ISBN: 978-1-4704-5173-8
Series, Volume: AMS/MAA Textbooks, Volume 54
Published: 30 August 2019; Copyright
Year: 2019; Pages: 399; Hardcover; TEXT/54
Differential Equations
Undergraduate and graduate students interested in differential equations.
Lectures on Differential Equations provides a clear and concise presentation of differential
equations for undergraduates and beginning graduate students. There is more than
enough material here for a year-long course. In fact, the text developed from the authorfs
notes for three courses: the undergraduate introduction to ordinary differential equations, the
undergraduate course in Fourier analysis and partial differential equations, and a first graduate
course in differential equations. The first four chapters cover the classical syllabus for the
undergraduate ODE course leavened by a modern awareness of computing and qualitative
methods. The next two chapters contain a well-developed exposition of linear and nonlinear
systems with a similarly fresh approach. The final two chapters cover boundary value problems,
Fourier analysis, and the elementary theory of PDEs.
The author makes a concerted effort to use plain language and to always start from a simple
example or application. The presentation should appeal to, and be readable by, students, especially
students in engineering and science. Without being excessively theoretical, the book does
address a number of unusual topics: Masserafs theorem, Lyapunovfs inequality, the isoperimetric
inequality, numerical solutions of nonlinear boundary value problems, and more. There are
also some new approaches to standard topics including a rethought presentation of series solutions
and a nonstandard, but more intuitive, proof of the existence and uniqueness theorem.
The collection of problems is especially rich and contains many very challenging exercises.
Philip Korman is professor of mathematics at the University of Cincinnati. He is the author
of over one hundred research articles in differential equations and the monograph Global
Solution Curves for Semilinear Elliptic Equations. Korman has served on the editorial boards of
Communications on Applied Nonlinear Analysis, Electronic Journal of Differential Equations, SIAM
Review, and Differential Equations and Applications.
ISBN: 978-1-4704-4932-2
Series, Volume: Pure and Applied Undergraduate Texts, Volume 39
Published: 17 August 2019; Copyright Year: 2019;
Pages: 416; Hardcover
AMSTEXT/39
Algebra and Algebraic Geometry
Supplementary Text
Undergraduate students interested in the introduction to proofs and elementary
concepts in abstract algebra.
This book introduces students to the world of advanced mathematics using algebraic
structures as a unifying theme. Having no prerequisites beyond precalculus and an
interest in abstract reasoning, the book is suitable for students of math education, computer
science or physics who are looking for an easy-going entry into discrete mathematics, induction
and recursion, groups and symmetry, and plane geometry. In its presentation, the book
takes special care to forge linguistic and conceptual links between formal precision and underlying
intuition, tending toward the concrete, but continually aiming to extend studentsf comfort
with abstraction, experimentation, and non-trivial computation.
The main part of the book can be used as the basis for a transition-to-proofs course that balances
theory with examples, logical care with intuitive plausibility, and has sufficient informality
to be accessible to students with disparate backgrounds. For students and instructors who
wish to go further, the book also explores the Sylow theorems, classification of finitely-generated
Abelian groups, and discrete groups of Euclidean plane transformations.
ISBN: 978-1-4704-5087-8
Series, Volume: Colloquium Publications, Volume 65
Published: 10 August 2019; CopyrightYear: 2019;
Pages: 444; Hardcover; List Price: US$99; Itemcode:
COLL/65
Discrete Mathematics and Combinatorics
Supplementary Text
Graduate students and researchers interested in graph theory.
Graphs are usually represented as geometric objects drawn in the plane, consisting
of nodes and curves connecting them. The main message of this book is that such a representation
is not merely a way to visualize the graph, but an important mathematical tool. It is
obvious that this geometry is crucial in engineering, for example, if you want to understand
rigidity of frameworks and mobility of mechanisms. But even if there is no geometry directly
connected to the graph-theoretic problem, a well-chosen geometric embedding has mathematical
meaning and applications in proofs and algorithms. This book surveys a number of such
connections between graph theory and geometry: among others, rubber band representations,
coin representations, orthogonal representations, and discrete analytic functions. Applications
are given in information theory, statistical physics, graph algorithms and quantum physics.
The book is based on courses and lectures that the author has given over the last few decades
and offers readers with some knowledge of graph theory, linear algebra, and probability a thorough
introduction to this exciting new area with a large collection of illuminating examples
and exercises.
Geometric representations of graphs lead to significant insights in the study of graph properties and
their algorithmic aspects. This book is a thorough study of the subject written by the pioneer of many of
the results in the area. It is a fascinating manuscript written by a superb mathematician who is also a
fantastic expositor.
Noga Alon, Princeton University and Tel Aviv University
A beautiful book, rich in intuition, insights, and examples, from one of the masters of combinatorics,
geometry, and graph theory. This book presents old friends of graph theory in a new light and introduces
more recent developments, providing connections to many areas in combinatorics, analysis, algorithms,
and physics. Those of us who know graph theory still have much to learn from this presentation;
for those who are new to the field, the book is a wonderful gift and invitation to participate.
?Jennifer Chayes, Microsoft Research
Laszlo Lovasz is one of the most prominent experts in discrete mathematics. The book is unique and
inspiring for students and researchers as well. The author succeeded to show the wealth and beauty of
the subject.
Endre Szemeredi, Rutgers University
ISBN: 978-1-4704-5082-3
Series, Volume: Mathematical Surveys and Monographs, Volume 239
Published: 2 August 2019; Copyright Year: 2019;
Pages: 560; Hardcover;
SURV/239
Analysis
Graduate students and researchers interested in classical functional analysis.
The study of the classical Dirichlet space is one of the central topics on the intersection
of the theory of holomorphic functions and functional analysis. It was introduced
about100 years ago and continues to be an area of active current research. The theory is related
to such important themes as multipliers, reproducing kernels, and Besov spaces, among others.
The authors present the theory of the Dirichlet space and related spaces starting with classical
results and including some quite recent achievements like Dirichlet-type spaces of functions in
several complex variables and the corona problem.
The first part of this book is an introduction to the function theory and operator theory of
the classical Dirichlet space, a space of holomorphic functions on the unit disk defined by a
smoothness criterion. The Dirichlet space is also a Hilbert space with a reproducing kernel, and
is the model for the dyadic Dirichlet space, a sequence space defined on the dyadic tree. These
various viewpoints are used to study a range of topics including the Pick property, multipliers,
Carleson measures, boundary values, zero sets, interpolating sequences, the local Dirichlet integral,
shift invariant subspaces, and Hankel forms. Recurring themes include analogies, sometimes
weak and sometimes strong, with the classical Hardy space; and the analogy with the
dyadic Dirichlet space.
The final chapters of the book focus on Besov spaces of holomorphic functions on the complex
unit ball, a class of Banach spaces generalizing the Dirichlet space. Additional techniques
are developed to work with the nonisotropic complex geometry, including a useful invariant
definition of local oscillation and a sophisticated variation on the dyadic Dirichlet space.
Descriptions are obtained of multipliers, Carleson measures, interpolating sequences, and multiplier
interpolating sequences; Ý estimates are obtained to prove corona theorems.
ISBN: 978-1-4704-5086-1
Series, Volume: Mathematical Surveys and Monographs, Volume 240
Published: 2 August 2019; Copyright Year: 2019;
Pages: 299; Hardcover;
Algebra and Algebraic Geometry
Graduate students and researchers interested in algebra.
This book explores applications of Jordan theory to the theory of Lie algebras. It
begins with the general theory of nonassociative algebras and of Lie algebras and then focuses
on properties of Jordan elements of special types. Then it proceeds to the core of the book, in
which the author explains how properties of the Jordan algebra attached to a Jordan element
of a Lie algebra can be used to reveal properties of the Lie algebra itself. One of the special
features of this book is that it carefully explains Zelmanovfs seminal results on infinite-dimensional
Lie algebras from this point of view.
The book is suitable for advanced graduate students and researchers who are interested in
learning how Jordan algebras can be used as a powerful tool to understand Lie algebras,
including infinite-dimensional Lie algebras. Although the book is on an advanced and rather
specialized topic, it spends some time developing necessary introductory material, includes
exercises for the reader, and is accessible to a student who has finished their basic graduate
courses in algebra and has some familiarity with Lie algebras in an abstract algebraic setting.
ISBN: 978-1-4704-3782-4
Series, Volume: Contemporary Mathematics, Volume 733
Published: 18 August 2019; Copyright Year: 2019;
Pages: 300; Softcover;
Itemcode: CONM/733
Algebra and Algebraic Geometry
Graduate students and research mathematicians interested in functional analysis,
operator theory, SCV, interval, convex, algebraic geometry, and the history of mathematics.
This is the first of two volumes dedicated to the centennial of the distinguished
mathematician Selim Grigorievich Krein. The companion volume is Contemporary
Mathematics, Volume 734.
Krein was a major contributor to functional analysis, operator theory, partial differential equations,
fluid dynamics, and other areas, and the author of several influential monographs in
these areas. He was a prolific teacher, graduating 83 Ph.D. students. Krein also created and ran,
for many years, the annual Voronezh Winter Mathematical Schools, which significantly influenced
mathematical life in the former Soviet Union.
The articles contained in this volume are written by prominent mathematicians, former students
and colleagues of Selim Krein, as well as lecturers and participants of Voronezh Winter
Schools. They are devoted to a variety of contemporary problems in functional analysis, operator
theory, several complex variables, topological dynamics, and algebraic, convex, and integral
geometry.