Author: Iain Adamson
Publisher: Springer Science & Business Media
ISBN: 0817681388
Category : Mathematics
Languages : en
Pages : 145
Book Description
This book is a companion to A general topology workbook published by Birkhiiuser last year. In an ideal world the order of publication would have been reversed, for the notation and some of the results of the present book are used in the topology book and on the other hand (the reader may be assured) no topology is used here. Both books share the word Workbook in their titles. They are based on the principle that for at least some branches of mathematics a good way for a student to learn is to be presented with a clear statement of the definitions of the terms with which the subject is concerned and then to be faced with a collection of problems involving the terms just defined. In adopting this approach with my Dundee students of set theory and general topology I found it best not to differentiate too precisely between simple illustrative examples, easy exercises and results which in conventional textbooks would be labelled as Theorems.
A Set Theory Workbook
Author: Iain Adamson
Publisher: Springer Science & Business Media
ISBN: 0817681388
Category : Mathematics
Languages : en
Pages : 145
Book Description
This book is a companion to A general topology workbook published by Birkhiiuser last year. In an ideal world the order of publication would have been reversed, for the notation and some of the results of the present book are used in the topology book and on the other hand (the reader may be assured) no topology is used here. Both books share the word Workbook in their titles. They are based on the principle that for at least some branches of mathematics a good way for a student to learn is to be presented with a clear statement of the definitions of the terms with which the subject is concerned and then to be faced with a collection of problems involving the terms just defined. In adopting this approach with my Dundee students of set theory and general topology I found it best not to differentiate too precisely between simple illustrative examples, easy exercises and results which in conventional textbooks would be labelled as Theorems.
Publisher: Springer Science & Business Media
ISBN: 0817681388
Category : Mathematics
Languages : en
Pages : 145
Book Description
This book is a companion to A general topology workbook published by Birkhiiuser last year. In an ideal world the order of publication would have been reversed, for the notation and some of the results of the present book are used in the topology book and on the other hand (the reader may be assured) no topology is used here. Both books share the word Workbook in their titles. They are based on the principle that for at least some branches of mathematics a good way for a student to learn is to be presented with a clear statement of the definitions of the terms with which the subject is concerned and then to be faced with a collection of problems involving the terms just defined. In adopting this approach with my Dundee students of set theory and general topology I found it best not to differentiate too precisely between simple illustrative examples, easy exercises and results which in conventional textbooks would be labelled as Theorems.
A Book of Set Theory
Author: Charles C Pinter
Publisher: Courier Corporation
ISBN: 0486497089
Category : Mathematics
Languages : en
Pages : 259
Book Description
"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--
Publisher: Courier Corporation
ISBN: 0486497089
Category : Mathematics
Languages : en
Pages : 259
Book Description
"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--
Classic Set Theory
Author: D.C. Goldrei
Publisher: Routledge
ISBN: 1351460609
Category : Mathematics
Languages : en
Pages : 300
Book Description
Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbersDefining natural numbers in terms of setsThe potential paradoxes in set theoryThe Zermelo-Fraenkel axioms for set theoryThe axiom of choiceThe arithmetic of ordered setsCantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.
Publisher: Routledge
ISBN: 1351460609
Category : Mathematics
Languages : en
Pages : 300
Book Description
Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbersDefining natural numbers in terms of setsThe potential paradoxes in set theoryThe Zermelo-Fraenkel axioms for set theoryThe axiom of choiceThe arithmetic of ordered setsCantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.
Basic Set Theory
Author: Nikolai Konstantinovich Vereshchagin
Publisher: American Mathematical Soc.
ISBN: 0821827316
Category : Mathematics
Languages : en
Pages : 130
Book Description
The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in courses on analysis, algebra, or topology, even though it is sufficiently important, interesting, and simple to merit its own leisurely treatment. This book provides just that: a leisurely exposition for a diversified audience. It is suitable for a broad range of readers, from undergraduate students to professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma. The text introduces all main subjects of ``naive'' (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject.
Publisher: American Mathematical Soc.
ISBN: 0821827316
Category : Mathematics
Languages : en
Pages : 130
Book Description
The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in courses on analysis, algebra, or topology, even though it is sufficiently important, interesting, and simple to merit its own leisurely treatment. This book provides just that: a leisurely exposition for a diversified audience. It is suitable for a broad range of readers, from undergraduate students to professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma. The text introduces all main subjects of ``naive'' (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject.
Problems and Theorems in Classical Set Theory
Author: Peter Komjath
Publisher: Springer Science & Business Media
ISBN: 0387362193
Category : Mathematics
Languages : en
Pages : 492
Book Description
This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of mathematics, including algebra, combinatorics, topology and real analysis. Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution.
Publisher: Springer Science & Business Media
ISBN: 0387362193
Category : Mathematics
Languages : en
Pages : 492
Book Description
This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of mathematics, including algebra, combinatorics, topology and real analysis. Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution.
A Stroll Through Cecily's Sets
Author: Joshua Cook
Publisher:
ISBN: 9781073606276
Category :
Languages : en
Pages : 32
Book Description
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.
Publisher:
ISBN: 9781073606276
Category :
Languages : en
Pages : 32
Book Description
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 the Continuum Hypothesis
Author: Paul J. Cohen
Publisher: Courier Corporation
ISBN: 0486469212
Category : Mathematics
Languages : en
Pages : 196
Book Description
This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.
Publisher: Courier Corporation
ISBN: 0486469212
Category : Mathematics
Languages : en
Pages : 196
Book Description
This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.
Set Theory: The Structure of Arithmetic
Author: Norman T. Hamilton
Publisher: Courier Dover Publications
ISBN: 0486830470
Category : Mathematics
Languages : en
Pages : 289
Book Description
This text is formulated on the fundamental idea that much of mathematics, including the classical number systems, can best be based on set theory. 1961 edition.
Publisher: Courier Dover Publications
ISBN: 0486830470
Category : Mathematics
Languages : en
Pages : 289
Book Description
This text is formulated on the fundamental idea that much of mathematics, including the classical number systems, can best be based on set theory. 1961 edition.
Set Theory and its Philosophy
Author: Michael Potter
Publisher: Clarendon Press
ISBN: 0191556432
Category : Philosophy
Languages : en
Pages : 362
Book Description
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
Publisher: Clarendon Press
ISBN: 0191556432
Category : Philosophy
Languages : en
Pages : 362
Book Description
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
Set Theory for the Working Mathematician
Author: Krzysztof Ciesielski
Publisher: Cambridge University Press
ISBN: 9780521594653
Category : Mathematics
Languages : en
Pages : 256
Book Description
Presents those methods of modern set theory most applicable to other areas of pure mathematics.
Publisher: Cambridge University Press
ISBN: 9780521594653
Category : Mathematics
Languages : en
Pages : 256
Book Description
Presents those methods of modern set theory most applicable to other areas of pure mathematics.