modular forms
Special topics
Part II
Solutions to problems in Part I
Special topics
A short guide for further reading
References
Index
Part of Cambridge Monographs on Mathematical Physics
Date Published: February 2015
availability: Available
format: Paperback
isbn: 9781107438057
Classical solutions play an important role in quantum field theory, high-energy physics and cosmology. Real-time soliton solutions give rise to particles, such as magnetic monopoles, and extended structures, such as domain walls and cosmic strings, that have implications for early universe cosmology. Imaginary-time Euclidean instantons are responsible for important nonperturbative effects, while Euclidean bounce solutions govern transitions between metastable states. Written for advanced graduate students and researchers in elementary particle physics, cosmology and related fields, this book brings the reader up to the level of current research in the field. The first half of the book discusses the most important classes of solitons: kinks, vortices and magnetic monopoles. The cosmological and observational constraints on these are covered, as are more formal aspects, including BPS solitons and their connection with supersymmetry. The second half is devoted to Euclidean solutions, with particular emphasis on Yang?Mills instantons and on bounce solutions.
1. Introduction
2. One-dimensional solitons
3. Solitons in more dimensions - vortices and strings
4. Some topology
5. Magnetic monopoles with U(1) charges
6. Magnetic monopoles in larger gauge groups
7. Cosmological implications and experimental bounds
8. BPS solitons, supersymmetry, and duality
9. Euclidean solutions
10. Yang?Mills instantons
11. Instantons, fermions, and physical consequences
12. Vacuum decay
Appendixes
References
Index.
Part of Mathematical Sciences Research Institute Publications
Date Published: April 2015
availability: Available
format: Hardback
isbn: 9781107011038
This title is not currently available for evaluation. However, if you are interested in the title for your course we can consider offering an evaluation copy. To register your interest please contact asiamktg@cambridge.org providing details of the course you are teaching.
Combinatorial games are the strategy games that people like to play, for example chess, Hex, and Go. They differ from economic games in that there are two players who play alternately with no hidden cards and no dice. These games have a mathematical structure that allows players to analyse them in the abstract. Games of No Chance 4 contains the first comprehensive explorations of misere (last player to move loses) games, extends the theory for some classes of normal-play (last player to move wins) games and extends the analysis for some specific games. It includes a tutorial for the very successful approach to analysing misere impartial games and the first attempt at using it for misere partisan games. Hex and Go are featured, as well as new games: Toppling Dominoes and Maze. Updated versions of Unsolved Problems in Combinatorial Game Theory and the Combinatorial Games Bibliography complete the volume.
1. Peeking at partizan misere quotients Meghan R. Allen
2. A survey about solitaire clobber Laurent Beaudou, Eric Duchene and Sylvain Gravier
3. Monte-Carlo approximation of temperature Tristan Cazenave
4. Retrograde analysis of woodpush Tristan Cazenave and Richard J. Nowakowski
5. Narrow misere dots-and-boxes Sebastien Collette, Erik D. Demaine, Martin L. Demaine and Stefan Langerman
6. Toppling conjectures Alex Fink, Richard J. Nowakowski, Aaron Siegel and David Wolfe
7. Harnessing the unwieldy MEX function Aviezri Fraenkel and Udi Peled
8. The rat game and the mouse game Aviezri Fraenkel
9. A ruler regularity in hexadecimal games J. P. Grossman and Richard J. Nowakowski
10. A handicap strategy for hex Philip Henderson and Ryan Hayward
11. Restrictions of m-wythoff nim and p-complementary Beatty sequences Urban Larsson
12. Computer analysis of sprouts with nimbers Julien Lemoine and Simon Viennot
13. Navigating the MAZE Neil McKay, Richard J. Nowakowski and Angela Siegel
14. Evaluating territories of Go positions with capturing races Teigo Nakamura
15. Artificial intelligence for bidding Hex Sam Payne and Elina Robeva
16. Nimbers in partizan games Carlos Pereira Dos Santos and Jorge Nuno Silva
17. Misere canonical forms of partizan games Aaron Siegel
18. The structure and classification of misere quotients Aaron Siegel
19. An algorithm for computing indistinguishability quotients in misere impartial combinatorial games Mike Weimerskirch
20. Unsolved problems in combinatorial games Richard J. Nowakowski
21. Combinatorial games: selected short bibliography with a succinct gourmet introduction Aviezri Fraenkel and Richard J. Nowakowski.