February New Math books
Infinite Powers: How Calculus Reveals the Secrets of the Universe
Infinite Powers: How Calculus Reveals the Secrets of the Universe: QA303.2 .S78 2019
Author(s): Steven Strogatz
Boston : Houghton Mifflin Harcourt 
NEW YORK TIMES BESTSELLER “Marvelous . . . an array of witty and astonishing stories . . . to illuminate how calculus has helped bring into being our contemporary world.”—The Washington Post From preeminent math personality and author of The Joy of x, a brilliant and endlessly appealing explanation of calculus – how it works and why it makes our lives immeasurably better. Without calculus, we wouldn’t have cell phones, TV, GPS, or ultrasound. We wouldn’t have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket. Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz’s brilliantly creative, down‐to‐earth history shows that calculus is not about complexity; it’s about simplicity. It harnesses an unreal number—infinity—to tackle real‐world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous. Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves (a phenomenon predicted by calculus). Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes “backwards” sometimes; how to make electricity with magnets; how to ensure your rocket doesn’t miss the moon; how to turn the tide in the fight against AIDS. As Strogatz proves, calculus is truly the language of the universe. By unveiling the principles of that language, Infinite Powers makes us marvel at the world anew.
Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers
Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers: QA3 .Z56 2020
Author(s): Robert J. Zimmer
Chicago ; University of Chicago Press 
Robert J. Zimmer is best known in mathematics for the highly influential conjectures and program that bear his name. Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers brings together some of the most significant writings by Zimmer, which lay out his program and contextualize his work over the course of his career. Zimmer’s body of work is remarkable in that it involves methods from a variety of mathematical disciplines, such as Lie theory, differential geometry, ergodic theory and dynamical systems, arithmetic groups, and topology, and at the same time offers a unifying perspective. After arriving at the University of Chicago in 1977, Zimmer extended his earlier research on ergodic group actions to prove his cocycle superrigidity theorem which proved to be a pivotal point in articulating and developing his program. Zimmer’s ideas opened the door to many others, and they continue to be actively employed in many domains related to group actions in ergodic theory, geometry, and topology. In addition to the selected papers themselves, this volume opens with a foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis, as well as a substantial introductory essay by Zimmer recounting the course of his career in mathematics. The volume closes with an afterword by Fisher on the most recent developments around the Zimmer program.
Work Smarter, Not Harder: A Framework for Math Teaching and Learning
Work Smarter, Not Harder: A Framework for Math Teaching and Learning: QA20.F67 L362 2019
Author(s): Teruni Lamberg
Lanham, Maryland : Rowman & Littlefield 
Learn how to get results in math teaching and learning by working smarter not harder! A framework for math teaching that integrates the Common Core standards of mathematical practice as a natural part of teaching is provided. This researched based framework that address the process of teaching has been tested and refined by hundreds of teachers.
Classroom-Ready Number Talks for Kindergarten, First and Second Grade Teachers: 1000 Interactive Activities and Strategies That Teach Number Sense and Math Facts
Classroom-Ready Number Talks for Kindergarten, First and Second Grade Teachers: 1000 Interactive Activities and Strategies That Teach Number Sense and Math Facts: QA135.6 .H84 2019
Author(s): Nancy Hughes
Berkeley, CA Ulysses Press 
A wide variety of ready-to-use number talks that help kindergarten through second-grade students learn math concepts in fun and easy ways Bringing the exciting teaching method of number talks into your classroom has never been easier. Simply choose from the hundreds of great ideas in this book and get going, with no extra time wasted! From activities on addition and subtraction to fractions and decimals, Classroom-Ready Number Talks for Kindergarten, First and Second Grade Teachers includes: Grade-level specific strategies Number talk how-tos Visual and numerical examples Scaffolding suggestions Common core alignments Questions to build understanding Reduce time spent lesson planning and preparing materials and enjoy more time engaging your students in learning important math concepts! These ready-to-use number talks are sure to foster a fresh and exciting learning environment in your classroom, as well as help your students increase their comprehension of numbers and mathematical principles.
Introduction to Approximate Groups
Introduction to Approximate Groups: QA174.2 .T65 2020
Author(s): Matthew C. H. Tointon
Cambridge ; Cambridge University Press 2020.
Approximate groups have shot to prominence in recent years, driven both by rapid progress in the field itself and by a varied and expanding range of applications. This text collects, for the first time in book form, the main concepts and techniques into a single, self-contained introduction. The author presents a number of recent developments in the field, including an exposition of his recent result classifying nilpotent approximate groups. The book also features a considerable amount of previously unpublished material, as well as numerous exercises and motivating examples. It closes with a substantial chapter on applications, including an exposition of Breuillard, Green and Tao's celebrated approximate-group proof of Gromov's theorem on groups of polynomial growth. Written by an author who is at the forefront of both researching and teaching this topic, this text will be useful to advanced students and to researchers working in approximate groups and related areas.
Stochastic Models for Fractional Calculus
Stochastic Models for Fractional Calculus: QA314 .M44 2019
Author(s): Mark M. Meerschaert, Alla Sikorskii, Mohsen Zayernouri
Boston, USA De Gruyter; Walter de Gruyter 
Fractional calculus is a rapidly growing field of research, at the interface between probability, differential equations, and mathematical physics. It is used to model anomalous diffusion, in which a cloud of particles spreads in a different manner than traditional diffusion. This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. In this book, we will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level, using ideas from probability. It covers basic limit theorems for random variables and random vectors with heavy tails. This includes regular variation, triangular arrays, infinitely divisible laws, random walks, and stochastic process convergence in the Skorokhod topology. The basic ideas of fractional calculus and anomalous diffusion are closely connected with heavy tail limit theorems. Heavy tails are applied in finance, insurance, physics, geophysics, cell biology, ecology, medicine, and computer engineering. The goal of this book is to prepare graduate students in probability for research in the area of fractional calculus, anomalous diffusion, and heavy tails. Many interesting problems in this area remain open. This book will guide the motivated reader to understand the essential background needed to read and unerstand current research papers, and to gain the insights and techniques needed to begin making their own contributions to this rapidly growing field.
Ordinary Differential Operators
Ordinary Differential Operators: QA329.4 .W36 2019
Author(s): Aiping Wang, Anton Zettl
Providence, Rhode Island : American Mathematical Society 
In 1910 Herman Weyl published one of the most widely quoted papers of the 20th century in Analysis, which initiated the study of singular Sturm-Liouville problems. The work on the foundations of Quantum Mechanics in the 1920s and 1930s, including the proof of the spectral theorem for unbounded self-adjoint operators in Hilbert space by von Neumann and Stone, provided some of the motivation for the study of differential operators in Hilbert space with particular emphasis on self-adjoint operators and their spectrum. Since then the topic developed in several directions and many results and applications have been obtained. In this monograph the authors summarize some of these directions discussing self-adjoint, symmetric, and dissipative operators in Hilbert and Symplectic Geometry spaces. Part I of the book covers the theory of differential and quasi-differential expressions and equations, existence and uniqueness of solutions, continuous and differentiable dependence on initial data, adjoint expressions, the Lagrange Identity, minimal and maximal operators, etc. In Part II characterizations of the symmetric, self-adjoint, and dissipative boundary conditions are established. In particular, the authors prove the long standing Deficiency Index Conjecture. In Part III the symmetric and self-adjoint characterizations are extended to two-interval problems. These problems have solutions which have jump discontinuities in the interior of the underlying interval. These jumps may be infinite at singular interior points. Part IV is devoted to the construction of the regular Green's function. The construction presented differs from the usual one as found, for example, in the classical book by Coddington and Levinson.
Fast Direct Solvers for Elliptic PDEs
Fast Direct Solvers for Elliptic PDEs: QA377 .M283365 2020
Author(s): Per-Gunnar Martinsson
Philadelphia, PA : Society for Industrial and Applied Mathematics 
Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE. This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and data-sparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques. Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with data-sparse matrices.
Where Do Numbers Come From?
Where Do Numbers Come From?: QA241 .K6697 2020
Author(s): T. W. Körner
Cambridge ; Cambridge University Press 
A clear, entertaining development of the number systems required in any course of modern mathematics.
Mathematics of Shapes and Applications
Mathematics of Shapes and Applications: QA612.7 .M355 2020
Author(s): Sergey Kushnarev, Anqi Qiu, Laurent Younes
New Jersey : World Scientific 
Understanding how a single shape can incur a complex range of transformations, while defining the same perceptually obvious figure, entails a rich and challenging collection of problems, at the interface between applied mathematics, statistics and computer science. The program on Mathematics of Shapes and Applications, was held at the Institute for Mathematical Sciences at the National University of Singapore in 2016. It provided discussions on theoretical developments and numerous applications in computer vision, object recognition and medical imaging.The analysis of shapes is an example of a mathematical problem directly connected with applications while offering deep open challenges to theoretical mathematicians. It has grown, over the past decades, into an interdisciplinary area in which researchers studying infinite-dimensional Riemannian manifolds (global analysis) interact with applied mathematicians, statisticians, computer scientists and biomedical engineers on a variety of problems involving shapes.The volume illustrates this wealth of subjects by providing new contributions on the metric structure of diffeomorphism groups and shape spaces, recent developments on deterministic and stochastic models of shape evolution, new computational methods manipulating shapes, and new statistical tools to analyze shape datasets. In addition to these contributions, applications of shape analysis to medical imaging and computational anatomy are discussed, leading, in particular, to improved understanding of the impact of cognitive diseases on the geometry of the brain.