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"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"--
Book Synopsis A Book of Set Theory by : Charles C Pinter
Download or read book A Book of Set Theory written by Charles C Pinter and published by Courier Corporation. This book was released on 2014-07-23 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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"--
This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.
Book Synopsis Elements of Set Theory by : Herbert B. Enderton
Download or read book Elements of Set Theory written by Herbert B. Enderton and published by Academic Press. This book was released on 1977-05-23 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.
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.
Book Synopsis Set Theory: The Structure of Arithmetic by : Norman T. Hamilton
Download or read book Set Theory: The Structure of Arithmetic written by Norman T. Hamilton and published by Courier Dover Publications. This book was released on 2018-05-16 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
What this book is about. The theory of sets is a vibrant, exciting math ematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foun dation ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "ab stract sets," including the Axiom of Choice, transfinite recursion, and car dinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning.
Book Synopsis Notes on Set Theory by : Yiannis Moschovakis
Download or read book Notes on Set Theory written by Yiannis Moschovakis and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: What this book is about. The theory of sets is a vibrant, exciting math ematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foun dation ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "ab stract sets," including the Axiom of Choice, transfinite recursion, and car dinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning.
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.
Book Synopsis Set Theory and the Continuum Hypothesis by : Paul J. Cohen
Download or read book Set Theory and the Continuum Hypothesis written by Paul J. Cohen and published by Courier Corporation. This book was released on 2008-12-09 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Written by a prominent analyst Paul. R. Halmos, this book is the most famous, popular, and widely used textbook in the subject. The book is readable for its conciseness and clear explanation. This emended edition is with completely new typesetting and corrections. Asymmetry of the book cover is due to a formal display problem. Actual books are printed symmetrically. Please look at the paperback edition for the correct image. The free PDF file available on the publisher's website www.bowwowpress.org
Book Synopsis Naive Set Theory by : Paul Halmos
Download or read book Naive Set Theory written by Paul Halmos and published by . This book was released on 2019-06 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a prominent analyst Paul. R. Halmos, this book is the most famous, popular, and widely used textbook in the subject. The book is readable for its conciseness and clear explanation. This emended edition is with completely new typesetting and corrections. Asymmetry of the book cover is due to a formal display problem. Actual books are printed symmetrically. Please look at the paperback edition for the correct image. The free PDF file available on the publisher's website www.bowwowpress.org
This book is designed for use in a one semester problem-oriented course in undergraduate set theory. The combination of level and format is somewhat unusual and deserves an explanation. Normally, problem courses are offered to graduate students or selected undergraduates. I have found, however, that the experience is equally valuable to ordinary mathematics majors. I use a recent modification of R. L. Moore's famous method developed in recent years by D. W. Cohen [1]. Briefly, in this new approach, projects are assigned to groups of students each week. With all the necessary assistance from the instructor, the groups complete their projects, carefully write a short paper for their classmates, and then, in the single weekly class meeting, lecture on their results. While the em phasis is on the student, the instructor is available at every stage to assure success in the research, to explain and critique mathematical prose, and to coach the groups in clear mathematical presentation. The subject matter of set theory is peculiarly appropriate to this style of course. For much of the book the objects of study are familiar and while the theorems are significant and often deep, it is the methods and ideas that are most important. The necessity of rea soning about numbers and sets forces students to come to grips with the nature of proof, logic, and mathematics. In their research they experience the same dilemmas and uncertainties that faced the pio neers.
Book Synopsis An Outline of Set Theory by : James M. Henle
Download or read book An Outline of Set Theory written by James M. Henle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed for use in a one semester problem-oriented course in undergraduate set theory. The combination of level and format is somewhat unusual and deserves an explanation. Normally, problem courses are offered to graduate students or selected undergraduates. I have found, however, that the experience is equally valuable to ordinary mathematics majors. I use a recent modification of R. L. Moore's famous method developed in recent years by D. W. Cohen [1]. Briefly, in this new approach, projects are assigned to groups of students each week. With all the necessary assistance from the instructor, the groups complete their projects, carefully write a short paper for their classmates, and then, in the single weekly class meeting, lecture on their results. While the em phasis is on the student, the instructor is available at every stage to assure success in the research, to explain and critique mathematical prose, and to coach the groups in clear mathematical presentation. The subject matter of set theory is peculiarly appropriate to this style of course. For much of the book the objects of study are familiar and while the theorems are significant and often deep, it is the methods and ideas that are most important. The necessity of rea soning about numbers and sets forces students to come to grips with the nature of proof, logic, and mathematics. In their research they experience the same dilemmas and uncertainties that faced the pio neers.
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.
Book Synopsis Classic Set Theory by : D.C. Goldrei
Download or read book Classic Set Theory written by D.C. Goldrei and published by Routledge. This book was released on 2017-09-06 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Presents those methods of modern set theory most applicable to other areas of pure mathematics.
Book Synopsis Set Theory for the Working Mathematician by : Krzysztof Ciesielski
Download or read book Set Theory for the Working Mathematician written by Krzysztof Ciesielski and published by Cambridge University Press. This book was released on 1997-08-28 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents those methods of modern set theory most applicable to other areas of pure mathematics.
Set theory is a branch of mathematics with a special subject matter, the infinite, but also a general framework for all modern mathematics, whose notions figure in every branch, pure and applied. This Element will offer a concise introduction, treating the origins of the subject, the basic notion of set, the axioms of set theory and immediate consequences, the set-theoretic reconstruction of mathematics, and the theory of the infinite, touching also on selected topics from higher set theory, controversial axioms and undecided questions, and philosophical issues raised by technical developments.
Book Synopsis Set Theory by : John P. Burgess
Download or read book Set Theory written by John P. Burgess and published by Cambridge University Press. This book was released on 2022-03-10 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set theory is a branch of mathematics with a special subject matter, the infinite, but also a general framework for all modern mathematics, whose notions figure in every branch, pure and applied. This Element will offer a concise introduction, treating the origins of the subject, the basic notion of set, the axioms of set theory and immediate consequences, the set-theoretic reconstruction of mathematics, and the theory of the infinite, touching also on selected topics from higher set theory, controversial axioms and undecided questions, and philosophical issues raised by technical developments.
