Problems And Theorems In Classical Set Theory
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Problems And Theorems In Classical Set Theory
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Author : Peter Komjath
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-02
Problems And Theorems In Classical Set Theory written by Peter Komjath 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 2006-05-02 with Mathematics categories.
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.
40 Puzzles And Problems In Probability And Mathematical Statistics
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Author : Wolf Schwarz
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-25
40 Puzzles And Problems In Probability And Mathematical Statistics written by Wolf Schwarz 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 2007-11-25 with Mathematics categories.
This book is based on the view that cognitive skills are best acquired by solving challenging, non-standard probability problems. Many puzzles and problems presented here are either new within a problem solving context (although as topics in fundamental research they are long known) or are variations of classical problems which follow directly from elementary concepts. A small number of particularly instructive problems is taken from previous sources which in this case are generally given. This book will be a handy resource for professors looking for problems to assign, for undergraduate math students, and for a more general audience of amateur scientists.
Exercises In Modules And Rings
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Author : T.Y. Lam
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-08
Exercises In Modules And Rings written by T.Y. Lam 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 2009-12-08 with Mathematics categories.
The idea of writing this book came roughly at the time of publication of my graduate text Lectures on Modules and Rings, Springer GTM Vol. 189, 1999. Since that time, teaching obligations and intermittent intervention of other projects caused prolonged delays in the work on this volume. Only a lucky break in my schedule in 2006 enabled me to put the finishing touches on the completion of this long overdue book. This book is intended to serve a dual purpose. First, it is designed as a "problem book" for Lectures. As such, it contains the statements and full solutions of the many exercises that appeared in Lectures. Second, this book is also offered as a reference and repository for general information in the theory of modules and rings that may be hard to find in the standard textbooks in the field. As a companion volume to Lectures, this work covers the same math ematical material as its parent work; namely, the part of ring theory that makes substantial use of the notion of modules. The two books thus share the same table of contents, with the first half treating projective, injective, and flat modules, homological and uniform dimensions, and the second half dealing with noncommutative localizations and Goldie's theorems, maximal rings of quotients, Frobenius and quasi-Frobenius rings, conclud ing with Morita's theory of category equivalences and dualities.
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.
Lectures On Real Valued Functions
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Author : Alexander Kharazishvili
language : en
Publisher: Springer Nature
Release Date : 2025-08-23
Lectures On Real Valued Functions written by Alexander Kharazishvili and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-23 with Mathematics categories.
This book offers several topics of mathematical analysis which are closely connected with significant properties of real-valued functions of various types (such as semi-continuous functions, monotone functions, convex functions, measurable functions, additive and linear functionals, etc.). Alongside with fairly traditional themes of real analysis and classical measure theory, more profound questions are thoroughly discussed in the book – appropriate extensions and restrictions of functions, oscillation functions and their characterization, discontinuous functions on resolvable topological spaces, pointwise limits of finite sums of periodic functions, some general results on invariant and quasi-invariant measures, the structure of non-measurable sets and functions, the Baire property of functions on topological spaces and its connections with measurability properties of functions, logical and set-theoretical aspects of the behavior of real-valued functions.
Introduction To Combinatorial Methods In Geometry
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Author : Alexander Kharazishvili
language : en
Publisher: CRC Press
Release Date : 2024-05-07
Introduction To Combinatorial Methods In Geometry written by Alexander Kharazishvili and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-07 with Mathematics categories.
This book offers an introduction to some combinatorial (also, set-theoretical) approaches and methods in geometry of the Euclidean space Rm. The topics discussed in the manuscript are due to the field of combinatorial and convex geometry. The author’s primary intention is to discuss those themes of Euclidean geometry which might be of interest to a sufficiently wide audience of potential readers. Accordingly, the material is explained in a simple and elementary form completely accessible to the college and university students. At the same time, the author reveals profound interactions between various facts and statements from different areas of mathematics: the theory of convex sets, finite and infinite combinatorics, graph theory, measure theory, classical number theory, etc. All chapters (and also the five Appendices) end with a number of exercises. These provide the reader with some additional information about topics considered in the main text of this book. Naturally, the exercises vary in their difficulty. Among them there are almost trivial, standard, nontrivial, rather difficult, and difficult. As a rule, more difficult exercises are marked by asterisks and are provided with necessary hints. The material presented is based on the lecture course given by the author. The choice of material serves to demonstrate the unity of mathematics and variety of unexpected interrelations between distinct mathematical branches.
Logic Colloquium 2007
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Author : Françoise Delon
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-07
Logic Colloquium 2007 written by Françoise Delon 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 2010-06-07 with Mathematics categories.
The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume, Logic Colloquium 2007, with contributions from plenary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. This volume covers many areas of contemporary logic: model theory, proof theory, set theory, and computer science, as well as philosophical logic, including tutorials on cardinal arithmetic, on Pillay's conjecture, and on automatic structures. This volume will be invaluable for experts as well as those interested in an overview of central contemporary themes in mathematical logic.
Horizons Of Combinatorics
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Author : Ervin Gyori
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-20
Horizons Of Combinatorics written by Ervin Gyori 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 2008-10-20 with Mathematics categories.
Hungarian mathematics has always been known for discrete mathematics, including combinatorial number theory, set theory and recently random structures, and combinatorial geometry. The recent volume contains high level surveys on these topics with authors mostly being invited speakers for the conference "Horizons of Combinatorics" held in Balatonalmadi, Hungary in 2006. The collection gives an overview of recent trends and results in a large part of combinatorics and related topics.
Formal Aspects Of Component Software
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Author : Farhad Arbab
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-15
Formal Aspects Of Component Software written by Farhad Arbab 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 2012-12-15 with Computers categories.
This book constitutes revised selected papers of the 8th International Workshop on Formal Aspects of Component Software, FACS 2011, held in Oslo, Norway in September 2011. The 18 full papers presented together with 3 invited talks were carefully reviewed and selected from 46 submissions. They cover the topics of formal models for software components and their interaction, design and verification methods for software components and services, formal methods and modeling languages for components and services, industrial or experience reports, and case studies, autonomic components and self-managed applications, models for QoS and other extra-functional properties (e.g., trust, compliance, security) of components and services, formal and rigorous approaches to software adaptation and self-adaptive systems, and components for real-time, safety-critical, secure, and/or embedded systems.
Logical Foundations Of Computer Science
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Author : Sergei Artemov
language : en
Publisher: Springer Nature
Release Date : 2021-12-16
Logical Foundations Of Computer Science written by Sergei Artemov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-16 with Mathematics categories.
This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2022, held in Deerfield Beach, FL, USA, in January 2022. The 23 revised full papers were carefully reviewed and selected from 35 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda and combinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple-agent system logics; logics of proof and justification; non-monotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; other logics in computer science.