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Graph Theory presents a natural,
reader-friendly way to learn some of the essential ideas of graph
theory starting from first principles. The format is similar to the
companion text, Combinatorics: A Problem Oriented Approach also by
Daniel A. Marcus, in that it combines the features of a textbook with
those of a problem workbook. The material is presented through a
series of approximately 360 strategically placed problems with
connecting text. This is supplemented by 280 additional problems that
are intended to be used as homework assignments. Concepts of graph
theory are introduced, developed, and reinforced by working through
leading questions posed in the problems.
This problem-oriented
format is intended to promote active involvement by the reader while
always providing clear direction. This approach figures prominently on
the presentation of proofs, which become more frequent and elaborate
as the book progresses. Arguments are arranged in digestible chunks
and always appear along with concrete examples to keep the readers
firmly grounded in their motivation.
Spanning tree algorithms,
Euler paths, Hamilton paths and cycles, planar graphs, independence
and covering, connections and obstructions, and vertex and edge
colorings make up the core of the book. Hall's Theorem, the
Konig-Egervary Theorem, Dilworth's Theorem and the Hungarian algorithm
to the optional assignment problem, matrices, and latin squares are
also explored.
This work could be the basis for a very nice one-semester "transition" course in which students evolve from users of theorems to creators of proofs. With their intuitive appeal and pictorial representations, graphs may be a better basis than analysis and limits for such a transtion.
-- Choice
Reprinted edition available: TEXT/53
Graph Theory presents a natural, reader-friendly way
to learn some of the essential ideas of graph theory starting from
first principles. The format is similar to the companion text,
Combinatorics: A Problem Oriented Approach also by Daniel
A. Marcus, in that it combines the features of a textbook with those
of a problem workbook. The material is presented through a series of
approximately 360 strategically placed problems with connecting
text. This is supplemented by 280 additional problems that are
intended to be used as homework assignments. Concepts of graph theory
are introduced, developed, and reinforced by working through leading
questions posed in the problems.
This problem-oriented format is intended to promote active
involvement by the reader while always providing clear direction. This
approach figures prominently on the presentation of proofs, which
become more frequent and elaborate as the book progresses. Arguments
are arranged in digestible chunks and always appear along with
concrete examples to keep the readers firmly grounded in their
motivation.
Spanning tree algorithms, Euler paths, Hamilton paths and cycles,
planar graphs, independence and covering, connections and
obstructions, and vertex and edge colorings make up the core of the
book. Hall's Theorem, the Konig-Egervary Theorem, Dilworth's Theorem
and the Hungarian algorithm to the optional assignment problem,
matrices, and latin squares are also explored.
This work could be the basis for a very nice one-semester "transition" course in which students evolve from users of theorems to creators of proofs. With their intuitive appeal and pictorial representations, graphs may be a better basis than analysis and limits for such a transtion.
-- Choice
This is a comprehensive textbook on modern algebra written by an
internationally renowned specialist. It covers material traditionally found in
advanced undergraduate and basic graduate courses and presents it in a lucid
style. The author includes almost no technically difficult proofs, and
reflecting his point of view on mathematics, he tries wherever possible to
replace calculations and difficult deductions with conceptual proofs and to
associate geometric images to algebraic objects. The effort spent on the part
of students in absorbing these ideas will pay off when they turn to solving
problems outside of this textbook.
Another important feature is the presentation of most topics on several
levels, allowing students to move smoothly from initial acquaintance with the
subject to thorough study and a deeper understanding. Basic topics are
included, such as algebraic structures, linear algebra, polynomials, and
groups, as well as more advanced topics, such as affine and projective spaces,
tensor algebra, Galois theory, Lie groups, and associative algebras and their
representations. Some applications of linear algebra and group theory to
physics are discussed.
The book is written with extreme care and contains over 200 exercises and 70
figures. It is ideal as a textbook and also suitable for independent study for advanced
undergraduates and graduate students.
Advanced undergraduates, graduate students and research mathematicians interested in algebra.
This is a masterly textbook on basic algebra. It is, at the same time, demanding and down-to-earth, challenging and user-friendly, abstract and concrete, concise and comprehensible, and above all extremely educating, inspiring and enlightening.
-- Zentralblatt MATH
Great book! The author's teaching experience shows in every chapter.
-- E. Zelmanov, University of California, San Diego
Vinberg has written an algebra book that is excellent, both as a classroom text or for self-study. It starts with the most basic concepts and builds in orderly fashion to moderately advanced topics … Well motivated examples help the student … to master the material thoroughly, and exercises test one's growing skill in addition to covering useful auxiliary facts … years of teaching abstract algebra have enabled Vinberg to say the right thing at the right time.
-- Irving Kaplansky, MSRI
This book,
Part I is a listing of the forms by number. In this
part each form is given together with a listing of all statements
known to be equivalent to it (equivalent in set theory without the
axiom of choice). In Part II the forms are arranged by topic. In
Part III we describe the models of set theory which are used to show
non-implications between forms. Part IV, the notes section, contains
definitions, summaries of important sub-areas and proofs that are not
readily available elsewhere. Part V gives references for the
relationships between forms and Part VI is the bibliography.
Part VII is contained on the floppy disk which is enclosed in the
book. It contains a table with form numbers as row and column
headings. The entry in the table in row \(n\), column \(k\) gives the status
of the implication “form \(n\) implies form \(k\)”. Software for
easily extracting information from the table is also provided.
Features:
Mathematicians with a primary interest in set theory and who do research on the axiom of choice; philosophers interested in the role of the axiom of choice in the foundations of mathematics.
This volume is a veritable encyclopedia, produced with impeccable scholarship, surveying the vast literature of theorems whose proof requires some form of a choice principle. This is the subject matter of this monograph in which the reader can find with ease the required information, including all pertinent definitions and references to the literature. The book also contains some new results, with proofs supplied in the section of notes. All in all, the authors and the publisher are to be congratulated for having produced such an outstanding monograph.
-- Mathematical Reviews
Optical Illusions in Rome is a beautifully
written and richly illustrated guide that takes the reader on a tour
through ingenious uses of geometry to create illusory impressions of
space and grandeur in Italian Renaissance art and architecture in the
Eternal City. The book takes us to some of the most striking and
historically important uses of optical illusion and includes works of
Peruzzi, Borromini, and Pozzo. The artworks are analyzed geometrically
and placed in their historical context. The notes on visiting the art
described make the volume the perfect companion for a study trip to
Rome. A chapter on the principles of perspective geometry and a
collection of exercises make the book a wonderful resource for a
module on perspective in a geometry or art history course. The
mathematical discussion is kept at a level accessible to a reader with
a familiarity with high school geometry.
Kirsti Andersen is a distinguished historian of mathematics and
emerita faculty at Aarhus University. Her previous book, The Geometry
of an Art, is widely recognized as the definitive work on the history
of the use of perspective in European art. Viktor Blåsjö, the
translator, is a historian of mathematics on the faculty at Utrecht
University. Blåsjö has won both the Ford and Pólya prizes
for expository writing from the Mathematical Association of America.
Undergraduate and graduate students and researchers interested in art, perspective, and mathematical tourism.
Random matrix theory has many roots and many branches in mathematics,
statistics, physics, computer science, data science, numerical
analysis, biology, ecology, engineering, and operations research. This
book provides a snippet of this vast domain of study, with a
particular focus on the notations of universality and
integrability. Universality shows that many systems behave the same
way in their large scale limit, while integrability provides a route
to describe the nature of those universal limits. Many of the ten
contributed chapters address these themes, while others touch on
applications of tools and results from random matrix theory.
This book is appropriate for graduate students and researchers
interested in learning techniques and results in random matrix theory
from different perspectives and viewpoints. It also captures a moment
in the evolution of the theory, when the previous decade brought major
break-throughs, prompting exciting new directions of research.
Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute.
Graduate students and researchers interested in random matrix theory and its many applications.
This volume contains the proceedings of the
workshop on Recent Trends in Operator Theory and Applications (RTOTA
2018), held from May 3–5, 2018, at the University of Memphis, Memphis,
Tennessee.
The articles introduce topics from operator theory to graduate
students and early career researchers. Each such article provides
insightful references, selection of results with articulation to
modern research and recent advances in the area.
Topics addressed in this volume include: generalized numerical
ranges and their application to study perturbation of operators, and
connections to quantum error correction; a survey of results on
Toeplitz operators, and applications of Toeplitz operators to the
study of reproducing kernel functions; results on the 2-local
reflexivity problem of a set of operators; topics from the theory of
preservers; and recent trends on the study of quotients of tensor
product spaces and tensor operators. It also includes research
articles that present overviews of state-of-the-art techniques from
operator theory as well as applications to recent research trends and
open questions. A goal of all articles is to introduce topics within
operator theory to the general public.
Graduate students and research mathematicians interested in operator theorists, functional analysis, and geometry of Banach spaces.
Noncommutative Rings provides a cross-section of ideas, techniques, and results that give the reader an idea of that part of algebra which concerns itself with noncommutative rings. In the space of 200 pages, Herstein covers the Jacobson radical, semisimple rings, commutativity theorems, simple algebras, representations of finite groups, polynomial identities, Goldie's theorem, and the Golod–Shafarevitch theorem. Almost every practicing ring theorist has studied portions of this classic monograph.
Herstein's book is a guided tour through a gallery of masterpieces. The author's style is always elegant and his proofs always enlightening … I had a lot of pleasure when I first read this book while I was an undergraduate student attending to a course given by C. Procesi at the University of Rome. Today, I appreciate even more the author's mastery and real gift for exposition.
-- Fabio Mainardi, MAA Reviews
Topology Through Inquiry is a comprehensive introduction to
point-set, algebraic, and geometric topology, designed to support
inquiry-based learning (IBL) courses for upper-division undergraduate
or beginning graduate students. The book presents an enormous amount
of topology, allowing an instructor to choose which topics to
treat. The point-set material contains many interesting topics well
beyond the basic core, including continua and metrizability. Geometric
and algebraic topology topics include the classification of
2-manifolds, the fundamental group, covering spaces, and homology
(simplicial and singular). A unique feature of the introduction to
homology is to convey a clear geometric motivation by starting with
mod 2 coefficients.
The authors are acknowledged masters of IBL-style teaching. This
book gives students joy-filled, manageable challenges that
incrementally develop their knowledge and skills. The exposition
includes insightful framing of fruitful points of view as well as
advice on effective thinking and learning. The text presumes only a
modest level of mathematical maturity to begin, but students who work
their way through this text will grow from mathematics students into
mathematicians.
Michael Starbird is a University of Texas Distinguished Teaching
Professor of Mathematics. Among his works are two other co-authored
books in the Mathematical Association of America's (MAA) Textbook
series. Francis Su is the Benediktsson-Karwa Professor of Mathematics
at Harvey Mudd College and a past president of the MAA. Both authors
are award-winning teachers, including each having received the MAA's
Haimo Award for distinguished teaching. Starbird and Su are, jointly
and individually, on lifelong missions to make learning—of mathematics
and beyond—joyful, effective, and available to everyone. This book
invites topology students and teachers to join in the adventure.
Undergraduate and graduate students interested in topology and Inquiry Based Learning (IBL).
Combinatorics is mathematics of enumeration,
existence, construction, and optimization questions concerning finite
sets. This text focuses on the first three types of questions and
covers basic counting and existence principles, distributions,
generating functions, recurrence relations, Pólya theory,
combinatorial designs, error correcting codes, partially ordered sets,
and selected applications to graph theory including the enumeration of
trees, the chromatic polynomial, and introductory Ramsey theory. The
only prerequisites are single-variable calculus and familiarity with
sets and basic proof techniques.
The text emphasizes the brands of
thinking that are characteristic of combinatorics: bijective and
combinatorial proofs, recursive analysis, and counting problem
classification. It is flexible enough to be used for undergraduate
courses in combinatorics, second courses in discrete mathematics,
introductory graduate courses in applied mathematics programs, as well
as for independent study or reading courses. What makes this text a
guided tour are the approximately 350 reading questions spread
throughout its eight chapters. These questions provide checkpoints for
learning and prepare the reader for the end-of-section exercises of
which there are over 470. Most sections conclude with Travel Notes
that add color to the material of the section via anecdotes, open
problems, suggestions for further reading, and biographical
information about mathematicians involved in the
discoveries.
This is a well-written, reader-friendly, and self-contained undergraduate course on combinatorics, focusing on enumeration. The book includes plenty of exercises, and about half of them come with hints.
-- M. Bona, Choice Magazine
… The delineation of the topics is first rate—better than I have ever seen in any other book. … CAGT has both good breadth and great presentation; it is in fact a new standard in presentation for combinatorics, essential as a resource for any instructor, including those teaching out of a different text. For the student: If you are just starting to build a library in combinatorics, this should be your first book.
-- The UMAP Journal
… [This book] is an excellent candidate for a special topics course for mathematics majors; with the broad spectrum of applications that course can simultaneously be an advanced and a capstone course. This book would be an excellent selection for the textbook of such a course. … This book is the best candidate for a textbook in combinatorics that I have encountered.
-- Charles Ashbacher