Download or read book The Joy of Abstraction written by Eugenia Cheng and published by Cambridge University Press. This book was released on 2022-10-13 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematician and popular science author Eugenia Cheng is on a mission to show you that mathematics can be flexible, creative, and visual. This joyful journey through the world of abstract mathematics into category theory will demystify mathematical thought processes and help you develop your own thinking, with no formal mathematical background needed. The book brings abstract mathematical ideas down to earth using examples of social justice, current events, and everyday life – from privilege to COVID-19 to driving routes. The journey begins with the ideas and workings of abstract mathematics, after which you will gently climb toward more technical material, learning everything needed to understand category theory, and then key concepts in category theory like natural transformations, duality, and even a glimpse of ongoing research in higher-dimensional category theory. For fans of How to Bake Pi, this will help you dig deeper into mathematical concepts and build your mathematical background.
Download or read book The Joy of Abstraction written by Eugenia Cheng and published by Cambridge University Press. This book was released on 2022-10-13 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: A uniquely accessible introduction to abstract mathematics and category theory written by popular science author of How to Bake Pi.
Download or read book Abstract and Concrete Categories written by Jiri Adamek and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This up-to-date introductory treatment employs category theory to explore the theory of structures. Its unique approach stresses concrete categories and presents a systematic view of factorization structures, offering a unifying perspective on earlier work and summarizing recent developments. Numerous examples, ranging from general to specific, illuminate the text. 1990 edition, updated 2004.
Download or read book The Art of Logic in an Illogical World written by Eugenia Cheng and published by Basic Books. This book was released on 2018-09-11 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: How both logical and emotional reasoning can help us live better in our post-truth world In a world where fake news stories change election outcomes, has rationality become futile? In The Art of Logic in an Illogical World, Eugenia Cheng throws a lifeline to readers drowning in the illogic of contemporary life. Cheng is a mathematician, so she knows how to make an airtight argument. But even for her, logic sometimes falls prey to emotion, which is why she still fears flying and eats more cookies than she should. If a mathematician can't be logical, what are we to do? In this book, Cheng reveals the inner workings and limitations of logic, and explains why alogic -- for example, emotion -- is vital to how we think and communicate. Cheng shows us how to use logic and alogic together to navigate a world awash in bigotry, mansplaining, and manipulative memes. Insightful, useful, and funny, this essential book is for anyone who wants to think more clearly.
Download or read book The Joy of X written by Steven Henry Strogatz and published by Houghton Mifflin Harcourt. This book was released on 2012 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: A delightful tour of the greatest ideas of math, showing how math intersects with philosophy, science, art, business, current events, and everyday life, by an acclaimed science communicator and regular contributor to the "New York Times."
Download or read book Beyond Infinity written by Eugenia Cheng and published by Profile Books. This book was released on 2017-03-09 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: SHORTLISTED FOR THE 2017 ROYAL SOCIETY SCIENCE BOOK PRIZE Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.
Download or read book The Joy of SET written by Liz McMahon and published by Princeton University Press. This book was released on 2019-07-09 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Have you ever played the addictive card game SET? Have you ever wondered about the connections between games and mathematics? . . . The Joy of SET takes readers on a fascinating journey into this seemingly simple card game and reveals its surprisingly deep and diverse mathematical dimensions. Absolutely no mathematical background is necessary to enjoy this book - all you need is a sense of curiosity and adventure. Originally invented in 1974 by Marsha Falco and officially released in 1991, SET has gained a widespread, loyal following. SET's eighty-one cards consist of one, two, or three symbols of different shapes (diamond, oval, squiggle), shadings (solid, striped, open), and colors (green, purple, red). In order to win, players must identify 'sets' of three cards for which each characteristic is the same - or different - on all the cards. SET's strategic and unique design opens connections to a plethora of mathematical disciplines, including geometry, modular arithmetic, combinatorics, probability, linear algebra, and computer simulations. The Joy of SET looks at these areas as well as avenues for further mathematical exploration. As the authors show, the relationship between SET and mathematics runs in both directions - playing this game has generated new mathematics, and the math has led to new questions about the game itself."--Provided by publisher.
Download or read book x y written by Eugenia Cheng and published by Profile Books. This book was released on 2020-07-16 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: From imaginary numbers to the fourth dimension and beyond, mathematics has always been about imagining things that seem impossible at first glance. In x+y, Eugenia Cheng draws on the insights of higher-dimensional mathematics to reveal a transformative new way of talking about the patriarchy, mansplaining and sexism: a way that empowers all of us to make the world a better place. Using precise mathematical reasoning to uncover everything from the sexist assumptions that make society a harder place for women to live to the limitations of science and statistics in helping us understand the link between gender and society, Cheng's analysis replaces confusion with clarity, brings original thinking to well worn arguments - and provides a radical, illuminating and liberating new way of thinking about the world and women's place in it.
Download or read book Introduction to Abstract Harmonic Analysis written by Lynn H. Loomis and published by Courier Corporation. This book was released on 2013-05-09 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a prominent figure in the field of harmonic analysis, this classic monograph is geared toward advanced undergraduates and graduate students and focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition.
Download or read book Basic Category Theory for Computer Scientists written by Benjamin C. Pierce and published by MIT Press. This book was released on 1991-08-07 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Contents Tutorial • Applications • Further Reading
Download or read book Abstraction in Art and Nature written by Nathan Cabot Hale and published by Courier Corporation. This book was released on 2012-06-19 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this stimulating, thought-provoking guide, a noted sculptor and teacher demonstrates how to discover a rich new design source in the abstractions inherent in natural forms. Through systematic study of such properties as line, form, shape, mass, pattern, light and dark, space, proportion, scale, perspective, and color as they appear in nature, students can learn to utilize the infinite variety and diversity of those elements as a wellspring of creative abstraction. The author invites students to learn the necessary techniques through a series of projects devoted to exploring and drawing plants, animals, birds, landscapes, seascapes, skies, and more. Lines of growth and structure, water and liquid forms, weather and atmospheric patterns, luminosity in plants and animals, earth colors and lightning are among the sources of abstraction available to the artist who is aware of them. This book will train you to see and use these elements and many more. An intriguing blend of art, psychology, and the natural sciences, Abstraction in Art and Nature is profusely illustrated with over 370 photographs, scientific illustrations, diagrams, and reproductions of works by the great masters. It not only offers a mind-stretching new way of learning and teaching basic design, but deepens our awareness of the natural environment. In short, Mr. Hale's book is an indispensable guide that artists, teachers, and students will want to have close at hand for instruction, inspiration, and practical guidance.
Download or read book The Joy of Finite Mathematics written by Chris P. Tsokos and published by Academic Press. This book was released on 2015-10-27 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Joy of Finite Mathematics: The Language and Art of Math teaches students basic finite mathematics through a foundational understanding of the underlying symbolic language and its many dialects, including logic, set theory, combinatorics (counting), probability, statistics, geometry, algebra, and finance. Through detailed explanations of the concepts, step-by-step procedures, and clearly defined formulae, readers learn to apply math to subjects ranging from reason (logic) to finance (personal budget), making this interactive and engaging book appropriate for non-science, undergraduate students in the liberal arts, social sciences, finance, economics, and other humanities areas. The authors utilize important historical facts, pose interesting and relevant questions, and reference real-world events to challenge, inspire, and motivate students to learn the subject of mathematical thinking and its relevance. The book is based on the authors' experience teaching Liberal Arts Math and other courses to students of various backgrounds and majors, and is also appropriate for preparing students for Florida's CLAST exam or similar core requirements. - Highlighted definitions, rules, methods, and procedures, and abundant tables, diagrams, and graphs, clearly illustrate important concepts and methods - Provides end-of-chapter vocabulary and concept reviews, as well as robust review exercises and a practice test - Contains information relevant to a wide range of topics, including symbolic language, contemporary math, liberal arts math, social sciences math, basic math for finance, math for humanities, probability, and the C.L.A.S.T. exam - Optional advanced sections and challenging problems are included for use at the discretion of the instructor - Online resources include PowerPoint Presentations for instructors and a useful student manual
Download or read book The Joy of Not Knowing written by Marcelo Staricoff and published by Routledge. This book was released on 2020-12-30 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Joy of Not Knowing takes every aspect of the curriculum and of school life and transforms it into a personalised, meaningful and enjoyable experience for all. It offers readers an innovative, theoretical and practical guide to establish a values-based, enquiry-led and challenge-rich learning to learn approach to teaching and learning and to school leadership. This thought-provoking guide provides the reader with a wealth of whole-class, easy-to-implement, malleable, practical ideas and case studies that can be personalised to the vision of each setting, age-group and curriculum. It brings together, as a whole-school framework, the strategies that have been shown to have the greatest impact on practitioner’s professional fulfilment and on children’s life chances, love of learning, intrinsic motivation and enthusiasm for wanting to know. The Joy of Not Knowing enables schools to launch the academic year with a bespoke JONK Learning to Learn Week that enables every student to succeed develops philosophical, creative and critical problem-solving and multi-lingual thinking skills establishes collaborative cultures of thinking, learning and leadership informs practice through active action research incorporates a values-led democratic approach to school life nurtures school-pupil-family-community partnerships Designed for school leaders and practitioners at all levels and across all ages, this practical guide shows how all students can thrive and develop the dispositions of successful lifelong learners and global citizens.
Download or read book Conceptual Mathematics written by F. William Lawvere and published by Cambridge University Press. This book was released on 2009-07-30 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.
Download or read book Molly and the Mathematical Mysteries written by Eugenia Cheng and published by Big Picture Press. This book was released on 2021-03-30 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: Find the clues and lift the flaps on this mathematical mystery! Join Molly as she ventures into a curious world where nothing is quite as it seems. A trail of clues leads from scene to scene, presenting Molly with a number of challenges. But who is leaving the clues, and where will they lead? This interactive mystery shows math isn't just about numbers—it’s about imagination! An explorative and creative approach to the world of mathematics.
Download or read book An Introduction to Abstract Mathematics written by Robert J. Bond and published by Waveland Press. This book was released on 2007-08-24 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bond and Keane explicate the elements of logical, mathematical argument to elucidate the meaning and importance of mathematical rigor. With definitions of concepts at their disposal, students learn the rules of logical inference, read and understand proofs of theorems, and write their own proofs all while becoming familiar with the grammar of mathematics and its style. In addition, they will develop an appreciation of the different methods of proof (contradiction, induction), the value of a proof, and the beauty of an elegant argument. The authors emphasize that mathematics is an ongoing, vibrant disciplineits long, fascinating history continually intersects with territory still uncharted and questions still in need of answers. The authors extensive background in teaching mathematics shines through in this balanced, explicit, and engaging text, designed as a primer for higher- level mathematics courses. They elegantly demonstrate process and application and recognize the byproducts of both the achievements and the missteps of past thinkers. Chapters 1-5 introduce the fundamentals of abstract mathematics and chapters 6-8 apply the ideas and techniques, placing the earlier material in a real context. Readers interest is continually piqued by the use of clear explanations, practical examples, discussion and discovery exercises, and historical comments.
Download or read book Concrete Abstractions written by Max Hailperin and published by Max Hailperin. This book was released on 1999 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: CONCRETE ABSTRACTIONS offers students a hands-on, abstraction-based experience of thinking like a computer scientist. This text covers the basics of programming and data structures, and gives first-time computer science students the opportunity to not only write programs, but to prove theorems and analyze algorithms as well. Students learn a variety of programming styles, including functional programming, assembly-language programming, and object-oriented programming (OOP). While most of the book uses the Scheme programming language, Java is introduced at the end as a second example of an OOP system and to demonstrate concepts of concurrent programming.
