AMS Chelsea Publishing: An Imprint of the American Mathematical Society
This book is a reprint of the third edition of the classic book on complex analysis. It is a rigorous introduction on an elementary level to the theory of analytic functions of one complex variable and is intended to be used by first year graduate students and advanced undergraduate students.
The book covers standard topics in an introductory complex analysis course. The presentation is slanted toward the geometric approach to complex analysis, with a lot of material on conformal mappings, the Riemann mapping theorem, Dirichlet's problem (the existence of a harmonic function with given boundary values), the monodromy theorem, and consideration of the kinds of regions that the Cauchy integral theorem holds for. It also covers such analytic topics as power series, contour integrals, and infinite products. The coverage of special functions is concise but reasonably complete. The presentation is concise, clear, and thorough, and is still fresh today, more than thirty years after its last revision.
Graduate and undergraduate students interested in teaching and learning complex analysis.
AMS Chelsea Publishing, Volume: 385
2021; 331 pp; Softcover
MSC: Primary 30;
Print ISBN: 978-1-4704-6767-8
Product Code: CHEL/385
Not yet published
Expected publication date November 26, 2021
This text introduces students to the theory and practice of differential equations, which are fundamental to the mathematical formulation of problems in physics, chemistry, biology, economics, and other sciences. The book is ideally suited for undergraduate or beginning graduate students in mathematics, and will also be useful for students in the physical sciences and engineering who have already taken a three-course calculus sequence.
This second edition incorporates much new material, including sections on the Laplace transform and the matrix Laplace transform, a section devoted to Bessel's equation, and sections on applications of variational methods to geodesics and to rigid body motion. There is also a more complete treatment of the Runge-Kutta scheme, as well as numerous additions and improvements to the original text. Students finishing this book will be well prepared for advanced studies in dynamical systems, mathematical physics, and partial differential equations.
Undergraduate and graduate students interested in differential equations.
Pure and Applied Undergraduate Texts Volume: 52
2022; 388 pp; Softcover
MSC: Primary 34;
Print ISBN: 978-1-4704-6762-3
Product Code: AMSTEXT/52
The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. Building bridges between these two subject areas is fruitful in two ways. Through tropical geometry optimization algorithms become applicable to questions in algebraic geometry. Conversely, looking at topics in optimization through the tropical geometry lens adds an additional layer of structure. The author covers contemporary research topics that are relevant for applications such as phylogenetics, neural networks, combinatorial auctions, game theory, and computational complexity. This self-contained book grew out of several courses given at Technische Universitat Berlin and elsewhere, and the main prerequisite for the reader is a basic knowledge in polytope theory. It contains a good number of exercises, many examples, beautiful figures, as well as explicit tools for computations using polymake.
Graduate students and researchers interested in combinatorial, polyhedral, and optimization aspects (as opposed to algebraic geometry aspects) of tropical geometry.
Graduate Studies in Mathematics, Volume: 219
2021; 398 pp; Hardcover
MSC: Primary 14; 52; 90;
Print ISBN: 978-1-4704-6653-4
Product Code: GSM/219
Not yet published
Expected publication date January 29, 2022
Part of Institute of Mathematical Statistics Textbooks
DATE PUBLISHED: October 2021
FORMAT: HardbackISBN: 9781108415323
Applications of queueing network models have multiplied in the last generation, including scheduling of large manufacturing systems, control of patient flow in health systems, load balancing in cloud computing, and matching in ride sharing. These problems are too large and complex for exact solution, but their scale allows approximation. This book is the first comprehensive treatment of fluid scaling, diffusion scaling, and many-server scaling in a single text presented at a level suitable for graduate students. Fluid scaling is used to verify stability, in particular treating max weight policies, and to study optimal control of transient queueing networks. Diffusion scaling is used to control systems in balanced heavy traffic, by solving for optimal scheduling, admission control, and routing in Brownian networks. Many-server scaling is studied in the quality and efficiency driven Halfin?Whitt regime and applied to load balancing in the supermarket model and to bipartite matching in ride-sharing applications.
80 figures and more than 300 challenging exercises
Extensive solutions manual for most exercises
Consolidates current research in the field and an overview of three key approaches in one text
Product details
DATE PUBLISHED: October 2021
FORMAT: Hardback
ISBN: 9781108415323
DIMENSIONS: 235 x 158 x 30 mm
WEIGHT: 0.8kg
Part of London Mathematical Society Lecture Note Series
This volume contains eight research papers inspired by the 2019 'Equivariant Topology and Derived Algebra' conference, held at the Norwegian University of Science and Technology, Trondheim in honour of Professor J. P. C. Greenlees' 60th birthday. These papers, written by experts in the field, are intended to introduce complex topics from equivariant topology and derived algebra while also presenting novel research. As such this book is suitable for new researchers in the area and provides an excellent reference for established researchers. The inter-connected topics of the volume include: algebraic models for rational equivariant spectra; dualities and fracture theorems in chromatic homotopy theory; duality and stratification in tensor triangulated geometry; Mackey functors, Tambara functors and connections to axiomatic representation theory; homotopy limits and monoidal Bousfield localization of model categories.
PUBLICATION PLANNED FOR: December 202
1FORMAT: Paperback
ISBN: 9781108931946
LENGTH: 356 pages
DIMENSIONS: 229 x 152 x 20 mm
WEIGHT: 0.53kg
The continued and dramatic rise in the size of data sets has meant that new methods are required to model and analyze them. This timely account introduces topological data analysis (TDA), a method for modeling data by geometric objects, namely graphs and their higher-dimensional versions: simplicial complexes. The authors outline the necessary background material on topology and data philosophy for newcomers, while more complex concepts are highlighted for advanced learners. The book covers all the main TDA techniques, including persistent homology, cohomology, and Mapper. The final section focuses on the diverse applications of TDA, examining a number of case studies drawn from monitoring the progression of infectious diseases to the study of motion capture data. Mathematicians moving into data science, as well as data scientists or computer scientists seeking to understand this new area, will appreciate this self-contained resource which explains the underlying technology and how it can be used.
Introduces the basic theory assuming as little prior knowledge as possible
Provides many extensive examples of topological data analysis in use
Covers all the main topological data analysis techniques
Product details
PUBLICATION PLANNED FOR: January 2022
FORMAT: Hardback
ISBN: 9781108838658
DIMENSIONS: 244 x 170 mm