Edited by Hari Bercovici: Indiana University, Bloomington,
Dumitru Gaspar: West University of Timi?oara, Romania,
Dan Timotin: Romanian Academy, Bucharest, Romania,
Florian-Horia Vasilescu: University of Lille, France

Operator Theory: Themes and Variations:
Conference Proceedings, Timioara, June 27-July 2, 2016

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.

Readership

Graduate students and research mathematicians interested in operator theory.

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Ion Colojoar: University of Bucharest, Romania,
Aurelian Gheondea: Bilkent University, Ankara, Turkey and IMAR, Bucharest, Romania

Lectures on Representations of Locally Compact Groups

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.

Readership

Graduate students and researchers interested in representations of locally compact groups.

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Jonathan K. Hodge: Grand Valley State University, Allendale, MI,
Richard E. Klima: Appalachian State University, Boone, NC

The Mathematics of Voting and Elections:
A Hands-On Approach: Second Edition

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.

Readership

Undergraduate students and general readers interested in mathematical aspects of various voting procedures.

Table of Contents

Matthew Katz: Pennsylvania State University, University Park, PA,
Jan Reimann: Pennsylvania State University, University Park, PA

An Introduction to Ramsey Theory:
Fast Functions, Infinity, and Metamathematics

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

Readership

Undergraduate and graduate students and researchers interested in combinatorics and mathematical logic.

Table of Content

Edited by Carolyn Yackel: Mercer University, Macon, GA,
sarah-marie belcastro: MathILy, Mathematical Staircase, Inc.,
Holyoke, MA and Smith College, Northampton, MA

Figuring Fibers

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!

Readership

Undergraduate and graduate students and researchers interested in mathematical themes in needlework and fiber arts (e.g. crocheting, knitting, quilting).

Table of Contents

Edited by Michael W. Mahoney: University of California, Berkeley, Berkeley, CA,
John C. Duchi: Stanford University, Stanford, CA,
Anna C. Gilbert: University of Michigan, Ann Arbor, MI

The Mathematics of Data

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.

Readership

Graduate students and researchers interested in applied mathematics of data.

Table of Contents

Edited by Chiu-Chu Melissa Liu: Columbia University, New York, NY,
Motohico Mulase: University of California, Davis, Davis, CA

Topological Recursion and its Influence in Analysis, Geometry, and Topology

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.

Readership

Graduate students and researchers interested in topological recursion and its applications in various areas of mathematics.

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