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Graphs, Matrices, and Designs: Festschrift In Honor Of Norman J. Pullman
by ReesExamines partitions and covers of graphs and digraphs, latin squares, pairwise balanced designs with prescribed block sizes, ranks and permanents, extremal graph theory, Hadamard matrices and graph factorizations. This book is designed to be of interest to applied mathematicians, computer scientists and communications researchers.
Graphs, Networks and Algorithms
by Dieter JungnickelFrom the reviews of the previous editions ".... The book is a first class textbook and seems to be indispensable for everybody who has to teach combinatorial optimization. It is very helpful for students, teachers, and researchers in this area. The author finds a striking synthesis of nice and interesting mathematical results and practical applications. ... the author pays much attention to the inclusion of well-chosen exercises. The reader does not remain helpless; solutions or at least hints are given in the appendix. Except for some small basic mathematical and algorithmic knowledge the book is self-contained. ..." K.Engel, Mathematical Reviews 2002 The substantial development effort of this text, involving multiple editions and trailing in the context of various workshops, university courses and seminar series, clearly shows through in this new edition with its clear writing, good organisation, comprehensive coverage of essential theory, and well-chosen applications. The proofs of important results and the representation of key algorithms in a Pascal-like notation allow this book to be used in a high-level undergraduate or low-level graduate course on graph theory, combinatorial optimization or computer science algorithms. The well-worked solutions to exercises are a real bonus for self study by students. The book is highly recommended. P .B. Gibbons, Zentralblatt für Mathematik 2005 Once again, the new edition has been thoroughly revised. In particular, some further material has been added: more on NP-completeness (especially on dominating sets), a section on the Gallai-Edmonds structure theory for matchings, and about a dozen additional exercises - as always, with solutions. Moreover, the section on the 1-factor theorem has been completely rewritten: it now presents a short direct proof for the more general Berge-Tutte formula. Several recent research developments are discussed and quite a few references have been added.
Graphs on Surfaces: Dualities, Polynomials, and Knots
by Joanna A. Ellis-Monaghan Iain MoffattGraphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applications. The authors illustrate the interdependency between duality, medial graphs and knots; how this interdependency is reflected in algebraic invariants of graphs and knots; and how it can be exploited to solve problems in graph and knot theory. Taking a constructive approach, the authors emphasize how generalized duals and related ideas arise by localizing classical constructions, such as geometric duals and Tait graphs, and then removing artificial restrictions in these constructions to obtain full extensions of them to embedded graphs. The authors demonstrate the benefits of these generalizations to embedded graphs in chapters describing their applications to graph polynomials and knots. Graphs on Surfaces: Dualities, Polynomials, and Knots also provides a self-contained introduction to graphs on surfaces, generalized duals, topological graph polynomials, and knot polynomials that is accessible both to graph theorists and to knot theorists. Directed at those with some familiarity with basic graph theory and knot theory, this book is appropriate for graduate students and researchers in either area. Because the area is advancing so rapidly, the authors give a comprehensive overview of the topic and include a robust bibliography, aiming to provide the reader with the necessary foundations to stay abreast of the field. The reader will come away from the text convinced of advantages of considering these higher genus analogues of constructions of plane and abstract graphs, and with a good understanding of how they arise.
Graphs Theory and Applications: With Exercises and Problems (Wiley-iste Ser.)
by Jean-Claude FournierThis book provides a pedagogical and comprehensive introduction to graph theory and its applications. It contains all the standard basic material and develops significant topics and applications, such as: colorings and the timetabling problem, matchings and the optimal assignment problem, and Hamiltonian cycles and the traveling salesman problem, to name but a few. Exercises at various levels are given at the end of each chapter, and a final chapter presents a few general problems with hints for solutions, thus providing the reader with the opportunity to test and refine their knowledge on the subject. An appendix outlines the basis of computational complexity theory, in particular the definition of NP-completeness, which is essential for algorithmic applications.
Grasping Mysteries: Girls Who Loved Math
by Jeannine AtkinsLearn about seven groundbreaking women in math and science in this gorgeously written biographical novel-in-verse, a companion to the &“original and memorable&” (Booklist, starred review) Finding Wonders: Three Girls Who Changed Science.After a childhood spent looking up at the stars, Caroline Herschel was the first woman to discover a comet and to earn a salary for scientific research. Florence Nightingale was a trailblazing nurse whose work reformed hospitals and one of the founders of the field of medical statistics. The first female electrical engineer, Hertha Marks Ayrton registered twenty-six patents for her inventions. Marie Tharp helped create the first map of the entire ocean floor, which helped scientists understand our subaquatic world and suggested how the continents shifted. A mathematical prodigy, Katherine Johnson calculated trajectories and launch windows for many NASA projects including the Apollo 11 mission. Edna Lee Paisano, a citizen of the Nez Perce Nation, was the first Native American to work full time for the Census Bureau, overseeing a large increase in American Indian and Alaskan Native representation. And Vera Rubin studied more than two hundred galaxies and found the first strong evidence for dark matter. Told in vibrant, evocative poems, this stunning novel celebrates seven remarkable women who used math as their key to explore the mysteries of the universe and grew up to do innovative work that changed the world.
Grassmann and Stiefel Varieties over Composition Algebras (RSME Springer Series #9)
by Marek Golasiński Francisco Gómez RuizThis monograph deals with matrix manifolds, i.e., manifolds for which there is a natural representation of their elements as matrix arrays. Classical matrix manifolds (Stiefel, Grassmann and flag manifolds) are studied in a more general setting. It provides tools to investigate matrix varieties over Pythagorean formally real fields. The presentation of the book is reasonably self-contained. It contains a number of nontrivial results on matrix manifolds useful for people working not only in differential geometry and Riemannian geometry but in other areas of mathematics as well. It is also designed to be readable by a graduate student who has taken introductory courses in algebraic and differential geometry.
The Grassmannian Variety
by V. Lakshmibai Justin BrownThis book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties. Research of Grassmannian varieties is centered at the crossroads of commutative algebra, algebraic geometry, representation theory, and combinatorics. Therefore, this text uniquely presents an exciting playing field for graduate students and researchers in mathematics, physics, and computer science, to expand their knowledge in the field of algebraic geometry. The standard monomial theory (SMT) for the Grassmannian varieties and their Schubert subvarieties are introduced and the text presents some important applications of SMT including the Cohen-Macaulay property, normality, unique factoriality, Gorenstein property, singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. This text would serve well as a reference book for a graduate work on Grassmannian varieties and would be an excellent supplementary text for several courses including those in geometry of spherical varieties, Schubert varieties, advanced topics in geometric and differential topology, representation theory of compact and reductive groups, Lie theory, toric varieties, geometric representation theory, and singularity theory. The reader should have some familiarity with commutative algebra and algebraic geometry.
Gravitational Wave Science with Machine Learning (Springer Series in Astrophysics and Cosmology)
by Elena CuocoThis book highlights the state of the art of machine learning applied to the science of gravitational waves. The main topics of the book range from the search for astrophysical gravitational wave signals to noise suppression techniques and control systems using machine learning-based algorithms. During the four years of work in the COST Action CA17137-A network for Gravitational Waves, Geophysics and Machine Learning (G2net), the collaboration produced several original publications as well as tutorials and lectures in the training schools we organized. The book encapsulates the immense amount of finding and achievements. It is a timely reference for young researchers approaching the analysis of data from gravitational wave experiments, with alternative approaches based on the use of artificial intelligence techniques.
Gravitational Waves: A History of Discovery
by Hartmut GroteThe historic detection of gravitational waves on September 14, 2015, prompted by the highly energetic fusion of two black holes, has made events in the universe "audible" for the first time. This expansion of the scientific sensorium has opened a new chapter in astronomy and already led to, among others, fascinating new insights about the abundance of black holes, the collision of neutron stars, and the origin of heavy chemical elements. The history of this event, which is epochal for physics, is reconstructed in this book, along with a walk-through of the main principles of how the detectors operate and a discussion of how the search for gravitational waves is conducted. The book concludes with an update of the latest detections and developments to date and a brief look into the future of this exciting research field. This book is accessible to non-specialist readers from a general audience and is also an excellent introduction to the topic for undergraduates in physics. Features: Provides an introduction to the historic discovery of gravitational waves Explains the inner workings of the detectors and the search to find the waves hidden in the data Authored by a renowned specialist involved in the ground-breaking discovery Hartmut Grote is a Professor of physics at Cardiff University, UK. His main expertise is in experimental gravitational-wave physics, and he has worked on building and improving gravitational wave detectors for over 20 years. From 2009 to 2017, he was the scientific leader of the British-German gravitational-wave detector: GEO600.
Gravitational Waves: A New Window to the Universe
by Ajit Kembhavi Pushpa KhareGravitational waves were first predicted by Albert Einstein in 1916, a year after the development of his new theory of gravitation known as the general theory of relativity. This theory established gravitation as the curvature of space-time produced by matter and energy. To be discernible even to the most sensitive instruments on Earth, the waves have to be produced by immensely massive objects like black holes and neutron stars which are rotating around each other, or in the extreme situations which prevail in the very early ages of the Universe. This book presents the story of the prediction of gravitational waves by Albert Einstein, the early attempts to detect the waves, the development of the LIGO detector, the first detection in 2016, the subsequent detections and their implications. All concepts are described in some detail, without the use of any mathematics and advanced physics which are needed for a full understanding of the subject. The book also contains description of electromagnetism, Einstein’s special theory and general theory of relativity, white dwarfs, neutron stars and black holes and other concepts which are needed for understanding gravitational waves and their effects. Also described are the LIGO detectors and the cutting edge technology that goes into building them, and the extremely accurate measurements that are needed to detect gravitational waves. The book covers these ideas in a simple and lucid fashion which should be accessible to all interested readers. The first detection of gravitational waves was given a lot of space in the print and electronic media. So, the curiosity of the non-technical audience has been aroused about what gravitational waves really are and why they are so important. This book seeks to answer such questions.
Gravitational Waves from a Quantum Field Theory Perspective (Lecture Notes in Physics #1013)
by Subhendra MohantyThis book treats the subject of gravitational waves (GWs) production in binary stars or black-holes and in the early universe, using tools of quantum field theory which are familiar to graduate students and researchers in particle physics. A special focus is given to the generation of templates of gravitational wave signals from Feynman diagram calculations of transition amplitudes, which interests active researchers in GWs. The book presents field theory concepts, like supersymmetry realized in spinning binaries and soft-graviton theorems, that can have practical applications in novel GW signals, like the memory effect. The book also aims at specialists in both GWs and particle physics addressing cosmological models of phase transition and inflation that can be tested in observations at terrestrial and space based interferometers, pulsar timing arrays, and the cosmic microwave anisotropy observations.
Gravity: A Ladybird Expert Book
by Jim Al-KhaliliHow does gravity work? Learn from the experts in the ALL-NEW LADYBIRD EXPERT SERIESDiscover the vast and momentus effects of this profound force on the world around us, written by celebrated physicist and broadcaster Jim Al-Khalili.Inside you will learn:- What is Gravity?- How does it work?- And why are there extreme gravitational environments?Above all, discover how gravity controls the shape of space and the passage of time itself, influencing the history and destiny of the entire Universe.IT'S SO MUCH MORE THAN 'WHAT GOES UP MUST COME DOWN.'Gravity is a fascinating and authoritative introduction to a phenomenon as familiar to us as breathing.Learn about other topics in the Ladybird Experts series including The Big Bang, Quantum Physics, Climate Change and Evolution.
Gravity, a Geometrical Course: Development of the Theory and Basic Physical Applications
by Pietro Giuseppe Frè'Gravity, a Geometrical Course' presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications, updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book, divided in two volumes, is a rich resource for graduate students and those who wish to gain a deep knowledge of the subject without an instructor. Volume One is dedicated to the development of the theory and basic physical applications. It guides the reader from the foundation of special relativity to Einstein field equations, illustrating some basic applications in astrophysics. A detailed account of the historical and conceptual development of the theory is combined with the presentation of its mathematical foundations. Differentiable manifolds, fibre-bundles, differential forms, and the theory of connections are covered, with a sketchy introduction to homology and cohomology. (Pseudo)-Riemannian geometry is presented both in the metric and in the vielbein approach. Physical applications include the motions in a Schwarzschild field leading to the classical tests of GR (light-ray bending and periastron advance) discussion of relativistic stellar equilibrium, white dwarfs, Chandrasekhar mass limit and polytropes. An entire chapter is devoted to tests of GR and to the indirect evidence of gravitational wave emission. The formal structure of gravitational theory is at all stages compared with that of non gravitational gauge theories, as a preparation to its modern extension, namely supergravity, discussed in the second volume. Pietro Frè is Professor of Theoretical Physics at the University of Torino, Italy and is currently serving as Scientific Counsellor of the Italian Embassy in Moscow. His scientific passion lies in supergravity and all allied topics, since the inception of the field, in 1976. He was professor at SISSA, worked in the USA and at CERN. He has taught General Relativity for 15 years. He has previously two scientific monographs, "Supergravity and Superstrings" and "The N=2 Wonderland", He is also the author of a popular science book on cosmology and two novels, in Italian.
Gravity, a Geometrical Course
by Pietro Giuseppe Frè'Gravity, a Geometrical Course' presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications, updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book is divided in two volumes. Volume Two is covers black holes, cosmology and an introduction to supergravity. The aim of this volume is two-fold. It completes the presentation of GR and it introduces the reader to theory of gravitation beyond GR, which is supergravity. Starting with a short history of the black hole concept, the book covers the Kruskal extension of the Schwarzschild metric, the causal structures of Lorentzian manifolds, Penrose diagrams and a detailed analysis of the Kerr-Newman metric. An extensive historical account of the development of modern cosmology is followed by a detailed presentation of its mathematical structure, including non-isotropic cosmologies and billiards, de Sitter space and inflationary scenarios, perturbation theory and anisotropies of the Cosmic Microwave Background. The last three chapters deal with the mathematical and conceptual foundations of supergravity in the frame of free differential algebras. Branes are presented both as classical solutions of the bulk theory and as world-volume gauge theories with particular emphasis on the geometrical interpretation of kappa-supersymmetry. The rich bestiary of special geometries underlying supergravity lagrangians is presented, followed by a chapter providing glances on the equally rich collection of special solutions of supergravity. Pietro Frè is Professor of Theoretical Physics at the University of Torino, Italy and is currently serving as Scientific Counsellor of the Italian Embassy in Moscow. His scientific passion lies in supergravity and all allied topics, since the inception of the field, in 1976. He was professor at SISSA, worked in the USA and at CERN. He has taught General Relativity for 15 years. He has previously two scientific monographs, "Supergravity and Superstrings" and "The N=2 Wonderland", He is also the author of a popular science book on cosmology and two novels, in Italian.
Gravity, Cosmology, and Astrophysics: A Journey of Exploration and Discovery with Female Pioneers (Lecture Notes in Physics #1022)
by Betti Hartmann Jutta KunzThis book is a compilation of enlightening tutorial essays, showcasing the forefront of research by exceptional female scientists. This invaluable collection provides graduate students and researchers in the field with an engaging and pedagogical introduction to a wide range of compelling topics. Delve into the depths of theoretical and observational realms, exploring intriguing subjects including modified gravity models, quantum gravity, fields in curved space-time, particle dynamics, gravitational waves, and enigmatic black holes. Embracing both the theoretical foundations and the practical applications, this comprehensive edited volume offers an accessible and all-encompassing panorama of gravity and cosmology. Moreover, it shines a much-needed spotlight on the significant contributions made by remarkable women across the globe, fostering recognition and admiration for their indispensable role in shaping this ever-evolving field.
The Gravity of Math: How Geometry Rules the Universe
by Steve Nadis Shing-Tung YauOne of the preeminent mathematicians of the past half century shows how physics and math were combined to give us the theory of gravity and the dizzying array of ideas and insights that has come from it Mathematics is far more than just the language of science. It is a critical underpinning of nature. The famed physicist Albert Einstein demonstrated this in 1915 when he showed that gravity—long considered an attractive force between massive objects—was actually a manifestation of the curvature, or geometry, of space and time. But in making this towering intellectual leap, Einstein needed the help of several mathematicians, including Marcel Grossmann, who introduced him to the geometrical framework upon which his theory rest. In The Gravity of Math, Steve Nadis and Shing-Tung Yau consider how math can drive and sometimes even anticipate discoveries in physics. Examining phenomena like black holes, gravitational waves, and the Big Bang, Nadis and Yau ask: Why do mathematical statements, derived solely from logic, provide the best descriptions of our physical world? The Gravity of Math offers an insightful and compelling look into the power of mathematics—whose reach, like that of gravity, can extend to the edge of the universe.
Gray Dawn: How the Coming Age Will Transform America and the World
by Peter G. PetersonHow Aging is changing our world.
GRE Math Prep Course
by Jeff Kolby Derrick VaughnEvery year, students pay $1,000 and more to test prep companies to prepare for the math section of the GRE. Now you can get the same preparation in a book. Although the GRE math section is difficult, it is very learnable. GRE Math Prep Course presents a thorough analysis of GRE math and introduces numerous analytic techniques that will help you immensely, not only on the GRE but in graduate school as well. Features: * Comprehensive Review: Twenty-three chapters provide complete review of GRE math. * Practice: Includes 164 examples and more than 600 exercises! Arranged from easy to medium to hard to very hard. * Diagnostic Test: The diagnostic test measures your strengths and weaknesses and directs you to areas you need to study more. * Duals: These are pairs of similar problems in which only one property is different. They illustrate the process of creating GRE questions. * If your target is a 700+ score, this is the book!
GRE Quantitative Reasoning Bible
by Victoria WoodThe purpose of this book is to provide you with a thorough review of tested math concepts and to teach you new strategies for approaching the Quantitative Reasoning section on the GRE.
GRE Test Prep Flash Cards: Geometry (Exambusters GRE Workbook #6 of 6)
by Ace Inc.<P><P><i>Advisory: Bookshare has learned that this book offers only partial accessibility. We have kept it in the collection because it is useful for some of our members. Benetech is actively working on projects to improve accessibility issues such as these.</i><P><P> 450 questions and answers that focus on essential geometry theorems, postulates, concepts, and definitions. Includes complementary diagrams. <P><P>Topics: Lines and Angles, Triangles, Proofs, Perpendicular Lines, Parallel Lines, Angle Sums, Quadrilaterals, Medians, Altitudes and Bisectors, Circles, Ratio and Proportion, Similar Polygons, Circles and Regular Polygons, Inequalities, Locus, Coordinate Geometry <P>EXAMBUSTERS GRE Prep Workbooks provide comprehensive, fundamental GRE review--one fact at a time--to prepare students to take practice GRE tests. Each GRE study guide focuses on one specific subject area covered on the GRE exam. From 300 to 600 questions and answers, each volume in the GRE series is a quick and easy, focused read. Reviewing GRE flash cards is the first step toward more confident GRE preparation and ultimately, higher GRE exam scores!
GRE Test Prep Flash Cards: Algebra (Exambusters GRE Workbook #5 of 6)
by Ace Inc.<P><P><i>Advisory: Bookshare has learned that this book offers only partial accessibility. We have kept it in the collection because it is useful for some of our members. Benetech is actively working on projects to improve accessibility issues such as these.</i><P><P> 450 questions and answers that highlight introductory algebra definitions, problems, and concepts. <P><P>Topics: Algebraic Concepts, Sets, Variables, Exponents, Properties of Numbers, Simple Equations, Signed Numbers, Monomials, Polynomials, Additive and Multiplicative Inverse, Word Problems, Prime Numbers, Factoring, Algebraic Fractions, Ratio and Proportion, Variation, Radicals, Quadratic Equations <P> EXAMBUSTERS GRE Prep Workbooks provide comprehensive, fundamental GRE review--one fact at a time--to prepare students to take practice GRE tests. Each GRE study guide focuses on one specific subject area covered on the GRE exam. From 300 to 600 questions and answers, each volume in the GRE series is a quick and easy, focused read. Reviewing GRE flash cards is the first step toward more confident GRE preparation and ultimately, higher GRE exam scores!
The Great Book of Philadelphia Sports Lists (Completely Revised and Updated Edition)
by Glen Macnow Big Daddy GrahamWhen it comes to sports talk, no city has more to say than Philadelphia.With their 2007 The Great Book of Philadelphia Sports Lists, WIP sports radio hosts Glen Macnow and Big Daddy Graham compiled dozens of sports lists to stir up dialog and debate within the buzzing Philadelphia sports community (and beyond).A lot has happened in Philly sports since 2007 -- the Phillies' 2008 World Series win; the Eagles' record-breaking 2017 season, now-famous Philly Special play, and Super Bowl LII victory over the Patriots; the Sixers' "Trust the Process" campaign; and, of course, Gritty -- so now Glen and Big Daddy are back with dozens of new lists to keep the conversation fresh, ranking things like:The most overrated and underrated players in Philly sports historyThe top 10 Philadelphia sports quotesThe 10 worst Eagles draft picks everThe greatest duos in Philly sports historyThe 10 best sports movies set in PhiladelphiaThe worst bosses in Philly sports historyand much more!
Great Calculations
by Colin PaskScience is based not only on observation and experiment, but on theory as well. As Einstein said, "Theory tells us what to measure." And theories are often crystallized into succinct calculations, like those made using Einstein's famous E = mc2. This book looks at fifty such great calculations, exploring how and why they were developed and assessing their impact on the history of science.As the author shows, many significant scientific calculations are quite simple and fairly easy to understand, even for readers will little math background. But their implications can be surprising and profound.For example, what links a famous comet and the cost of an annuity? Why do scientists claim there is "dark matter" in the universe if it can't be observed? How does carbon-based life on Earth depend on a quirk of nuclear physics? The answer to each question is an illuminating calculation. This accessible, engaging book will help you understand these breakthroughs and how they changed our view of life and the world.From the Trade Paperback edition.
Great Circles: The Transits of Mathematics and Poetry (Mathematics, Culture, and the Arts)
by Emily Rolfe GrosholzThis volume explores the interaction of poetry and mathematics by looking at analogies that link them. The form that distinguishes poetry from prose has mathematical structure (lifting language above the flow of time), as do the thoughtful ways in which poets bring the infinite into relation with the finite. The history of mathematics exhibits a dramatic narrative inspired by a kind of troping, as metaphor opens, metonymy and synecdoche elaborate, and irony closes off or shifts the growth of mathematical knowledge. The first part of the book is autobiographical, following the author through her discovery of these analogies, revealed by music, architecture, science fiction, philosophy, and the study of mathematics and poetry. The second part focuses on geometry, the circle and square, launching us from Shakespeare to Housman, from Euclid to Leibniz. The third part explores the study of dynamics, inertial motion and transcendental functions, from Descartes to Newton, and in 20th c. poetry. The final part contemplates infinity, as it emerges in modern set theory and topology, and in contemporary poems, including narrative poems about modern cosmology.
The Great Demographic Illusion: Majority, Minority, and the Expanding American Mainstream
by Richard AlbaWhy the number of young Americans from mixed families is surging and what this means for the country’s future Americans are under the spell of a distorted and polarizing story about their country’s future―the majority-minority narrative―which contends that inevitable demographic changes will create a society with a majority made up of minorities for the first time in the United States’s history. The Great Demographic Illusion reveals that this narrative obscures a more transformative development: the rising numbers of young Americans from ethno-racially mixed families, consisting of one white and one nonwhite parent. Examining the unprecedented significance of mixed parentage in the twenty-first-century United States, Richard Alba looks at how young Americans with this background will play pivotal roles in the country’s demographic future.Assembling a vast body of evidence, Alba explores where individuals of mixed parentage fit in American society. Most participate in and reshape the mainstream, as seen in their high levels of integration into social milieus that were previously white dominated. Yet, racism is evident in the very different experiences of individuals with black-white heritage. Alba’s portrait squares in key ways with the history of immigrant-group assimilation, and indicates that, once again, mainstream American society is expanding and becoming more inclusive.Nevertheless, there are also major limitations to mainstream expansion today, especially in its more modest magnitude and selective nature, which hinder the participation of black Americans and some other people of color. Alba calls for social policies to further open up the mainstream by correcting the restrictions imposed by intensifying economic inequality, shape-shifting racism, and the impaired legal status of many immigrant families.Countering rigid demographic beliefs and predictions, The Great Demographic Illusion offers a new way of understanding American society and its coming transformation.