The Joy Of Abstraction

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The Joy of Abstraction

Author : Eugenia Cheng
Publisher : Cambridge University Press
Page : 440 pages
File Size : 55,9 Mb
Release : 2022-10-13
Category : Mathematics
ISBN : 9781108861014

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The Joy of Abstraction by Eugenia Cheng Pdf

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.

Abstract and Concrete Categories

Author : Jiri Adamek,Horst Herrlich,George E. Strecker
Publisher : Unknown
Page : 0 pages
File Size : 50,7 Mb
Release : 2009
Category : Categories (Mathematics)
ISBN : 0486469344

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Abstract and Concrete Categories by Jiri Adamek,Horst Herrlich,George E. Strecker Pdf

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.

The Art of Logic in an Illogical World

Author : Eugenia Cheng
Publisher : Basic Books
Page : 321 pages
File Size : 50,5 Mb
Release : 2018-09-11
Category : Mathematics
ISBN : 9781541672505

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The Art of Logic in an Illogical World by Eugenia Cheng Pdf

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.

Beyond Infinity

Author : Eugenia Cheng
Publisher : Profile Books
Page : 204 pages
File Size : 48,9 Mb
Release : 2017-03-09
Category : Mathematics
ISBN : 9781782830818

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Beyond Infinity by Eugenia Cheng Pdf

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.

x + y

Author : Eugenia Cheng
Publisher : Basic Books
Page : 213 pages
File Size : 48,9 Mb
Release : 2020-08-25
Category : Social Science
ISBN : 9781541646513

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x + y by Eugenia Cheng Pdf

A brilliant mathematician examines the complexity of gender and society and forges a path out of inequality. Why are men in charge? After years in the male-dominated field of mathematics and in the female-dominated field of art, Eugenia Cheng has heard the question many times. In x + y, Cheng argues that her mathematical specialty -- category theory -- reveals why. Category theory deals more with context, relationships, and nuanced versions of equality than with intrinsic characteristics. Category theory also emphasizes dimensionality: much as a cube can cast a square or diamond shadow, depending on your perspective, so too do gender politics appear to change with how we examine them. Because society often rewards traits that it associates with males, such as competitiveness, we treat the problems those traits can create as male. But putting competitive women in charge will leave many unjust relationships in place. If we want real change, we need to transform the contexts in which we all exist, and not simply who we think we are. Praise for Eugenia Cheng "[Eugenia Cheng's] tone is clear, clever and friendly . . . she is rigorous and insightful. . . . [She is] a lucid and nimble expositor." --- Alex Bellos, New York Times Book Review "Dr. Cheng . . . has a knack for brushing aside conventions and edicts, like so many pie crumbs from a cutting board." --- Natalie Angier, New York Times

The Joy of Finite Mathematics

Author : Chris P. Tsokos,Rebecca D. Wooten
Publisher : Academic Press
Page : 554 pages
File Size : 50,9 Mb
Release : 2015-10-27
Category : Mathematics
ISBN : 9780128029855

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The Joy of Finite Mathematics by Chris P. Tsokos,Rebecca D. Wooten Pdf

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

The Joy of SET

Author : Liz McMahon,Gary Gordon,Hannah Gordon,Rebecca Gordon
Publisher : Princeton University Press
Page : 320 pages
File Size : 49,9 Mb
Release : 2019-07-09
Category : Games & Activities
ISBN : 9780691192321

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The Joy of SET by Liz McMahon,Gary Gordon,Hannah Gordon,Rebecca Gordon Pdf

"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.

Deleuze, The Dark Precursor

Author : Eleanor Kaufman
Publisher : JHU Press
Page : 260 pages
File Size : 48,5 Mb
Release : 2012-09-01
Category : Literary Criticism
ISBN : 9781421406480

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Deleuze, The Dark Precursor by Eleanor Kaufman Pdf

A thoughtful and original analysis of the writings of influential French philosopher Gilles Deleuze. Gilles Deleuze is considered one of the most important French philosophers of the twentieth century. Eleanor Kaufman situates Deleuze in relation to others of his generation, such as Jean-Paul Sartre, Pierre Klossowski, Maurice Blanchot, and Claude Lévi-Strauss, and she engages the provocative readings of Deleuze by Alain Badiou and Slavoj Žižek. Deleuze, The Dark Precursor is organized around three themes that critically overlap: dialectic, structure, and being. Kaufman argues that Deleuze's work is deeply concerned with these concepts, even when he advocates for the seemingly opposite notions of univocity, nonsense, and becoming. By drawing on scholastic thought and reading somewhat against the grain, Kaufman suggests that these often-maligned themes allow for a nuanced, even positive reflection on apparently negative states of being, such as extreme inertia. This attention to the negative or minor category has implications that extend beyond philosophy and into feminist theory, film, American studies, anthropology, and architecture.

Abstraction in Art and Nature

Author : Nathan Cabot Hale
Publisher : Courier Corporation
Page : 292 pages
File Size : 43,6 Mb
Release : 2012-06-19
Category : Art
ISBN : 9780486142302

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Abstraction in Art and Nature by Nathan Cabot Hale Pdf

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.

Basic Category Theory for Computer Scientists

Author : Benjamin C. Pierce
Publisher : MIT Press
Page : 117 pages
File Size : 43,5 Mb
Release : 1991-08-07
Category : Computers
ISBN : 9780262326452

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Basic Category Theory for Computer Scientists by Benjamin C. Pierce Pdf

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

An Introduction to Category Theory

Author : Harold Simmons
Publisher : Cambridge University Press
Page : 128 pages
File Size : 40,8 Mb
Release : 2011-09-22
Category : Mathematics
ISBN : 9781139503327

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An Introduction to Category Theory by Harold Simmons Pdf

Category theory provides a general conceptual framework that has proved fruitful in subjects as diverse as geometry, topology, theoretical computer science and foundational mathematics. Here is a friendly, easy-to-read textbook that explains the fundamentals at a level suitable for newcomers to the subject. Beginning postgraduate mathematicians will find this book an excellent introduction to all of the basics of category theory. It gives the basic definitions; goes through the various associated gadgetry, such as functors, natural transformations, limits and colimits; and then explains adjunctions. The material is slowly developed using many examples and illustrations to illuminate the concepts explained. Over 200 exercises, with solutions available online, help the reader to access the subject and make the book ideal for self-study. It can also be used as a recommended text for a taught introductory course.

Foundations of Abstract Mathematics

Author : David C. Kurtz
Publisher : McGraw-Hill Companies
Page : 216 pages
File Size : 53,8 Mb
Release : 1992
Category : Mathematics
ISBN : STANFORD:36105129676024

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Foundations of Abstract Mathematics by David C. Kurtz Pdf

This text is designed for the average to strong mathematics major taking a course called Transition to Higher Mathematics, Introduction to Proofs, or Fundamentals of Mathematics. It provides a transition to topics covered in advanced mathematics and covers logic, proofs and sets and emphasizes two important mathematical activities - finding examples of objects with specified properties and writing proofs.

The Joy of Art

Author : Carolyn Schlam
Publisher : Simon and Schuster
Page : 352 pages
File Size : 48,9 Mb
Release : 2020-04-07
Category : Art
ISBN : 9781621537052

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The Joy of Art by Carolyn Schlam Pdf

An Artist’s Insights on Art Appreciation Written by a practicing artist, this book decodes and maps the basic elements of visual art, leading the reader to a greater understanding and appreciation. Not an art history lesson per se, this illustrated guide is rather a tool kit to make the study of art and a visit to the museum truly rewarding. An entertaining and informative read, The Joy of Art offers the reader: A working art vocabulary to help you identify and explain what you’re looking at Answers to many of the questions you may have about visual art in general A summary of the basic criteria to consider when looking at art Highlights of the primary art genres and an introduction to the artists who pursued them Many visual examples of aesthetic considerations and practices Interesting facts about your favorite artists and clues to why they made the choices they did A few games to test your new skills The Joy of Art contains 150 color photographs and many interesting insights from an artist-author who takes readers behind the curtain and into the studio to uncover what actually goes into making a work of art. If you love art, this book will take your appreciation to a new level. Not only will your enjoyment of art increase, you’ll be able to clearly communicate your understanding to others.

Categories for the Working Mathematician

Author : Saunders Mac Lane
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 41,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475747218

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Categories for the Working Mathematician by Saunders Mac Lane Pdf

An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.

The Joy of Teaching

Author : Harry Hazel
Publisher : Wipf and Stock Publishers
Page : 158 pages
File Size : 43,9 Mb
Release : 2010-01-01
Category : Self-Help
ISBN : 9781606086131

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The Joy of Teaching by Harry Hazel Pdf

Over the centuries, multitudes of women and men have gone into teaching as their chosen profession. Most successful instructors find joy in teaching and are glad to share that joy with others. Harry Hazel is one teacher who has found his forty years in the classroom highly satisfying. In this book, he not only includes insights from other Canadian and American teachers he once interviewed, but he primarily reflects on a long and happy career. While the material in this book is slanted toward college teaching, many of the techniques could also be applied to other levels of instruction, such as elementary, secondary, or adult education. Key principles include Motivating yourself Motivating students Polishing your speaking skills Taking the pain out of writing Making the joy last