A Set Theory Workbook
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A Set Theory Workbook
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Author : Iain Adamson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-10
A Set Theory Workbook written by Iain Adamson 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 2012-09-10 with Mathematics categories.
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
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Author : Charles C Pinter
language : en
Publisher: Courier Corporation
Release Date : 2014-07-23
A Book Of Set Theory written by Charles C Pinter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-23 with Mathematics categories.
"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"--
An Outline Of Set Theory
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Author : James M. Henle
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
An Outline Of Set Theory written by James M. Henle 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 2012-12-06 with Mathematics categories.
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.
Set Theory The Structure Of Arithmetic
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Author : Norman T. Hamilton
language : en
Publisher: Courier Dover Publications
Release Date : 2018-05-16
Set Theory The Structure Of Arithmetic written by Norman T. Hamilton and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-16 with Mathematics categories.
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.
Introduction To The Theory Of Sets
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Author : Joseph Breuer
language : en
Publisher: Courier Corporation
Release Date : 2012-08-09
Introduction To The Theory Of Sets written by Joseph Breuer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-09 with Mathematics categories.
This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.
Set Theory And The Continuum Hypothesis
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Author : Paul J. Cohen
language : en
Publisher: Courier Corporation
Release Date : 2008-12-09
Set Theory And The Continuum Hypothesis written by Paul J. Cohen and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-09 with Mathematics categories.
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.
Classic Set Theory
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Author : D.C. Goldrei
language : en
Publisher: Routledge
Release Date : 2017-09-06
Classic Set Theory written by D.C. Goldrei and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-06 with Mathematics categories.
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
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Author : Azriel Levy
language : en
Publisher: Courier Corporation
Release Date : 2012-06-11
Basic Set Theory written by Azriel Levy and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-11 with Mathematics categories.
Although this book deals with basic set theory (in general, it stops short of areas where model-theoretic methods are used) on a rather advanced level, it does it at an unhurried pace. This enables the author to pay close attention to interesting and important aspects of the topic that might otherwise be skipped over. Written for upper-level undergraduate and graduate students, the book is divided into two parts. The first covers pure set theory, including the basic notions, order and well-foundedness, cardinal numbers, the ordinals, and the axiom of choice and some of its consequences. The second part deals with applications and advanced topics, among them a review of point set topology, the real spaces, Boolean algebras, and infinite combinatorics and large cardinals. A helpful appendix deals with eliminability and conservation theorems, while numerous exercises supply additional information on the subject matter and help students test their grasp of the material. 1979 edition. 20 figures.
A General Topology Workbook
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Author : Iain T. Adamson
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-11-29
A General Topology Workbook written by Iain T. Adamson 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 1995-11-29 with Mathematics categories.
This book has been called a Workbook to make it clear from the start that it is not a conventional textbook. Conventional textbooks proceed by giving in each section or chapter first the definitions of the terms to be used, the concepts they are to work with, then some theorems involving these terms (complete with proofs) and finally some examples and exercises to test the readers' understanding of the definitions and the theorems. Readers of this book will indeed find all the conventional constituents--definitions, theorems, proofs, examples and exercises but not in the conventional arrangement. In the first part of the book will be found a quick review of the basic definitions of general topology interspersed with a large num ber of exercises, some of which are also described as theorems. (The use of the word Theorem is not intended as an indication of difficulty but of importance and usefulness. ) The exercises are deliberately not "graded"-after all the problems we meet in mathematical "real life" do not come in order of difficulty; some of them are very simple illustrative examples; others are in the nature of tutorial problems for a conven tional course, while others are quite difficult results. No solutions of the exercises, no proofs of the theorems are included in the first part of the book-this is a Workbook and readers are invited to try their hand at solving the problems and proving the theorems for themselves.
Handbook Of Set Theory
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Author : Matthew Foreman
language : en
Publisher: Springer
Release Date : 2010-02-05
Handbook Of Set Theory written by Matthew Foreman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-05 with Mathematics categories.
Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.