Series: Cornerstones
2019, X, 229 p. 27 illus., 20 illus. in color.
Hardcover
9783030165130
Includes a new chapter that provides an in-depth exploration of CauchyRiemann geometry
Uses the concept of orthogonality to unify various mathematical topics
Includes accessible content designed to lead students from undergraduate to
research-level mathematics
This textbook provides a coherent, integrated look at various topics from undergraduate
analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier
transform on the real line, and then turns to the heart of the book, geometric considerations.
This chapter includes complex differential forms, geometric inequalities from one and several
complex variables, and includes some of the author's original results. The concept of
orthogonality weaves the material into a coherent whole. This textbook will be a useful
resource for upper-undergraduate students who intend to continue with mathematics, graduate
students interested in analysis, and researchers interested in some basic aspects of CauchyRiemann
(CR) geometry. The inclusion of several hundred exercises makes this book suitable
for a capstone undergraduate Honors class. This second edition contains a significant amount
of new material, including a new chapter dedicated to the CR geometry of the unit sphere. This
chapter builds upon the first edition by presenting recent results about groups associated with
CR sphere maps. From reviews of the first edition: The present book developed from the
teaching experiences of the author in several honors courses. …. All the topics are motivated
very nicely, and there are many exercises, which make the book ideal for a first-year graduate
course on the subject. …. The style is concise, always very neat, and proofs are given with full
details. Hence, I certainly suggest this nice textbook to anyone interested in the subject, even
for self-study. Fabio Nicola, Politecnico di Torino, Mathematical Reviews D’Angelo has written an
eminently readable book, including excellent explanations of pretty nasty stuff for even the
more gifted upper division players .... It certainly succeeds in hooking the present browser: I
like this book a great deal. Michael Berg, Loyola Marymount University, Mathematical
Association of America
Series: Compact Textbooks in Mathematics
1st ed. 2019, XV, 264 p. 27 illus., 2 illus. in color.
Softcover 9783030147679
Provides students with an accessible overview of the mathematical concepts
central to voting systems
Allows readers to engage with the material in a variety of ways, with chapters
that can be approached in any order
Includes a chapter on the mathematics of apportionment, a topic not always
covered in adequate detail
This textbook contains a rigorous exposition of the mathematical foundations of two of the
most important topics in politics and economics: voting and apportionment, at the level of
upper undergraduate and beginning graduate students. It stands out among comparable
books by providing, in one volume, an extensive and mathematically rigorous treatment of
these two topics. The text’s three chapters cover social choice, yes-no voting, and
apportionment, respectively, and can be covered in any order, allowing teachers ample
flexibility. Each chapter begins with an elementary introduction and several examples to
motivate the concepts and to gradually lead to more advanced material. Landmark theorems
are presented with detailed and streamlined proofs; those requiring more complex proofs, such
as Arrow’s theorems on dictatorship, Gibbard’s theorem on oligarchy, and Gardenfors’ theorem
on manipulation, are broken down into propositions and lemmas in order to make them easier
to grasp. Simple and intuitive notations are emphasized over non-standard, overly complicated
symbols. Additionally, each chapter ends with exercises that vary from computational to “prove
or disprove” types. The Mathematics of Voting and Apportionment will be particularly wellsuited
for a course in the mathematics of voting and apportionment for upper-level
undergraduate and beginning graduate students in economics, political science, or philosophy,
or for an elective course for math majors. In addition, this book will be a suitable read for to
any curious mathematician looking for an exposition to these unpublicized mathematical
applications. No political science prerequisites are needed.
Series: Association for Women in Mathematics Series
1st ed. 2019, VIII, 160 p. 20 illus., 3 illus. in color.
Hardcover
9783030194772
These proceedings collect several number theory articles, most of which were written in
connection to the workshop WIN4: Women in Numbers, held in August 2017, at the Banff
International Research Station (BIRS) in Banff, Alberta, Canada. It collects papers disseminating
research outcomes from collaborations initiated during the workshop as well as other original
research contributions involving participants of the WIN workshops. The workshop and this
volume are part of the WIN network, aimed at highlighting the research of women and gender
minorities in number theory as well as increasing their participation and boosting their
potential collaborations in number theory and related fields
Series: SpringerBriefs in Mathematics
1st ed. 2019, VIII, 96 p.
Softcover 9783030194543
Presents current approximation methods to encourage new research
Highlights several methods to determine moments
Features detailed examples
This book is a valuable resource for Graduate students and researchers interested in current
techniques and methods within the theory of moments in linear positive operators and
approximation theory. Moments are essential to the convergence of a sequence of linear
positive operators. Several methods are examined to determine moments including direct
calculations, recurrence relations, and the application of hypergeometric series. A collection of
operators in the theory of approximation are investigated through their moments and a variety
of results are surveyed with fundamental theories and recent developments. Detailed examples
are included to assist readers understand vital theories and potential applications.
Series: SpringerBriefs in Mathematics
1st ed. 2019, IX, 118 p.
Softcover 9783030181550
First book devoted to endotrivial modules
Collects 50 years of results and numerous examples
Includes background material and up-to-date references
This is an in-depth report on the endotrivial modules, an important class of modular
representations for finite groups. Following the historical development of the theory, the book
starts with a review of the necessary definitions and some key examples. The main results
obtained using traditional techniques are then presented, followed by more recent results such
as the work of Grodal inspired by algebraic topology. In the last part of the book original
methods are applied to obtain the group of endotrivial modules for certain very important
groups. An accessible reference collecting half a century of research on endotrivial modules,
this book will be of interest to researchers in algebra.
Series: Undergraduate Texts in Mathematics
1st ed. 2019, X, 232 p. 91 illus., 9 illus. in color.
Hardcover 9783030183073
Equips readers with the fundamentals of enumerative combinatorics with an
emphasis on generating function techniques
Promotes an engaging learning experience by utilizing Inquiry-Based
Learning (IBL)
Offers an accessible entry-point to enumerative combinatorics that builds
from minimal prerequisites to a selection of advanced topics
This textbook offers the opportunity to create a uniquely engaging combinatorics classroom by
embracing Inquiry-Based Learning (IBL) techniques. Readers are provided with a carefully
chosen progression of theorems to prove and problems to actively solve. Students will feel a
sense of accomplishment as their collective inquiry traces a path from the basics to important
generating function techniques. Beginning with an exploration of permutations and
combinations that culminates in the Binomial Theorem, the text goes on to guide the study of
ordinary and exponential generating functions. These tools underpin the in-depth study of
Eulerian, Catalan, and Narayana numbers that follows, and a selection of advanced topics that
includes applications to probability and number theory. Throughout, the theory unfolds via over
150 carefully selected problems for students to solve, many of which connect to state-of-theart
research. Inquiry-Based Enumerative Combinatorics is ideal for lower-division undergraduate
students majoring in math or computer science, as there are no formal mathematics
prerequisites. Because it includes many connections to recent research, students of any level
who are interested in combinatorics will also find this a valuable resource
Series: Interdisciplinary Applied Mathematics
1st ed. 2019, VIII, 412 p. 98 illus. in color.
Hardcover 9783030183189
Includes a companion set of interactive software for illuminating concepts and results
Consolidates many important concepts from a variety of sources
Includes an extensive mathematical primer on all related mathematics
This book builds inviscid flow analysis from an undergraduate-level treatment of potential flow
to the level required for research. The tools covered in this book allow the reader to develop
physics-based mathematical models for a variety of flows, including attached and separated
flows past wings, fins, and blades of various shapes undergoing arbitrary motions. The book
covers all of the ingredients of these models: the solution of potential flows about arbitrary
body shapes in two- and three-dimensional contexts, with a particular focus on conformal
mapping in the plane; the decomposition of the flow into contributions from ambient vorticity
and body motion; generalized edge conditions, of which the Kutta condition is a special case;
and the calculation of force and moment, with extensive treatments of added mass and the
influence of fluid vorticity. The book also contains an extensive primer with all of the necessary
mathematical tools. The concepts are demonstrated on several example problems, both
classical and modern.