The Joy Of Abstraction

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The Joy of Abstraction

Eugenia Cheng
The Joy of Abstraction Book PDF

Author : Eugenia Cheng
Publisher : Cambridge University Press
Page : 440 pages
File Size : 41,6 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

Jiri Adamek,Horst Herrlich,George E. Strecker
Abstract and Concrete Categories Book PDF

Author : Jiri Adamek,Horst Herrlich,George E. Strecker
Publisher : Unknown
Page : 0 pages
File Size : 50,9 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

Eugenia Cheng
The Art of Logic in an Illogical World Book PDF

Author : Eugenia Cheng
Publisher : Basic Books
Page : 321 pages
File Size : 53,5 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

Eugenia Cheng
Beyond Infinity Book PDF

Author : Eugenia Cheng
Publisher : Profile Books
Page : 204 pages
File Size : 51,9 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

Eugenia Cheng
x y Book PDF

Author : Eugenia Cheng
Publisher : Profile Books
Page : 128 pages
File Size : 47,9 Mb
Release : 2020-07-16
Category : Mathematics
ISBN : 9781782834434

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x+y by Eugenia Cheng Pdf

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.

The Joy of Finite Mathematics

Chris P. Tsokos,Rebecca D. Wooten
The Joy of Finite Mathematics Book PDF

Author : Chris P. Tsokos,Rebecca D. Wooten
Publisher : Academic Press
Page : 554 pages
File Size : 51,7 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

Liz McMahon,Gary Gordon,Hannah Gordon,Rebecca Gordon
The Joy of SET Book PDF

Author : Liz McMahon,Gary Gordon,Hannah Gordon,Rebecca Gordon
Publisher : Princeton University Press
Page : 320 pages
File Size : 51,8 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.

Abstraction in Art and Nature

Nathan Cabot Hale
Abstraction in Art and Nature Book PDF

Author : Nathan Cabot Hale
Publisher : Courier Corporation
Page : 292 pages
File Size : 46,8 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.

Foundations of Abstract Mathematics

David C. Kurtz
Foundations of Abstract Mathematics Book PDF

Author : David C. Kurtz
Publisher : McGraw-Hill Companies
Page : 216 pages
File Size : 51,5 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.

An Introduction to Category Theory

Harold Simmons
An Introduction to Category Theory Book PDF

Author : Harold Simmons
Publisher : Cambridge University Press
Page : 128 pages
File Size : 45,9 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.

An Introduction to Abstract Mathematics

Robert J. Bond,William J. Keane
An Introduction to Abstract Mathematics Book PDF

Author : Robert J. Bond,William J. Keane
Publisher : Waveland Press
Page : 344 pages
File Size : 45,7 Mb
Release : 2007-08-24
Category : Mathematics
ISBN : 9781478608059

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An Introduction to Abstract Mathematics by Robert J. Bond,William J. Keane Pdf

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.

Mathematics and the Unexpected

Ivar Ekeland
Mathematics and the Unexpected Book PDF

Author : Ivar Ekeland
Publisher : University of Chicago Press
Page : 160 pages
File Size : 45,7 Mb
Release : 1990-01-15
Category : Mathematics
ISBN : 9780226199900

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Mathematics and the Unexpected by Ivar Ekeland Pdf

"Not the least unexpected thing about Mathematics and the Unexpected is that a real mathematician should write not just a literate work, but a literary one."—Ian Stewart, New Scientist "In this brief, elegant treatise, assessable to anyone who likes to think, Ivar Ekelund explains some philosophical implications of recent mathematics. He examines randomness, the geometry involved in making predictions, and why general trends are easy to project (it will snow in January) but particulars are practically impossible (it will snow from 2 p.m. to 5 p.m. on the 21st)."—Village Voice

The Joy of Watercolor

Emma Block
The Joy of Watercolor Book PDF

Author : Emma Block
Publisher : Running Press Adult
Page : 500 pages
File Size : 47,5 Mb
Release : 2018-08-07
Category : Crafts & Hobbies
ISBN : 9780762465859

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The Joy of Watercolor by Emma Block Pdf

Enjoy the meditative art of watercolor with simple supplies, forty colorful illustrated lessons, and easy step-by-step instructions! For a soothing boost of creativity and whimsy, try your hand at watercolor. With a few simple steps, anyone can discover their artistic side and achieve moments of peace and tranquility. Forty straightforward lessons promise fun and colorful results -- no pressure and no skill required. This simple painting medium produces colorful, modern paintings to adorn invitations, gifts, and walls. The forty lessons cover useful topics like: Painting on vacation Painting your pets Layering colors Mixing colors Painting flowers and plants The supplies are simple: a basic palette of watercolors, a selection of brushes, and nice thick paper will do the job. Your bright, whimsical art is guaranteed to bring color to any gray day. It's never too late to pick up a new hobby -- start painting your own beautiful cards and artwork today!

The Joys of Haar Measure

Joe Diestel,Angela Spalsbury
The Joys of Haar Measure Book PDF

Author : Joe Diestel,Angela Spalsbury
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 48,8 Mb
Release : 2014-04-23
Category : Mathematics
ISBN : 9781470409357

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The Joys of Haar Measure by Joe Diestel,Angela Spalsbury Pdf

From the earliest days of measure theory, invariant measures have held the interests of geometers and analysts alike, with the Haar measure playing an especially delightful role. The aim of this book is to present invariant measures on topological groups, progressing from special cases to the more general. Presenting existence proofs in special cases, such as compact metrizable groups, highlights how the added assumptions give insight into just what the Haar measure is like; tools from different aspects of analysis and/or combinatorics demonstrate the diverse views afforded the subject. After presenting the compact case, applications indicate how these tools can find use. The generalisation to locally compact groups is then presented and applied to show relations between metric and measure theoretic invariance. Steinlage's approach to the general problem of homogeneous action in the locally compact setting shows how Banach's approach and that of Cartan and Weil can be unified with good effect. Finally, the situation of a nonlocally compact Polish group is discussed briefly with the surprisingly unsettling consequences indicated. The book is accessible to graduate and advanced undergraduate students who have been exposed to a basic course in real variables, although the authors do review the development of the Lebesgue measure. It will be a stimulating reference for students and professors who use the Haar measure in their studies and research.

Categories for the Working Mathematician

Saunders Mac Lane
Categories for the Working Mathematician Book PDF

Author : Saunders Mac Lane
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 47,6 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.