Sets For Mathematics
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Sets For Mathematics
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Author : F. William Lawvere
language : en
Publisher: Cambridge University Press
Release Date : 2003-01-27
Sets For Mathematics written by F. William Lawvere and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-27 with Mathematics categories.
In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.
Sets For Mathematics
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Author : F. W. Lawvere
language : en
Publisher:
Release Date : 2003
Sets For Mathematics written by F. W. Lawvere and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Electronic books categories.
Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. For the first time in a text, this book uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms which express universal properties of sums, products, mapping sets, and natural number recursion. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geometry and analysis, are made explicit and taken as special axioms. Functor categories are introduced in order to model the variable sets used in geometry, and to illustrate the failure of the axiom of choice. An appendix provides an explicit introduction to necessary concepts from logic, and an extensive glossary provides a window to the mathematical landscape.
Set Theory
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Author : Abhijit Dasgupta
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Set Theory written by Abhijit Dasgupta and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axioms and ends with the construction of the real numbers. The core Cantor–Dedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin's problems on projective sets using determinacy of infinite games and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a year-long course at the upper-undergraduate level. For shorter one-semester or one-quarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via self-study.
Sets Functions And Logic
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Author : Keith Devlin
language : en
Publisher: CRC Press
Release Date : 2003-11-24
Sets Functions And Logic written by Keith Devlin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-24 with Mathematics categories.
Keith Devlin. You know him. You've read his columns in MAA Online, you've heard him on the radio, and you've seen his popular mathematics books. In between all those activities and his own research, he's been hard at work revising Sets, Functions and Logic, his standard-setting text that has smoothed the road to pure mathematics for legions of undergraduate students. Now in its third edition, Devlin has fully reworked the book to reflect a new generation. The narrative is more lively and less textbook-like. Remarks and asides link the topics presented to the real world of students' experience. The chapter on complex numbers and the discussion of formal symbolic logic are gone in favor of more exercises, and a new introductory chapter on the nature of mathematics--one that motivates readers and sets the stage for the challenges that lie ahead. Students crossing the bridge from calculus to higher mathematics need and deserve all the help they can get. Sets, Functions, and Logic, Third Edition is an affordable little book that all of your transition-course students not only can afford, but will actually read...and enjoy...and learn from. About the Author Dr. Keith Devlin is Executive Director of Stanford University's Center for the Study of Language and Information and a Consulting Professor of Mathematics at Stanford. He has written 23 books, one interactive book on CD-ROM, and over 70 published research articles. He is a Fellow of the American Association for the Advancement of Science, a World Economic Forum Fellow, and a former member of the Mathematical Sciences Education Board of the National Academy of Sciences,. Dr. Devlin is also one of the world's leading popularizers of mathematics. Known as "The Math Guy" on NPR's Weekend Edition, he is a frequent contributor to other local and national radio and TV shows in the US and Britain, writes a monthly column for the Web journal MAA Online, and regularly writes on mathematics and computers for the British newspaper The Guardian.
Stories About Sets
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Author : N. Ya. Vilenkin
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Stories About Sets written by N. Ya. Vilenkin and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Stories About Sets discusses the cardinality of sets and mathematical concepts, such as function, curve, surface, dimensions, and the paradoxical properties of curves and surfaces. The book reviews sets, operations on sets, the empty set, subsets, the universal sets, intersection of sets, union of sets, partitioning of sets, and boolean algebras. The text also discusses the cardinality of sets, including equality between sets, countable sets, unequal sets, the uncountability of the continuum, the existence of transcendental numbers, and the enigmatic axiom. The book analyzes if a part can be equal to the whole (which turns out to be true if it is applied to infinite sets). The text also discusses the arithmetic of the infinite such as involving the multiplication of infinite cardinalities. The book explains some remarkable functions and curves, the Dirichlet's function, Cantor's set, points of fracture, and continuous functions whose graphs possess a tangent at no point. The text shows how to construct a closed curve of infinite length or a curve passing through all the points of a square. The book can prove interesting and highly educational for students with mathematic or algebra subjects, as well as for academicians involved in teaching statistics or mathematics.
Theory Of Sets
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Author : Erich Kamke
language : en
Publisher: Courier Corporation
Release Date : 1950-01-01
Theory Of Sets written by Erich Kamke and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1950-01-01 with Mathematics categories.
Introductory treatment emphasizes fundamentals, covering rudiments; arbitrary sets and their cardinal numbers; ordered sets and their ordered types; and well-ordered sets and their ordinal numbers. "Exceptionally well written." ? School Science and Mathematics.
A Stroll Through Cecily S Sets
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Author : Joshua Cook
language : en
Publisher:
Release Date : 2019-07-25
A Stroll Through Cecily S Sets written by Joshua Cook and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-25 with categories.
This is a children's book designed to introduce students to set theory, with an emphasis on strange concepts like empty sets, infinite sets, uncountable infinite sets, and more. This book is designed to make kids ask questions about math and set theory, not answer them. So if you don't want more questions, don't buy this. This book does explain what it easily can about set theory, it just introduces more things than it has time to explain! This book introduces abstract mathematics. Not counting, arithmetic, shapes, geometry, or even statistics. This isn't a book about science, physics, technology, or biology. It is a math book. It introduces fundamental math concepts in a visually appealing and gentle way without getting too hung up on the details. Normally set theory at this level is reserved for college, or a few lucky high school classes. This is not without reason: set theory is mostly used in proofs which are not often given to students until college. But proofs are just formal explanations for why things are true. Many US students only see proofs in geometry where set theory is not needed and the proofs are unlikely to be useful in the future: even if they pursue a stem degree. This may be sufficient for high school algebra, but leaves students unprepared and ignorant of what college level math is really like. Teaching students proper set theory is difficult, especially children, but just the basics can be the difference between being able to formally explain a proof or not. This book gives a resource to help introduce these concepts to children, even if it is not a complete resource. QUOTES Scott Aaronson: "It's extremely cute. It strikes me as a much better version of "New Math," which was an effort in the 1960s to start elementary school kids off on the right foot by teaching them about subsets, super sets, power sets, etc." FAQ Who should buy this book? Parents who want to encourage their children to learn more about math. Parents who are willing to learn with their children when they ask questions (unless you are a mathematician, this likely touches on some concepts you don't know or haven't thought about in a while). Teachers brave enough to introduce set theory or more esoteric concepts to their students. Children who want a pretty looking picture book that insists on some strange and peculiar things. Who should not buy this book? People who don't want to answer hard questions. People who don't want to help children with new vocabulary (it does its best to avoid technical terms, but some still made it in). People who have don't like their intuitions questioned. How much does this cover? It has 25 illustrated pages covering about one concept per page. It has a few extra non picture pages of context as well. It covers basic set operations, goes up to infinity even discussing some of the weird quirks of infinity, discusses how to build pairs out of sets, and more. It does not define functions, set builder notation, or logic in general. Can I use this as a textbook to teach set theory? NO! This is a brief gentle introduction to set theory. Someone should make a much longer set theory book if we want to actually teach this to elementary grade children. This would be doable, but would require a very different style than this book. Will this help my kid learn algebra (arithmetic, etc)? Probably not, unless someone is trying to prove why algebra and arithmetic work to them! What is set theory useful for? Simply put: math. But this also includes Computer Science (like data structures and algorithms), statistics, chemistry, physics, philosophy, and most kinds of engineering. If you want to prove something mathematically, you need set theory.
Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume I Set Theory
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Author : Douglas Cenzer
language : en
Publisher: World Scientific
Release Date : 2020-04-04
Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume I Set Theory written by Douglas Cenzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-04 with Mathematics categories.
This book provides an introduction to axiomatic set theory and descriptive set theory. It is written for the upper level undergraduate or beginning graduate students to help them prepare for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra.The book is designed as a flexible and accessible text for a one-semester introductory course in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered throughout the text.
Conceptions Of Set And The Foundations Of Mathematics
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Author : Luca Incurvati
language : en
Publisher: Cambridge University Press
Release Date : 2020-01-23
Conceptions Of Set And The Foundations Of Mathematics written by Luca Incurvati and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-23 with History categories.
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Numbers Sets And Axioms
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Author : A. G. Hamilton
language : en
Publisher: Cambridge University Press
Release Date : 1982
Numbers Sets And Axioms written by A. G. Hamilton and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
Following the success of Logic for Mathematicians, Dr Hamilton has written a text for mathematicians and students of mathematics that contains a description and discussion of the fundamental conceptual and formal apparatus upon which modern pure mathematics relies. The author's intention is to remove some of the mystery that surrounds the foundations of mathematics. He emphasises the intuitive basis of mathematics; the basic notions are numbers and sets and they are considered both informally and formally. The role of axiom systems is part of the discussion but their limitations are pointed out. Formal set theory has its place in the book but Dr Hamilton recognises that this is a part of mathematics and not the basis on which it rests. Throughout, the abstract ideas are liberally illustrated by examples so this account should be well-suited, both specifically as a course text and, more broadly, as background reading. The reader is presumed to have some mathematical experience but no knowledge of mathematical logic is required.