Theta Foundation International Book Series of Mathematical Texts
Volume: 23; 2018; 204 pp; Hardcover
MSC: Primary 00; 30; 42; 46; 47;
Print ISBN: 978-606-8443-09-6
A publication of the Theta Foundation
This volume contains the proceedings of the 26th International Conference
on Operator Theory, held from June 27-July 2, 2016, in Timioara, Romania.
It consists of a careful selection of papers.
One of the higlights is an extended presentation of the heliciodal method
in harmonic analysis.
Other subjects covered include function theory on the unit disc; free holomorphic
functions; applications of Toeplitz operators; traces on ideals of operators;
geodesics of projections on Hilbert space; preserver problems; Sturm Liouville
operators; and Bratteli diagrams.
Graduate students and research mathematicians interested in operator theory.
Theta Foundation International Book Series of Mathematical Texts
Volume: 24; 2018; 186 pp; Hardcover
MSC: Primary 22;
Print ISBN: 978-606-8443-10-2
This is a modern presentation of the theory of representations of locally
compact groups. In a small number of pages, the reader can get some of
the most important theorems on this subject. Many examples are provided.
Highlights of the volume include:
(1) A generous introduction explaining the origins of group theory and
their representations, the motivation for the main problems in this theory,
and the deep connections with modern physics.
(2) A solid presentation of the theory of topological groups and of Lie groups.
(3) Two proofs of the existence of Haar measures.
(4) The detailed study of continuous representations on general locally
convex spaces, with an emphasis on unitary representations of compact groups
on Hilbert spaces.
(5) A careful presentation of induced representations on locally convex spaces and G. W. Mackey's Theorem of Imprimitivity.
About half of the results included in this volume appear for the first
time in a book, while the theory of p-induced representations on locally
convex spaces is new. To facilitate reading, several appendices present
the concepts and basic results from general topology, differential manifolds,
abstract measures and integration, topological vector spaces, Banach spaces,
Banach algebras, C-algebras, and operator theory on Hilbert spaces.
Graduate students and researchers interested in representations of locally compact groups.
Mathematical World Volume: 30
2018; 238 pp; Softcover
MSC: Primary 91;
Print ISBN: 978-1-4704-4287-3
The Mathematics of Voting and Elections: A Hands-On Approach, Second Edition,
is an inquiry-based approach to the mathematics of politics and social
choice. The aim of the book is to give readers who might not normally choose
to engage with mathematics recreationally the chance to discover some interesting
mathematical ideas from within a familiar context, and to see the applicability
of mathematics to real-world situations. Through this process, readers
should improve their critical thinking and problem solving skills, as well
as broaden their views of what mathematics really is and how it can be
used
in unexpected ways. The book was written specifically for non-mathematical
audiences and requires virtually no mathematical prerequisites beyond basic
arithmetic. At the same time, the questions included are designed to challenge
both mathematical and non-mathematical audiences alike. More than giving
the right answers, this book asks the right questions.
The book is fun to read, with examples that are not just thought-provoking,
but also entertaining. It is written in a style that is casual without
being condescending. But the discovery-based approach of the book also
forces readers to play an active role in their learning, which should lead
to a sense of ownership of the main ideas in the book. And while the book
provides answers to some of the important questions in the field of mathematical
voting theory, it also leads readers to discover new questions and ways
to approach them. In addition to making small improvements in all the chapters,
this second edition contains several new chapters. Of particular interest
might be Chapter 12 which covers a host of topics related to gerrymandering.
Undergraduate students and general readers interested in mathematical aspects of various voting procedures.
Student Mathematical Library Volume: 87
2018; 207 pp; Softcover
MSC: Primary 05; 03;
Print ISBN: 978-1-4704-4290-3
This book takes the reader on a journey through Ramsey theory, from graph
theory and combinatorics to set theory to logic and metamathematics. Written
in an informal style with few requisites, it develops two basic principles
of Ramsey theory: many combinatorial properties persist under partitions,
but to witness this persistence, one has to start with very large objects.
The interplay between those two principles not only produces beautiful
theorems but also touches the very foundations of mathematics. In the course
of this book, the reader will learn about both aspects. Among the topics
explored are Ramsey's
theorem for graphs and hypergraphs, van der Waerden's theorem on arithmetic
progressions, infinite ordinals and cardinals, fast growing functions,
logic and provability, Godel incompleteness, and the Paris-Harrington theorem.
Quoting from the book, gThere seems to be a murky abyss lurking at the
bottom of mathematics. While in many ways we cannot hope to reach solid
ground, mathematicians have built impressive ladders that let us explore
the depths of this abyss and marvel at the limits and at the power of mathematical
reasoning at the same time. Ramsey theory is one of those ladders.h
Undergraduate and graduate students and researchers interested in combinatorics and mathematical logic.
Miscellaneous Books
2018; 232 pp; Hardcover
MSC: Primary 00; 05; 11; 52; 57; 28;
Print ISBN: 978-1-4704-2931-7
Pick up this book and dive into one of eight chapters relating mathematics
to fiber arts! Amazing exposition transports any interested person on a
mathematical exploration that is rigorous enough to capture the hearts
of mathematicians. The zenith of creativity is achieved as readers are
led to knit, crochet, quilt, or sew a project specifically designed to
illuminate the mathematics through its physical realization. The beautiful
finished pieces provide a visual understanding of the mathematics that
can be shared with those who view them. If you love mathematics or fiber
arts, this book is for you!
Undergraduate and graduate students and researchers interested in mathematical themes in needlework and fiber arts (e.g. crocheting, knitting, quilting).
IAS/Park City Mathematics Series Volume: 25
2018; 325 pp; Hardcover
MSC: Primary 15; 52; 60; 62; 65; 68; 90;
Print ISBN: 978-1-4704-3575-2
A co-publication of the AMS, IAS/Park City Mathematics Institute, and Society for Industrial and Applied Mathematics
Data science is a highly interdisciplinary field, incorporating ideas from
applied mathematics, statistics, probability, and computer science, as
well as many other areas. This book gives an introduction to the mathematical
methods that form the foundations of machine learning and data science,
presented by leading experts in computer science, statistics, and applied
mathematics. Although the chapters can be read independently, they are
designed to be read together as they lay out algorithmic, statistical,
and numerical approaches in diverse but complementary ways.
This book can be used both as a text for advanced undergraduate and beginning
graduate courses, and as a survey for researchers interested in understanding
how applied mathematics broadly defined is being used in data science.
It will appeal to anyone interested in the interdisciplinary foundations
of machine learning and data science.
Graduate students and researchers interested in applied mathematics of data.
Proceedings of Symposia in Pure Mathematics Volume: 100
2018; 549 pp; Hardcover
MSC: Primary 14; 53; 81;
Print ISBN: 978-1-4704-3541-7
This volume contains the proceedings of the 2016 AMS von Neumann Symposium
on Topological Recursion and its Influence in Analysis, Geometry, and Topology,
which was held from July 4?8, 2016, at the Hilton Charlotte University
Place, Charlotte, North Carolina.
The papers contained in the volume present a snapshot of rapid and rich
developments in the emerging research field known as topological recursion.
It has its origin around 2004 in random matrix theory and also in Mirzakhani's
work on the volume of moduli spaces of hyperbolic surfaces.
Topological recursion has played a fundamental role in connecting seemingly
unrelated areas of mathematics such as matrix models, enumeration of Hurwitz
numbers and Grothendieck's dessins d'enfants, Gromov-Witten invariants,
the A-polynomials and colored polynomial invariants of knots, WKB analysis,
and quantization of Hitchin moduli spaces. In addition to establishing
these topics, the volume includes survey papers on the most recent key
accomplishments: discovery of the unexpected relation to semi-simple cohomological
field theories and a solution to the remodeling conjecture. It also provides
a glimpse into
the future research direction; for example, connections with the Airy structures, modular functors, Hurwitz-Frobenius manifolds, and ELSV-type formulas.
Graduate students and researchers interested in topological recursion and its applications in various areas of mathematics.