Contemporary Mathematics, Volume: 541
2011; 257 pp; softcover
ISBN-13: 978-0-8218-4960-6
Expected publication date is May 28, 2011.
This book is based on a 10-day workshop given by leading experts in hyperbolic geometry, quantum topology and number theory, in June 2009 at Columbia University. Each speaker gave a minicourse consisting of three or four lectures aimed at graduate students and recent PhDs. The proceedings of this enormously successful workshop can serve as an introduction to this active research area in a way that is expository and broadly accessible to graduate students.
Although many ideas overlap, the twelve expository/research papers in this volume can be grouped into four rough categories:
(1) different approaches to the Volume Conjecture, and relations between the main quantum and geometric invariants;
(2) the geometry associated to triangulations of hyperbolic 3-manifolds;
(3) arithmetic invariants of hyperbolic 3-manifolds;
(4) quantum invariants associated to knots and hyperbolic 3-manifolds.
The workshop, the conference that followed, and these proceedings continue a long tradition in quantum and geometric topology of bringing together ideas from diverse areas of mathematics and physics, and highlights the importance of collaborative research in tackling big problems that require expertise in disparate disciplines.
Graduate students and research mathematicians interested in hyperbolic geometry, quantum topology and number theory.
H. Murakami -- An introduction to the volume conjecture
T. Dimofte and S. Gukov -- Quantum field theory and the volume conjecture
R. M. Kashaev -- R-matrix knot invariants and triangulations
S. Garoufalidis -- Knots and tropical curves
S. Baseilhac -- Quantum coadjoint action and the 6j-symbols of U_qsl_2
S. Garoufalidis -- What is a sequence of Nilsson type?
D. Futer and F. Gueritaud -- From angled triangulations to hyperbolic structures
F. Luo -- Triangulated 3-manifolds: From Haken's normal surfaces to Thurston's algebraic equation
J. S. Purcell -- An introduction to fully augmented links
G. S. Walsh -- Orbifolds and commensurability
W. D. Neumann -- Realizing arithmetic invariants of hyperbolic 3-manifolds
D. D. Long and A. W. Reid -- Fields of definition of canonical curves
2011; approx. 542 pp; hardcover
ISBN-13: 978-0-8218-5260-6
Expected publication date is June 4, 2011.
This is a textbook for pre-service elementary school teachers and for current teachers who are taking professional development courses. By emphasizing the precision of mathematics, the exposition achieves a logical and coherent account of school mathematics at the appropriate level for the readership. Wu provides a comprehensive treatment of all the standard topics about numbers in the school mathematics curriculum: whole numbers, fractions, and rational numbers. Assuming no previous knowledge of mathematics, the presentation develops the basic facts about numbers from the beginning and thoroughly covers the subject matter for grades K through 7.
Every single assertion is established in the context of elementary school mathematics in a manner that is completely consistent with the basic requirements of mathematics. While it is a textbook for pre-service elementary teachers, it is also a reference book that school teachers can refer to for explanations of well-known but hitherto unexplained facts. For example, the sometimes-puzzling concepts of percent, ratio, and rate are each given a treatment that is down to earth and devoid of mysticism. The fact that a negative times a negative is a positive is explained in a leisurely and comprehensible fashion.
Pre-service elementary school teachers and current teachers interested in a logical and coherent account of school mathematics.
Whole numbers
Place value
The basic laws of operations
The standard algorithms
The addition algorithm
The subtraction algorithm
The multiplication algorithm
The long division algorithm
The number line and the four operations revisited
What is a number?
Some comments on estimation
Numbers in base b
Fractions
Definitions of fraction and decimal
Equivalent fractions and FFFP
Addition of fractions and decimals
Equivalent fractions: further applications
Subtraction of fractions and decimals
Multiplication of fractions and decimals
Division of fractions
Complex fractions
Percent
Fundamental Assumption of School Mathematics (FASM)
Ratio and rate
Some interesting word problems
On the teaching of fractions in elementary school
Rational numbers
The (two-sided) number line
A different view of rational numbers
Adding and subtracting rational numbers
Adding and subtracting rational numbers redux
Multiplying rational numbers
Dividing rational numbers
Ordering rational numbers
Number theory
Divisibility rules
Primes and divisors
The Fundamental Theorem of Arithmetic (FTA)
The Euclidean algorithm
Applications
Pythagorean triples
More on decimals
Why finite decimals are important
Review of finite decimals
Scientific notation
Decimals
Decimal expansions of fractions
Bibliography
Index
Graduate Studies in Mathematics, Volume: 124
2011; approx. 858 pp; hardcover
ISBN-13: 978-0-8218-4819-7
Expected publication date is June 24, 2011.
Toric varieties form a beautiful and accessible part of modern algebraic geometry. This book covers the standard topics in toric geometry; a novel feature is that each of the first nine chapters contains an introductory section on the necessary background material in algebraic geometry. Other topics covered include quotient constructions, vanishing theorems, equivariant cohomology, GIT quotients, the secondary fan, and the minimal model program for toric varieties. The subject lends itself to rich examples reflected in the 134 illustrations included in the text. The book also explores connections with commutative algebra and polyhedral geometry, treating both polytopes and their unbounded cousins, polyhedra. There are appendices on the history of toric varieties and the computational tools available to investigate nontrivial examples in toric geometry.
Readers of this book should be familiar with the material covered in basic graduate courses in algebra and topology, and to a somewhat lesser degree, complex analysis. In addition, the authors assume that the reader has had some previous experience with algebraic geometry at an advanced undergraduate level. The book will be a useful reference for graduate students and researchers who are interested in algebraic geometry, polyhedral geometry, and toric varieties.
Graduate students and research mathematicians interested in algebraic geometry, polyhedral geometry, and toric varieties.
Basic theory of toric varieties
Affine toric varieties
Projective toric varieties
Normal toric varieties
Divisors on toric varieties
Homogeneous coordinates on toric varieties
Line bundles on toric varieties
Projective toric morphisms
The canonical divisor of a toric variety
Sheaf cohomology of toric varieties
Topics in toric geometry
Toric surfaces
Toric resolutions and toric singularities
The topology of toric varieties
Toric Hirzebruch-Riemann-Roch
Toric GIT and the secondary fan
Geometry of the secondary fan
The history of toric varieties
Computational methods
Spectral sequences
Bibliography
Index
Hardback
Series: Encyclopedia of Mathematics and its Applications (No. 143)
ISBN: 9780521768405
1 b/w illus.
Dimensions: 234 x 156 mm
available from August 2011
This comprehensive volume on ergodic control for diffusions highlights intuition alongside technical arguments. A concise account of Markov process theory is followed by a complete development of the fundamental issues and formalisms in control of diffusions. This then leads to a comprehensive treatment of ergodic control, a problem that straddles stochastic control and the ergodic theory of Markov processes. The interplay between the probabilistic and ergodic-theoretic aspects of the problem, notably the asymptotics of empirical measures on one hand, and the analytic aspects leading to a characterization of optimality via the associated Hamilton?Jacobi?Bellman equation on the other, is clearly revealed. The more abstract controlled martingale problem is also presented, in addition to many other related issues and models. Assuming only graduate-level probability and analysis, the authors develop the theory in a manner that makes it accessible to users in applied mathematics, engineering, finance and operations research.
Preface
1. Introduction
2. Controlled diffusions
3. Nondegenerate controlled diffusions
4. Various topics in nondegenerate diffusions
5. Controlled switching diffusions
6. Controlled martingale problems
7. Degenerate controlled diffusions
8. Controlled diffusions with partial observations
Appendix
References
Index of symbols
Subject index.
Paperback
Series: London Mathematical Society Lecture Note Series (No. 389)
ISBN: 9780521175616
12 b/w illus.
Dimensions: 228 x 152 mm
- available from July 2011
Random Fields on the Sphere presents a comprehensive analysis of isotropic spherical random fields. The main emphasis is on tools from harmonic analysis, beginning with the representation theory for the group of rotations SO(3). Many recent developments on the method of moments and cumulants for the analysis of Gaussian subordinated fields are reviewed. This background material is used to analyse spectral representations of isotropic spherical random fields and then to investigate in depth the properties of associated harmonic coefficients. Properties and statistical estimation of angular power spectra and polyspectra are addressed in full. The authors are strongly motivated by cosmological applications, especially the analysis of cosmic microwave background (CMB) radiation data, which has initiated a challenging new field of mathematical and statistical research. Ideal for mathematicians and statisticians interested in applications to cosmology, it will also interest cosmologists and mathematicians working in group representations, stochastic calculus and spherical wavelets.
Preface
1. Introduction
2. Background results in representation theory
3. Representations of SO(3) and harmonic analysis on S2
4. Background results in probability and graphical methods
5. Spectral representations
6. Characterizations of isotropy
7. Limit theorems for Gaussian subordinated random fields
8. Asymptotics for the sample power spectrum
9. Asymptotics for sample bispectra
10. Spherical needlets and their asymptotic properties
11. Needlets estimation of power spectrum and bispectrum
12. Spin random fields
Appendix
Bibliography
Index.