The Little Book of Mathematical Principles, Theories, & Things


Robert Solomon - 2008
    Rare Book

Race, Class, and Politics in the Cappuccino City


Derek S. Hyra - 2017
    Where the city’s most infamous open-air drug market once stood, a farmers’ market now sells grass-fed beef and homemade duck egg ravioli. On the corner where AM.PM carryout used to dish out soul food, a new establishment markets its $28 foie gras burger. Shaw is experiencing a dramatic transformation, from “ghetto” to “gilded ghetto,” where white newcomers are rehabbing homes, developing dog parks, and paving the way for a third wave coffee shop on nearly every block.Race, Class, and Politics in the Cappuccino City is an in-depth ethnography of this gilded ghetto. Derek S. Hyra captures here a quickly gentrifying space in which long-time black residents are joined, and variously displaced, by an influx of young, white, relatively wealthy, and/or gay professionals who, in part as a result of global economic forces and the recent development of central business districts, have returned to the cities earlier generations fled decades ago. As a result, America is witnessing the emergence of what Hyra calls “cappuccino cities.” A cappuccino has essentially the same ingredients as a cup of coffee with milk, but is considered upscale, and is double the price. In Hyra’s cappuccino city, the black inner-city neighborhood undergoes enormous transformations and becomes racially “lighter” and more expensive by the year.

Einstein's Wife: Work and Marriage in the Lives of Five Great Twentieth-Century Women


Andrea Gabor - 1995
    Among the women she profiles are Supreme Court Justice Sandra Day O'Connor, architect and urban planner Denise Scott Brown, and Mileva Maric Einstein, the scientist whose marriage to Einstein ended in tragedy.

The New Jim Crow: Mass Incarceration in the Age of Colorblindness


Michelle Alexander - 2010
    His great-grandfather was beaten to death by the Klu Klux Klan for attempting to vote. His grandfather was prevented from voting by Klan intimidation; his father was barred by poll taxes and literacy tests. Today, Cotton cannot vote because he, like many black men in the United States, has been labeled a felon and is currently on parole."As the United States celebrates the nation's "triumph over race" with the election of Barack Obama, the majority of young black men in major American cities are locked behind bars or have been labeled felons for life. Although Jim Crow laws have been wiped off the books, an astounding percentage of the African American community remains trapped in a subordinate status--much like their grandparents before them.In this incisive critique, former litigator-turned-legal-scholar Michelle Alexander provocatively argues that we have not ended racial caste in America: we have simply redesigned it. Alexander shows that, by targeting black men and decimating communities of color, the U.S. criminal justice system functions as a contemporary system of racial control, even as it formally adheres to the principle of color blindness. The New Jim Crow challenges the civil rights community--and all of us--to place mass incarceration at the forefront of a new movement for racial justice in America.

The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth


Paul Hoffman - 1998
    Based on a National Magazine Award-winning article, this masterful biography of Hungarian-born Paul Erdos is both a vivid portrait of an eccentric genius and a layman's guide to some of this century's most startling mathematical discoveries.

Everyday Antiracism: Getting Real About Race in School


Mica Pollock - 2008
    Topics range from using racial incidents as teachable moments and responding to the "n-word" to valuing students' home worlds, dealing daily with achievement gaps, and helping parents fight ethnic and racial misconceptions about their children. Questions following each essay prompt readers to examine and discuss everyday issues of race and opportunity in their own classrooms and schools.For educators and parents determined to move beyond frustrations about race, Everyday Antiracism is an essential tool.

Waking Up White: And Finding Myself in the Story of Race


Debby Irving - 2014
    By sharing her sometimes cringe-worthy struggle to understand racism and racial tensions, she offers a fresh perspective on bias, stereotypes, manners, and tolerance. As Irving unpacks her own long-held beliefs about colorblindness, being a good person, and wanting to help people of color, she reveals how each of these well-intentioned mindsets actually perpetuated her ill-conceived ideas about race. She also explains why and how she's changed the way she talks about racism, works in racially mixed groups, and understands the antiracism movement as a whole. Exercises at the end of each chapter prompt readers to explore their own racialized ideas. Waking Up White's personal narrative is designed to work well as a rapid read, a book group book, or support reading for courses exploring racial and cultural issues.

50 Mathematical Ideas You Really Need to Know


Tony Crilly - 2007
    Who invented zero? Why are there 60 seconds in a minute? Can a butterfly's wings really cause a storm on the far side of the world? In 50 concise essays, Professor Tony Crilly explains the mathematical concepts that allow use to understand and shape the world around us.

The Puzzler's Dilemma: From the Lighthouse of Alexandria to Monty Hall, a Fresh Look at Classic Conundrums of Logic, Mathematics, and Life


Derrick Niederman - 2012
    Among the old chestnuts he cracks wide open are the following classics: Knights and knaves The monk and the mountain The dominoes and the chessboard The unexpected hanging The Tower of HanoiUsing real-world analogies, infectious humor, and a fresh approach, this deceptively simple volume will challenge, amuse, enlighten, and surprise even the most experienced puzzle solver.

A New Kind of Science


Stephen Wolfram - 1997
    Wolfram lets the world see his work in A New Kind of Science, a gorgeous, 1,280-page tome more than a decade in the making. With patience, insight, and self-confidence to spare, Wolfram outlines a fundamental new way of modeling complex systems. On the frontier of complexity science since he was a boy, Wolfram is a champion of cellular automata--256 "programs" governed by simple nonmathematical rules. He points out that even the most complex equations fail to accurately model biological systems, but the simplest cellular automata can produce results straight out of nature--tree branches, stream eddies, and leopard spots, for instance. The graphics in A New Kind of Science show striking resemblance to the patterns we see in nature every day. Wolfram wrote the book in a distinct style meant to make it easy to read, even for nontechies; a basic familiarity with logic is helpful but not essential. Readers will find themselves swept away by the elegant simplicity of Wolfram's ideas and the accidental artistry of the cellular automaton models. Whether or not Wolfram's revolution ultimately gives us the keys to the universe, his new science is absolutely awe-inspiring. --Therese Littleton

The Classroom Chef: Sharpen Your Lessons, Season Your Classes, Make Math Meaninful


John Stevens - 2016
    You can use these ideas and methods as-is, or better yet, tweak them and create your own enticing educational meals. The message the authors share is that, with imagination and preparation, every teacher can be a Classroom Chef.

Algorithms


Sanjoy Dasgupta - 2006
    Emphasis is placed on understanding the crisp mathematical idea behind each algorithm, in a manner that is intuitive and rigorous without being unduly formal. Features include: The use of boxes to strengthen the narrative: pieces that provide historical context, descriptions of how the algorithms are used in practice, and excursions for the mathematically sophisticated.Carefully chosen advanced topics that can be skipped in a standard one-semester course, but can be covered in an advanced algorithms course or in a more leisurely two-semester sequence.An accessible treatment of linear programming introduces students to one of the greatest achievements in algorithms. An optional chapter on the quantum algorithm for factoring provides a unique peephole into this exciting topic. In addition to the text, DasGupta also offers a Solutions Manual, which is available on the Online Learning Center.Algorithms is an outstanding undergraduate text, equally informed by the historical roots and contemporary applications of its subject. Like a captivating novel, it is a joy to read. Tim Roughgarden Stanford University

Birth of a Theorem: A Mathematical Adventure


Cédric Villani - 2012
    Birth of a Theorem is Villani’s own account of the years leading up to the award. It invites readers inside the mind of a great mathematician as he wrestles with the most important work of his career.But you don’t have to understand nonlinear Landau damping to love Birth of a Theorem. It doesn’t simplify or overexplain; rather, it invites readers into collaboration. Villani’s diaries, emails, and musings enmesh you in the process of discovery. You join him in unproductive lulls and late-night breakthroughs. You’re privy to the dining-hall conversations at the world’s greatest research institutions. Villani shares his favorite songs, his love of manga, and the imaginative stories he tells his children. In mathematics, as in any creative work, it is the thinker’s whole life that propels discovery—and with Birth of a Theorem, Cédric Villani welcomes you into his.

Einstein's Heroes: Imagining the World Through the Language of Mathematics


Robyn Arianrhod - 2004
    Einstein's Heroes takes you on a journey of discovery about just such a miraculous language--the language of mathematics--one of humanity's mostamazing accomplishments. Blending science, history, and biography, this remarkable book reveals the mysteries of mathematics, focusing on the life and work of three of Albert Einstein's heroes: Isaac Newton, Michael Faraday, and especially James Clerk Maxwell, whose work directly inspired the theory of relativity. RobynArianrhod bridges the gap between science and literature, portraying mathematics as a language and arguing that a physical theory is a work of imagination involving the elegant and clever use of this language. The heart of the book illuminates how Maxwell, using the language of mathematics in a newand radical way, resolved the seemingly insoluble controversy between Faraday's idea of lines of force and Newton's theory of action-at-a-distance. In so doing, Maxwell not only produced the first complete mathematical description of electromagnetism, but actually predicted the existence of theradio wave, teasing it out of the mathematical language itself. Here then is a fascinating look at mathematics: its colorful characters, its historical intrigues, and above all its role as the uncannily accurate language of nature.

A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity


Peter Collier - 2012
    This user-friendly self-study guide is aimed at the general reader who is motivated to tackle that not insignificant challenge. The book is written using straightforward and accessible language, with clear derivations and explanations as well as numerous fully solved problems. For those with minimal mathematical background, the first chapter provides a crash course in foundation mathematics. The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Einstein field equations; the Schwarzschild solution (which gives a good approximation of the spacetime of our Solar System); simple black holes and relativistic cosmology. Following the historic 2015 LIGO (Laser Interferometer Gravitational-Wave Observatory) detection, there is now an additional chapter on gravitational waves, ripples in the fabric of spacetime that potentially provide a revolutionary new way to study the universe. Special relativity helps explain a huge range of non-gravitational physical phenomena and has some strangely counter-intuitive consequences. These include time dilation, length contraction, the relativity of simultaneity, mass-energy equivalence and an absolute speed limit. General relativity, the leading theory of gravity, is at the heart of our understanding of cosmology and black holes.Understand even the basics of Einstein's amazing theory and the world will never seem the same again. ContentsPrefaceIntroduction1 Foundation mathematics2 Newtonian mechanics3 Special relativity4 Introducing the manifold5 Scalars, vectors, one-forms and tensors6 More on curvature7 General relativity8 The Newtonian limit9 The Schwarzschild metric10 Schwarzschild black holes11 Cosmology12 Gravitational wavesAppendix: The Riemann curvature tensorBibliographyAcknowledgementsJanuary 2019. This third edition has been revised to make the material even more accessible to the enthusiastic general reader who seeks to understand the mathematics of relativity.