"The early chapters contain the topics from linear algebra that students need to know in order to read the rest of the book. The later chapters are devoted to advanced topics, which allow students with more experience to study more intricate types of frames. Toward that end, a Student Presentation section gives detailed proofs of fairly technical results with the intention that a student could work out these proofs independently and prepare a presentation to a class or research group. The authors have also presented some stories in the Anecdotes section about how this material has motivated and influenced their students."--BOOK JACKET.

Special relativity is the basis of many fields in modern physics: particle physics, quantum field theory, high-energy astrophysics, etc. This theory is presented here by adopting a four-dimensional point of view from the start. An outstanding feature of the book is that it doesn’t restrict itself to inertial frames but considers accelerated and rotating observers. It is thus possible to treat physical effects such as the Thomas precession or the Sagnac effect in a simple yet precise manner. In the final chapters, more advanced topics like tensorial fields in spacetime, exterior calculus and relativistic hydrodynamics are addressed. In the last, brief chapter the author gives a preview of gravity and shows where it becomes incompatible with Minkowsky spacetime. Well illustrated and enriched by many historical notes, this book also presents many applications of special relativity, ranging from particle physics (accelerators, particle collisions, quark-gluon plasma) to astrophysics (relativistic jets, active galactic nuclei), and including practical applications (Sagnac gyrometers, synchrotron radiation, GPS). In addition, the book provides some mathematical developments, such as the detailed analysis of the Lorentz group and its Lie algebra. The book is suitable for students in the third year of a physics degree or on a masters course, as well as researchers and any reader interested in relativity. Thanks to the geometric approach adopted, this book should also be beneficial for the study of general relativity. “A modern presentation of special relativity must put forward its essential structures, before illustrating them using concrete applications to specific dynamical problems. Such is the challenge (so successfully met!) of the beautiful book by Éric Gourgoulhon.” (excerpt from the Foreword by Thibault Damour)

Hilbert space frames have long served as a valuable tool for signal and image processing due to their resilience to additive noise, quantization, and erasures, as well as their ability to capture valuable signal characteristics. More recently, finite frame theory has grown into an important research topic in its own right, with a myriad of applications to pure and applied mathematics, engineering, computer science, and other areas. The number of research publications, conferences, and workshops on this topic has increased dramatically over the past few years, but no survey paper or monograph has yet appeared on the subject. Edited by two of the leading experts in the field, Finite Frames aims to fill this void in the literature by providing a comprehensive, systematic study of finite frame theory and applications. With carefully selected contributions written by highly experienced researchers, it covers topics including: * Finite Frame Constructions; * Optimal Erasure Resilient Frames; * Quantization of Finite Frames; * Finite Frames and Compressed Sensing; * Group and Gabor Frames; * Fusion Frames. Despite the variety of its chapters' source and content, the book's notation and terminology are unified throughout and provide a definitive picture of the current state of frame theory. With a broad range of applications and a clear, full presentation, this book is a highly valuable resource for graduate students and researchers across disciplines such as applied harmonic analysis, electrical engineering, quantum computing, medicine, and more. It is designed to be used as a supplemental textbook, self-study guide, or reference book.

When this volume was first published, plastic theory was the most modern method of structural analysis, and it made possible the direct design of steel frames in a way not available with only elastic methods. It is now recognized that this theory is also fundamental to structural design in materials such as reinforced concrete and aluminium. This is the first volume of a two-volume work by Professors Baker and Heyman that expounds and illustrates the methods of plastic design. Volume 1 gives the elements of the theory and covers the needs of most undergraduates and designers. A special feature of this work is the large number of exercises (140 in all) with answers. Volume 2 deals with advanced topics of theoretical analysis and practical design. The examples and the methods presented herein are extremely valuable to the engineer. The quality of the writing makes Professors Baker and Heyman's book a pleasure to read. Lord Baker (Sir John Fleetwood Baker, 1901-1985) was Professor of Mechanical Sciences and Head of the Department of Engineering at the University of Cambridge from 1943 to 1968. He was a Fellow of the Royal Society. Baker's pioneering research led to the development of the plastic theory of design, originally used for steel frames but now recognized as being valid for many structural materials, such as aluminium and reinforced concrete. Additionally, Baker was responsible for many curriculum innovations at the university and was the author of The Steel Skeleton, a two-volume work. Jacques Heyman is the former Head of the Department of Engineering at the University of Cambridge and the author of ten books, including The Stone Skeleton, Elements of the Theory of Structures, Structural Analysis: A Historical Approach, Elements of Stress Analysis, and the two-volume set Plastic Design of Frames: Volume 1. Fundamentals with Lord Baker and Volume 2. Applications. He is a Fellow of the Society of Antiquaries, the Institution of Civil Engineers, and the Royal Academy of Engineering. He acted as a consulting engineer for a number of English cathedrals and as a member of the Architectural Advisory Panel for Westminster Abbey and of the Cathedrals Fabric Commission for England, and he has served on many British standards committees. The Stone Skeleton won the Choice Outstanding Academic Books Award in 1996.

This volume provides accessible and self-contained research problems designed for undergraduate student projects, and simultaneously promotes the development of sustainable undergraduate research programs. The chapters in this work span a variety of topical areas of pure and applied mathematics and mathematics education. Each chapter gives a self-contained introduction on a research topic with an emphasis on the specific tools and knowledge needed to create and maintain fruitful research programs for undergraduates. Some of the topics discussed include:• Disease modeling• Tropical curves and surfaces• Numerical semigroups• Mathematics EducationThis volume will primarily appeal to undergraduate students interested in pursuing research projects and faculty members seeking to mentor them. It may also aid students and faculty participating in independent studies and capstone projects.

This textbook is an introduction to the theory and applications of finite tight frames, an area that has developed rapidly in the last decade. Stimulating much of this growth are the applications of finite frames to diverse fields such as signal processing, quantum information theory, multivariate orthogonal polynomials, and remote sensing. Featuring exercises and MATLAB examples in each chapter, the book is well suited as a textbook for a graduate course or seminar involving finite frames. The self-contained, user-friendly presentation also makes the work useful as a self-study resource or reference for graduate students, instructors, researchers, and practitioners in pure and applied mathematics, engineering, mathematical physics, and signal processing.

Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.

We’ve heard plenty from politicians and experts on affirmative action and higher education, about how universities should intervene—if at all—to ensure a diverse but deserving student population. But what about those for whom these issues matter the most? In this book, Natasha K. Warikoo deeply explores how students themselves think about merit and race at a uniquely pivotal moment: after they have just won the most competitive game of their lives and gained admittance to one of the world’s top universities. What Warikoo uncovers—talking with both white students and students of color at Harvard, Brown, and Oxford—is absolutely illuminating; and some of it is positively shocking. As she shows, many elite white students understand the value of diversity abstractly, but they ignore the real problems that racial inequality causes and that diversity programs are meant to solve. They stand in fear of being labeled a racist, but they are quick to call foul should a diversity program appear at all to hamper their own chances for advancement. The most troubling result of this ambivalence is what she calls the “diversity bargain,” in which white students reluctantly agree with affirmative action as long as it benefits them by providing a diverse learning environment—racial diversity, in this way, is a commodity, a selling point on a brochure. And as Warikoo shows, universities play a big part in creating these situations. The way they talk about race on campus and the kinds of diversity programs they offer have a huge impact on student attitudes, shaping them either toward ambivalence or, in better cases, toward more productive and considerate understandings of racial difference. Ultimately, this book demonstrates just how slippery the notions of race, merit, and privilege can be. In doing so, it asks important questions not just about college admissions but what the elite students who have succeeded at it—who will be the world’s future leaders—will do with the social inequalities of the wider world.

This highly readable book aims to ease the many challenges of starting undergraduate research. It accomplishes this by presenting a diverse series of self-contained, accessible articles which include specific open problems and prepare the reader to tackle them with ample background material and references. Each article also contains a carefully selected bibliography for further reading. The content spans the breadth of mathematics, including many topics that are not normally addressed by the undergraduate curriculum (such as matroid theory, mathematical biology, and operations research), yet have few enough prerequisites that the interested student can start exploring them under the guidance of a faculty member. Whether trying to start an undergraduate thesis, embarking on a summer REU, or preparing for graduate school, this book is appropriate for a variety of students and the faculty who guide them.

Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.