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Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.
LONGLISTED FOR THE 2024 DUBLIN LITERARY AWARD SHORTLISTED FOR THE ETHEL WILSON FICTION PRIZE THE GLOBE AND MAIL TOP 30 CANADIAN BOOKS TO READ IN 2023 CBC BOOKS WORKS OF CANADIAN FICTION TO READ IN THE FIRST HALF OF 2023 All talk, no action: The Mezzanine meets Ducks, Newburyport in this meandering and captivating debut It’s a hot summer night, and Hugh Dalgarno, a 31-year-old clerical worker, thinks his brain is broken. Over the course of a day and night in an uncannily depopulated public park, he will sift through the pieces and traverse the baroque landscape of his own thoughts: the theology of nosiness, the beauty of the arbutus tree, the pathos of Gene Hackman, the theory of quantum immortality, Louis Riel’s letter to an Irish newspaper, the baleful influence of Calvinism on the Scottish working class, the sea, the CIA, and, ultimately, thinking itself and how it may be represented in writing. The result is a strange, meandering sojourn, as if the history-haunted landscapes of W. G. Sebald’s The Rings of Saturn were shrunk down to a mere 85 acres. These digressions are anchored by remarks from the letters of Keats, by snatches of lyrics from Irish rebel songs and Scottish folk ballads, and, above all else, by the world-shattering call of the red-winged blackbird. "From the first page to the last I felt wholly captivated by Falling Hour and Hugh’s sensitive and far-ranging digressions. Morrison has captured the magic of Sebald and made it entirely his own, a curiously anti-capitalist exploration of what it means to live in a “fake” country. " – André Babyn, author of Evie of the Deepthorn "Falling Hour is a profound incantatory exhalation – a quiet triumph; to read it is to engage in a smart, humane and at times very funny conversation that you will never want to end." – Simon Okotie, author of After Absalon “A stellar debut novel by a stellar new talent. Falling Hour is written in a prose style that enlivens every page.” – Mauro Javier Cárdenas, author of Aphasia: A Novel "Falling Hour deserves mention as a notable debut along the estuary of modern fiction." – D. W. White, Atticus Books, Phoemix, AZ
2-Dimensional Categories is an introduction to 2-categories and bicategories, assuming only the most elementary aspects of category theory.
Many problems in number theory have simple statements, but their solutions require a deep understanding of algebra, algebraic geometry, complex analysis, group representations, or a combination of all four. The original simply stated problem can be obscured in the depth of the theory developed to understand it. This book is an introduction to some of these problems, and an overview of the theories used nowadays to attack them, presented so that the number theory is always at the forefront of the discussion. Lozano-Robledo gives an introductory survey of elliptic curves, modular forms, and $L$-functions. His main goal is to provide the reader with the big picture of the surprising connections among these three families of mathematical objects and their meaning for number theory. As a case in point, Lozano-Robledo explains the modularity theorem and its famous consequence, Fermat's Last Theorem. He also discusses the Birch and Swinnerton-Dyer Conjecture and other modern conjectures. The book begins with some motivating problems and includes numerous concrete examples throughout the text, often involving actual numbers, such as 3, 4, 5, $\frac{3344161}{747348}$, and $\frac{2244035177043369699245575130906674863160948472041} {8912332268928859588025535178967163570016480830}$. The theories of elliptic curves, modular forms, and $L$-functions are too vast to be covered in a single volume, and their proofs are outside the scope of the undergraduate curriculum. However, the primary objects of study, the statements of the main theorems, and their corollaries are within the grasp of advanced undergraduates. This book concentrates on motivating the definitions, explaining the statements of the theorems and conjectures, making connections, and providing lots of examples, rather than dwelling on the hard proofs. The book succeeds if, after reading the text, students feel compelled to study elliptic curves and modular forms in all their glory.
The Neumann Prize–winning, illustrated exploration of mathematics—from its timeless mysteries to its history of mind-boggling discoveries. Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, The Math Book covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic is lavishly illustrated with colorful art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems.
The 100+ Series, Pre-Algebra, offers in-depth practice and review for challenging middle school math topics such as ratios and proportions; rational numbers; and expressions and equations. Bonus activities on each page help extend the learning and activities, making these books perfect for daily review. Common Core State Standards have raised expectations for math learning, and many students in grades 6Ð8 are studying more accelerated math at younger ages. The 100+ Series provides the solution with titles that include over 100 targeted practice activities for learning algebra, geometry, and other advanced math topics. It also features over 100 reproducible, subject specific, practice pages to support standards-based instruction.
A hilarious reeducation in mathematics-full of joy, jokes, and stick figures-that sheds light on the countless practical and wonderful ways that math structures and shapes our world. In Math With Bad Drawings, Ben Orlin reveals to us what math actually is; its myriad uses, its strange symbols, and the wild leaps of logic and faith that define the usually impenetrable work of the mathematician. Truth and knowledge come in multiple forms: colorful drawings, encouraging jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Orlin shows us how to think like a mathematician by teaching us a brand-new game of tic-tac-toe, how to understand an economic crises by rolling a pair of dice, and the mathematical headache that ensues when attempting to build a spherical Death Star. Every discussion in the book is illustrated with Orlin's trademark "bad drawings," which convey his message and insights with perfect pitch and clarity. With 24 chapters covering topics from the electoral college to human genetics to the reasons not to trust statistics, Math with Bad Drawings is a life-changing book for the math-estranged and math-enamored alike.
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Foundations of higher dimensional category theory for graduate students and researchers in mathematics and mathematical physics.