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A short introduction ideal for students learning category theory for the first time.
Radical ideas for changing the justice system, rooted in the real-life experiences of those in overpoliced communities, from the acclaimed former federal prosecutor and author of Chokehold Paul Butler was an ambitious federal prosecutor, a Harvard Law grad who gave up his corporate law salary to fight the good fight—until one day he was arrested on the street and charged with a crime he didn't commit. In a book Harvard Law professor Charles Ogletree calls “a must-read,” Butler looks at places where ordinary citizens meet the justice system—as jurors, witnesses, and in encounters with the police—and explores what “doing the right thing” means in a corrupt system. No matter how powerless those caught up in the web of the law may feel, there is a chance to regain agency, argues Butler. Through groundbreaking and sometimes controversial methods—jury nullification (voting “not guilty” in drug cases as a form of protest), just saying “no” when the police request your permission to search, and refusing to work inside the system as a snitch or a prosecutor—ordinary people can tip the system towards actual justice. Let’s Get Free is an evocative, compelling look at the steps we can collectively take to reform our broken system.
This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online. For errata and updates, visit https://measure.axler.net/
This book provides a systematic in-depth analysis of nonparametric regression with random design. It covers almost all known estimates. The emphasis is on distribution-free properties of the estimates.
This book explains, in simple but accurate terms, how orthodox quantum mechanics works. The author, a distinguished theoretical physicist, shows how this theory, realistically interpreted, assigns an important role to our conscious free choices. Stapp claims that mainstream biology and neuroscience, despite nearly a century of quantum physics, still stick essentially to failed classical precepts in which mental intentions have no effect upon our bodily actions. He shows how quantum mechanics provides a rational basis for a better understanding of this connection, even allowing an explanation of certain phenomena currently held to be “paranormal”. These ideas have major implications for our understanding of ourselves and our mental processes, and thus also for the meaningfulness of our lives.
Anne Meyer and David Rose, who first laid out the principles of UDL, provide an ambitious, engaging discussion of new research and best practices. This book gives the UDL field an essential and authoritative learning resource for the coming years. In the 1990s, Anne Meyer, David Rose, and their colleagues at CAST introduced Universal Design for Learning (UDL) as a framework to improve teaching and learning in the digital age, sparking an international reform movement. Now Meyer and Rose return with Universal Design for Learning: Theory and Practice, an up-to-date multimedia online book (with print and e-book options) that leverages more than a decade of research and implementation. This is the first significant new statement on UDL since 2002, an ambitious, engaging exploration of ideas and best practices that provides the growing UDL field with an essential and authoritative learning resource for the coming years. This new work includes contributions from CAST's research and implementation teams as well as from many of CAST's collaborators in schools, universities, and research settings. Readers are invited to contribute ideas, perspectives, and examples from their own practice in an online community of practice. --
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.
Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.
This book offers the first comprehensive philosophical examination of the free speech ‘battles’ of the last decade, arguing for a critical republican conception of civility as an explanatory and prescriptive solution. Issues such as no-platforming and safe spaces, the increasing influence of Far-Right rhetoric on internet forums, the role of Twitter as a site of activist struggles, and the moral panics that surround ill-judged comments made by public figures, all provide a new set of challenges for society which demand a careful critical analysis. The author proposes a 'republican theory' of free speech, demonstrating how a conception of ‘critical’ civility, one which combines the importance of expressive respect with the responsibilities of contestation and vigilance, is required if we are to combat some of the most contentious speech-related conflicts facing contemporary society today.