Series: Springer Monographs in Mathematics
2015, I, 498 p. 514 illus.
Hardcover
ISBN 978-1-4939-2299-4
Due: March 14, 2015
Written by one the main contributors to the field
Goes beyond the formalism of the theory to explain the development and applications of the main ideas and results
Equips the reader with the background necessary to understand recent advances in homotopy theory and algebraic geometry
This monograph on the homotopy theory of topologized diagrams of spaces and spectra gives an expert account of a subject at the foundation of motivic homotopy theory and the theory of topological modular forms in stable homotopy theory.
Beginning with an introduction to the homotopy theory of simplicial sets and topos theory, the book covers core topics such as the unstable homotopy theory of simplicial presheaves and sheaves, localized theories, cocycles, descent theory, non-abelian cohomology, stacks, and local stable homotopy theory. A detailed treatment of the formalism of the subject is interwoven with explanations of the motivation, development, and nuances of ideas and results. The coherence of the abstract theory is elucidated through the use of widely applicable tools, such as Barr's theorem on Boolean localization, model structures on the category of simplicial presheaves on a site, and cocycle categories. A wealth of concrete examples convey the vitality and importance of the subject in topology, number theory, algebraic geometry, and algebraic K-theory.
Assuming basic knowledge of algebraic geometry and homotopy theory, Local Homotopy Theory will appeal to researchers and advanced graduate students seeking to understand and advance the applications of homotopy theory in multiple areas of mathematics and the mathematical sciences.
Preface.- 1 Introduction.- Part I Preliminaries.- 2 Homotopy theory of simplicial sets.- 3 Some topos theory.- Part II Simplicial presheaves and simplicial sheaves.- 4 Local weak equivalences.- 5 Local model structures.- 6 Cocycles.- 7 Localization theories.- Part III Sheaf cohomology theory.- 8 Homology sheaves and cohomology groups.- 9 Non-abelian cohomology.- Part IV Stable homotopy theory.- 10 Spectra and T-spectra.- 11 Symmetric T-spectra.- References.- Index.
2015, Approx. 520 p.
Softcover
ISBN 978-3-662-45170-0
Due: March 29, 2015
Revised and updated fourth edition offers a broader range of material
Offers a wide scope of methods and applications, making this a comprehensive treatment of the subject
Includes a wealth of examples and exercises?ideal for students in economics and finance
Quantlets in R and Matlab available online
Focusing on high-dimensional applications, this 4th edition presents the tools and concepts used in multivariate data analysis in a style that is also accessible for non-mathematicians and practitioners. It surveys the basic principles and emphasizes both exploratory and inferential statistics; a new chapter on Variable Selection (Lasso, SCAD and Elastic Net) has also been added. All chapters include practical exercises that highlight applications in different multivariate data analysis fields: in quantitative financial studies, where the joint dynamics of assets are observed; in medicine, where recorded observations of subjects in different locations form the basis for reliable diagnoses and medication; and in quantitative marketing, where consumersf preferences are collected in order to construct models of consumer behavior. All of these examples involve high to ultra-high dimensions and represent a number of major fields in big data analysis.
The fourth edition of this book on Applied Multivariate Statistical Analysis offers the following new features:
1. A new chapter on Variable Selection (Lasso, SCAD and Elastic Net)
2. All exercises are supplemented by R and MATLAB code that can be found on www.quantlet.de.
The practical exercises include solutions that can be found in Hardle, W. and Hlavka, Z., Multivariate Statistics: Exercises and Solutions.
I Descriptive Techniques: Comparison of Batches.- II Multivariate Random Variables: A Short Excursion into Matrix Algebra.- Moving to Higher Dimensions.- Multivariate Distributions.- Theory of the Multinormal.- Theory of Estimation.- Hypothesis Testing.- III Multivariate Techniques: Regression Models.- Variable Selection.- Decomposition of Data Matrices by Factors.- Principal Components Analysis.- Factor Analysis.- Cluster Analysis.- Discriminant Analysis.- Correspondence Analysis.- Canonical Correlation Analysis.- Multidimensional Scaling.- Conjoint Measurement Analysis.- Applications in Finance.- Computationally Intensive Techniques.- IV Appendix: Symbols and Notations.- Data.
Chapman and Hall/CRC 2014 557 pages
Series: Textbooks in Mathematics
"Krantz is a very prolific writer. He c creates excellent examples and problem sets."
Albert Boggess, Professor and Director of the School of Mathematics and Statistical Sciences, Arizona State University, Tempe, USA
Designed for a one- or two-semester undergraduate course, Differential Equations: Theory, Technique and Practice, Second Edition educates a new generation of mathematical scientists and engineers on differential equations. This edition continues to emphasize examples and mathematical modeling as well as promote analytical thinking to help students in future studies.
Improved exercise sets and examples
Reorganized material on numerical techniques
Enriched presentation of predator-prey problems
Updated material on nonlinear differential equations and dynamical systems
A new appendix that reviews linear algebra
In each chapter, lively historical notes and mathematical nuggets enhance studentsf reading experience by offering perspectives on the lives of significant contributors to the discipline. "Anatomy of an Application" sections highlight rich applications from engineering, physics, and applied science. Problems for review and discovery also give students some open-ended material for exploration and further learning.
World Scientific Series on Nonlinear Science Series A: Volume 87
This volume provides a broad introduction to nonlinear integral dynamical models and new classes of evolutionary integral equations. It may be used as an advanced textbook by postgraduate students to study integral dynamical models and their applications in machine learning, electrical and electronic engineering, operations research and image analysis.
Introduction and Overview
Volterra Models of Evolving Dynamical Systems:
Volterra Equations of the First Kind with Piecewise Continuous Kernels
Volterra Matrix Equation of the First Kind with Piecewise Continuous Kernels
Volterra Operator Equations of the First Kind with Piecewise Continuous Kernels
Generalized Solutions to the Volterra Equations with Piecewise Continuous Kernels and Sources
Nonlinear Models, Singularities and Control:
Nonlinear Hammerstein Integral Equations
Nonlinear Volterra Operator Equations with Non-invertible Operator
Nonlinear Differential Equations Near Branching Points
Convex Majorants Method in the Theory of Nonlinear Volterra Equations
Generalized Solutions to Nonlinear Volterra Equations of the First Kind
On Impulse Control of Nonlinear Dynamical Systems Based on the Volterra Series
Integral Models Applications:
The Volterra Models Applications
Suppression of Moire Patterns for Video Archive Restoration
Integral Models Applications in Electric Power Engineering
Readership: Graduate students and researchers in complex systems, mathematical modeling and machine learning.
260pp Nov 2014
ISBN: 978-981-4619-18-9 (hardcover)