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This is a college algebra-level textbook
written to provide the kind of mathematical knowledge and experiences
that students will need for courses in other fields, such as biology,
chemistry, business, finance, economics, and other areas that are
heavily dependent on data either from laboratory experiments or from
other studies. The focus is on the fundamental mathematical concepts
and the realistic problem-solving via mathematical modeling rather
than the development of algebraic skills that might be needed in
calculus.
Functions, Data, and Models presents college
algebra in a way that differs from almost all college algebra books
available today. Rather than going over material covered in high
school courses the Gordons teach something new. Students are given an
introduction to data analysis and mathematical modeling presented at a
level that students with limited algebraic skills can understand. The
book contains a rich set of exercises, many of which use real
data. Also included are thought experiments or what if questions that
are meant to stretch the student's mathematical thinking.
… On initial viewing, “Functions, Data and Models” may seem like a typical textbook, with all the usual key parts, including appendixes and answers to selected problems in the back of the book. However, on closer examination, readers will see and understand how the eight-chapter work differs from classic algebra books. The detailed preface includes messages for the student, messages for the instructor, and information on the book's philosophy. … The book would be a great resource for any algebra course. Highly recommended.
-- K.D. Holton, CHOICE Magazine
This textbook certainly sets the hook early when authors explain in the preface that the book's philosophy is to allow students to focus on mathematical ideas, not mathematical calculations. … As the authors point out in the introduction to this text, it contains enough material (in both depth and variety) to cover two semesters' worth of study. On the other hand, the interested instructor could easily design a syllabus covering a limited number of topics from the book to address the needs of a semester-long course. I highly recommend this text to instructors who seek to cultivate creativity and critical thinking in their college-algebra-level students
-- Hilary Fletcher, Mathematics and Computer Education
Functional analysis studies the algebraic, geometric, and topological
structures of spaces and operators that underlie many classical
problems. Individual functions satisfying specific equations are
replaced by classes of functions and transforms that are determined by
the particular problems at hand.
This book presents the basic facts of linear functional analysis as
related to fundamental aspects of mathematical analysis and their
applications. The exposition avoids unnecessary terminology and
generality and focuses on showing how the knowledge of these
structures clarifies what is essential in analytic problems.
The material in the first part of the book can be used for an introductory
course on functional analysis, with an emphasis on the role of duality.
The second part introduces distributions and Sobolev spaces and their
applications. Convolution and the Fourier transform are shown to be useful
tools for the study of partial differential equations. Fundamental
solutions and Green's functions are considered and the theory is
illustrated with several applications. In the last chapters, the Gelfand
transform for Banach algebras is used to present the spectral theory of
bounded and unbounded operators, which is then used in an introduction to
the basic axioms of quantum mechanics.
The presentation is intended to be accessible to readers whose
backgrounds include basic linear algebra, integration theory, and
general topology. Almost 240 exercises will help the reader in better
understanding the concepts employed.
This book is published in cooperation with Real Sociedad Matemática Española (RSME)
Graduate students interested in functional analysis, PDEs, analysis.
Overall, this is an interesting and well-written book, covering a lot of material. I found it very readable... The discussion is well motivated mathematically (there are few applications to other areas) and full details of proofs are given, so it is fairly self-contained.
-- Bryan P. Rynne, Mathematical Reviews
In 2007 Terry Tao began a mathematical blog to
cover a variety of topics, ranging from his own research and other
recent developments in mathematics, to lecture notes for his classes,
to nontechnical puzzles and expository articles. The first two years
of the blog have already been published by the American Mathematical
Society. The posts from the third year are being published in two
volumes. The present volume consists of a second course in real
analysis, together with related material from the blog.
The real analysis course assumes some familiarity with general
measure theory, as well as fundamental notions from undergraduate
analysis. The text then covers more advanced topics in measure
theory, notably the Lebesgue-Radon-Nikodym theorem and the Riesz
representation theorem, topics in functional analysis, such as Hilbert
spaces and Banach spaces, and the study of spaces of distributions and
key function spaces, including Lebesgue's \(L^p\) spaces and
Sobolev spaces. There is also a discussion of the general theory of
the Fourier transform.
The second part of the book addresses a number of auxiliary topics, such
as Zorn's lemma, the Carathéodory extension theorem, and the
Banach-Tarski paradox. Tao also discusses the epsilon regularisation
argument—a fundamental trick from soft analysis, from which the book
gets its title. Taken together, the book presents more than enough
material for a second graduate course in real analysis.
The second volume consists of technical and expository articles on
a variety of topics and can be read independently.
Graduate students interested in analysis.
It is a nice contribution to the current literature by one of the leading mathematicians in the world and can only be warmly recommended to everybody interested in these topics.
-- Monatshafte für Mathematik
Topology, the foundation of modern analysis, arose historically as a way to organize ideas like compactness and connectedness which had emerged from analysis. Similarly, recent work in dynamical systems theory has both highlighted certain topics in the pre-existing subject of topological dynamics (such as the construction of Lyapunov functions and various notions of stability) and also generated new concepts and results (such as attractors, chain recurrence, and basic sets). This book collects these results, both old and new, and organizes them into a natural foundation for all aspects of dynamical systems theory. No existing book is comparable in content or scope. Requiring background in point-set topology and some degree of “mathematical sophistication”, Akin's book serves as an excellent textbook for a graduate course in dynamical systems theory. In addition, Akin's reorganization of previously scattered results makes this book of interest to mathematicians and other researchers who use dynamical systems in their work.
Graduate students and research mathematicians interested in dynamical systems.
No other single text has heretofore presented such a unified treatment of these topological ideas at this level of generality.
-- Mathematical Reviews
This volume is the companion volume to
Distributed worldwide by the American Mathematical Society.
Graduate students, research mathematicians, educators, and mathematical physicists interested in functional analysis, operator algebras, and applications.
Organization (exercise groupings), extra index of volumes III and IV and the special bibliography will be very helpful in finding material for seminar or private projects.
-- Monatshefte für Mathematik
This volume, a joint publication with the American Institute of Physics, contains the proceedings of a symposium honoring the memory of Josiah Willard Gibbs, one of the giants of theoretical physics. Three articles provide perspectives on Gibbs, the man, and on the place his work occupies in the history of science. There are also contributions from leading scientists on statistical mechanics, thermodynamics, geophysics, number theory, general relativity, and economics.
This book shows readers how to begin using &latex; to create
high-quality documents. It also serves as a reference for all &latex;
users. In this completely revised edition, the authors cover the
&latex2e; standard and offer more details,
examples, exercises, tips, and tricks. They go beyond the core
installation to describe the key contributed packages that have become
essential to &latex; processing.
In the book, readers will find:
Graduate students and research mathematicians interested in &latex;.
This volume is the companion volume to
Distributed worldwide by the American Mathematical Society.
Graduate students, research mathematicians, educators, and mathematical physicists interested in functional analysis, operator algebras, and applications.
A fitting companion to the existing volumes and a welcome addition to the literature on functional analysis. The exercises … were carefully designed by the authors to illustrate the results of the text and to expand its scope … the authors' solutions … are models of clarity and efficiency, reflecting their vast experience and insight into the subject.
-- Mathematical Reviews
The organization (exercise groupings), extra index of Volumes III and IV and the special bibliography will be very helpful in finding material for seminar or private projects.
-- Monatshefte für Mathematik
The Yangians and twisted Yangians are remarkable associative algebras
taking their origins from the work of St. Petersburg's school of
mathematical physics in the 1980s. The general definitions were given
in subsequent work of Drinfeld and Olshansky, and these algebras have
since found numerous applications in and connections with mathematical
physics, geometry, representation theory, and combinatorics.
The book is an introduction to the theory of Yangians and twisted
Yangians, with a particular emphasis on the relationship with the
classical matrix Lie algebras. A special algebraic technique, the
\(R\)-matrix formalism, is developed and used as the main
instrument for describing the structure of Yangians. A detailed
exposition of the highest weight theory and the classification
theorems for finite-dimensional irreducible representations of these
algebras is given.
The Yangian perspective provides a unifying picture of several families
of Casimir elements for the classical Lie algebras and relations between
these families. The Yangian symmetries play a key role in explicit
constructions of all finite-dimensional irreducible representations of
the orthogonal and symplectic Lie algebras via weight bases of
Gelfand-Tsetlin type.
Graduate students and research mathematicians interested in representation theory and quantum groups.
This book is well written and will be indispensable for anyone working on Yangians. It will also be of interest for the new point of view it brings to branching rules. Some versions of the theorems proved hold for other algebras, in particular quantized enveloping algebras of finite and affine type. Each chapter concludes with examples of these versions, and bibliographic notes linking the chapter to the extensive bibliography at the end of the book.
-- Mathematical Reviews