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Presents recent developments in the areas of differential
equations, dynamical systems, and control of finke and infinite
dimensional systems. Focuses on current trends in differential
equations and dynamical system research-from Darameterdependence of
solutions to robui control laws for inflnite dimensional systems.
Since abstract algebra is so important to the study of advanced
mathematics, it is critical that students have a firm grasp of its
principles and underlying theories before moving on to further
study. To accomplish this, they require a concise, accessible,
user-friendly textbook that is both challenging and stimulating. A
First Graduate Course in Abstract Algebra is just such a textbook.
Divided into two sections, this book covers both the standard
topics (groups, modules, rings, and vector spaces) associated with
abstract algebra and more advanced topics such as Galois fields,
noncommutative rings, group extensions, and Abelian groups. The
author includes review material where needed instead of in a single
chapter, giving convenient access with minimal page turning. He
also provides ample examples, exercises, and problem sets to
reinforce the material. This book illustrates the theory of
finitely generated modules over principal ideal domains, discusses
tensor products, and demonstrates the development of determinants.
It also covers Sylow theory and Jordan canonical form. A First
Graduate Course in Abstract Algebra is ideal for a two-semester
course, providing enough examples, problems, and exercises for a
deep understanding. Each of the final three chapters is logically
independent and can be covered in any order, perfect for a
customized syllabus.
"Presents the structure of algebras appearing in representation
theory of groups and algebras with general ring theoretic methods
related to representation theory. Covers affine algebraic sets and
the nullstellensatz, polynomial and rational functions, projective
algebraic sets. Groebner basis, dimension of algebraic sets, local
theory, curves and elliptic curves, and more."
Since abstract algebra is so important to the study of advanced
mathematics, it is critical that students have a firm grasp of its
principles and underlying theories before moving on to further
study. To accomplish this, they require a concise, accessible,
user-friendly textbook that is both challenging and stimulating. A
First Graduate Course in Abstract Algebra is just such a textbook.
Divided into two sections, this book covers both the standard
topics (groups, modules, rings, and vector spaces) associated with
abstract algebra and more advanced topics such as Galois fields,
noncommutative rings, group extensions, and Abelian groups. The
author includes review material where needed instead of in a single
chapter, giving convenient access with minimal page turning. He
also provides ample examples, exercises, and problem sets to
reinforce the material. This book illustrates the theory of
finitely generated modules over principal ideal domains, discusses
tensor products, and demonstrates the development of determinants.
It also covers Sylow theory and Jordan canonical form. A First
Graduate Course in Abstract Algebra is ideal for a two-semester
course, providing enough examples, problems, and exercises for a
deep understanding. Each of the final three chapters is logically
independent and can be covered in any order, perfect for a
customized syllabus.
Significantly revised and expanded, this authoritative
reference/text comprehensively describes concepts in measure
theory, classical integration, and generalized Riemann integration
of both scalar and vector types-providing a complete and detailed
review of every aspect of measure and integration theory using
valuable examples, exercises, and applications. With more than 170
references for further investigation of the subject, this Second
Edition -provides more than 60 pages of new information, as well as
a new chapter on nonabsolute integrals -contains extended
discussions on the four basic results of Banach spaces -presents an
in-depth analysis of the classical integrations with many
applications, including integration of nonmeasurable functions,
Lebesgue spaces, and their properties -details the basic properties
and extensions of the Lebesgue-Caratheodory measure theory, as well
as the structure and convergence of real measurable functions
-covers the Stone isomorphism theorem, the lifting theorem, the
Daniell method of integration, and capacity theory Measure Theory
and Integration, Second Edition is a valuable reference for all
pure and applied mathematicians, statisticians, and mathematical
analysts, and an outstanding text for all graduate students in
these disciplines.
Employing a closed set-theoretic foundation for interval
computations, Global Optimization Using Interval Analysis
simplifies algorithm construction and increases generality of
interval arithmetic. This Second Edition contains an up-to-date
discussion of interval methods for solving systems of nonlinear
equations and global optimization problems. It expands and improves
various aspects of its forerunner and features significant new
discussions, such as those on the use of consistency methods to
enhance algorithm performance. Provided algorithms are guaranteed
to find and bound all solutions to these problems despite bounded
errors in data, in approximations, and from use of rounded
arithmetic.
"Contains proceedings of Varenna 2000, the international conference
on theory and numerical methods of the navier-Stokes equations,
held in Villa Monastero in Varenna, Lecco, Italy, surveying a wide
range of topics in fluid mechanics, including compressible,
incompressible, and non-newtonian fluids, the free boundary
problem, and hydrodynamic potential theory."
"Presents the structure of algebras appearing in representation
theory of groups and algebras with general ring theoretic methods
related to representation theory. Covers affine algebraic sets and
the nullstellensatz, polynomial and rational functions, projective
algebraic sets. Groebner basis, dimension of algebraic sets, local
theory, curves and elliptic curves, and more."
Presents the proceedings of the Second International Conference on
Commutative Ring Theory in Fes, Morocco. The text details
developments in commutative algebra, highlighting the theory of
rings and ideals. It explores commutative algebra's connections
with and applications to topological algebra and algebraic
geometry.
A comprehensive presentation of abstract algebra and an in-depth
treatment of the applications of algebraic techniques and the
relationship of algebra to other disciplines, such as number
theory, combinatorics, geometry, topology, differential equations,
and Markov chains.
A textbook for either a semester or year course for graduate
students of mathematics who have had at least one course in
topology. Introduces continuum theory through a combination of
classical and modern techniques. Annotation copyright Book News,
Inc. Portland, Or.
A textbook for a one-semester course in linear algebra for graduate
or upper-level undergraduate students of mathematics and
engineering. Employs a matrix perspective, and emphasizes training
in definitions, theorems, and proofs. Annotation copyright Book
News, Inc. Portland, Or.
"Contains proceedings of Varenna 2000, the international conference
on theory and numerical methods of the navier-Stokes equations,
held in Villa Monastero in Varenna, Lecco, Italy, surveying a wide
range of topics in fluid mechanics, including compressible,
incompressible, and non-newtonian fluids, the free boundary
problem, and hydrodynamic potential theory."
Contains numerous examples, in-depth case studies, end-of-chapter
prob This reference/text illuminates the most important results of
the Lyap Second Edition adds many detailed case studies Presenting
in detail fo r the first time in book form a basic framework for
the qualitative an alysis of general hybrid dynamical systems
involving a notion of gener alized time equations; and presents new
and expanded material on the s tability analysis of hybrid
dynamical systems and dynamical systems wi th discontinuous
dynamics.
Presents hyperspace fundamentals, offering a basic overview and a
foundation for further study. Topics include the topology for
hyperspaces, examples of geometric models for hyperspaces, 2x and
C(X) for Peano continua X, arcs in hyperspaces, the shape and
contractability of hyperspaces, hyperspaces and the fixed point
property, and Whitney maps. The text contains examples and
exercises throughout, and provides proofs for most results.
This book presents functional analysis over arbitrary valued fields
and investigates normed spaces and algebras over fields with
valuation, with attention given to the case when the norm and the
valuation are nonarchimedean. It considers vector spaces over
fields with nonarchimedean valuation.
In one exceptional volume, Abstract Algebra covers subject matter
typically taught over the course of two or three years and offers a
self-contained presentation, detailed definitions, and excellent
chapter-matched exercises to smooth the trajectory of learning
algebra from zero to one. Field-tested through advance use in the
ERASMUS educational project in Europe, this ambitious,
comprehensive book includes an original treatment of representation
of finite groups that avoids the use of semisimple ring theory and
explains sets, maps, posets, lattices, and other essentials of the
algebraic language; Peano's axioms and cardinality; groupoids,
semigroups, monoids, groups; and normal subgroups.
A presentation of results in p-adic Banach spaces, spaces over
fields with an infinite rank valuation, Frechet (and locally
convex) spaces with Schauder bases, function spaces, p-adic
harmonic analysis, and related areas. It showcases research results
in functional analysis over nonarchimedean valued complete fields.
It explores spaces of continuous functions, isometries, Banach Hopf
algebras, summability methods, fractional differentiation over
local fields, and adelic formulas for gamma- and beta-functions in
algebraic number theory.
Based largely on state space models, this text/reference utilizes
fundamental linear algebra and operator techniques to develop
classical and modern results in linear systems analysis and control
design. It presents stability and performance results for linear
systems, provides a geometric perspective on controllability and
observability, and develops state space realizations of transfer
functions. It also studies stabilizability and detectability,
constructs state feedback controllers and asymptotic state
estimators, covers the linear quadratic regulator problem in
detail, introduces H-infinity control, and presents results on
Hamiltonian matrices and Riccati equations.
Integrates fundamental techniques from algebraic geometry,
localization theory and ring theory, and demonstrates how each
topic is enhanced by interaction with others, providing new results
within a common framework. Technical conclusions are presented and
illustrated with concrete examples.
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