Discovering Modern Set Theory Ii Set Theoretic Tools For Every Mathematician
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Discovering Modern Set Theory Ii Set Theoretic Tools For Every Mathematician
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Author : Winfried Just
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Discovering Modern Set Theory Ii Set Theoretic Tools For Every Mathematician written by Winfried Just and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This is the second volume of a two-volume graduate text in set theory. The first volume covered the basics of modern set theory and was addressed primarily to beginning graduate students. The second volume is intended as a bridge between introductory set theory courses such as the first volume and advanced monographs that cover selected branches of set theory. The authors give short but rigorous introductions to set-theoretic concepts and techniques such as trees, partition calculus, cardinal invariants of the continuum, Martin's Axiom, closed unbounded and stationary sets, the Diamond Principle, and the use of elementary submodels. Great care is taken to motivate concepts and theorems presented.
Discovering Modern Set Theory Ii Set Theoretic Tools For Every Mathematician
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Author : Winfried Just and Martin Weese
language : en
Publisher: American Mathematical Soc.
Release Date :
Discovering Modern Set Theory Ii Set Theoretic Tools For Every Mathematician written by Winfried Just and Martin Weese and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
The second in a two-volume text for a graduate course or self- study in set theory. Volume I would be the best prerequisite, but any background would suffice that supplied a basic naive and axiomatic knowledge of set theory, and some knowledge of mathematical logic and general topology. Introduces various set- theory techniques that have been fertile applied in other fields. Bibliographic references are minimal. The member price is $29. Annotation copyrighted by Book News, Inc., Portland, OR
Discovering Modern Set Theory I The Basics
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Author : Winfried Just
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Discovering Modern Set Theory I The Basics written by Winfried Just and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This book bridges the gap between the many elementary introductions to set theory that are available today and the more advanced, specialized monographs. The authors have taken great care to motivate concepts as they are introduced. The large number of exercises included make this book especially suitable for self-study. Students are guided towards their own discoveries in a lighthearted, yet rigorous manner.
Fundamentals Of Mathematical Logic
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Author : Peter G. Hinman
language : en
Publisher: CRC Press
Release Date : 2018-10-08
Fundamentals Of Mathematical Logic written by Peter G. Hinman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-08 with Mathematics categories.
This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.
Key Concepts In Discrete Mathematics
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Author : Udayan Bhattacharya
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Key Concepts In Discrete Mathematics written by Udayan Bhattacharya and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Key Concepts in Discrete Mathematics" offers a comprehensive introduction to the fascinating realm of discrete mathematics, covering a diverse array of topics essential for students and professionals in computer science, mathematics, engineering, and related fields. Through clear explanations, illustrative examples, and engaging exercises, we provide readers with a solid foundation in discrete mathematics and its practical applications. Our book covers a wide range of topics, from fundamental concepts like sets, relations, and functions to advanced topics such as graph theory, combinatorics, and algorithm analysis. We present complex concepts in a clear and accessible manner, with detailed explanations and step-by-step examples guiding readers through each topic. We emphasize practical applications and real-world examples that demonstrate the relevance of discrete mathematics in various fields, including computer science, cryptography, network theory, and optimization. Abundant exercises and problems, ranging from basic to challenging, allow readers to practice and reinforce their understanding of key concepts and techniques. Additional online resources, including solutions to selected exercises, interactive quizzes, and supplementary materials, enhance the learning experience and provide opportunities for further exploration. Whether used as a textbook in a classroom setting or as a self-study guide, "Key Concepts in Discrete Mathematics" serves as an invaluable resource for students seeking to deepen their understanding and for educators and professionals interested in exploring this essential area of mathematics.
Almost Free Modules
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Author : P.C. Eklof
language : en
Publisher: Elsevier
Release Date : 2002-04-29
Almost Free Modules written by P.C. Eklof and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-29 with Mathematics categories.
This book provides a comprehensive exposition of the use of set-theoretic methods in abelian group theory, module theory, and homological algebra, including applications to Whitehead's Problem, the structure of Ext and the existence of almost-free modules over non-perfect rings. This second edition is completely revised and udated to include major developments in the decade since the first edition. Among these are applications to cotorsion theories and covers, including a proof of the Flat Cover Conjecture, as well as the use of Shelah's pcf theory to constuct almost free groups. As with the first edition, the book is largely self-contained, and designed to be accessible to both graduate students and researchers in both algebra and logic. They will find there an introduction to powerful techniques which they may find useful in their own work.
Introduction To The Mathematics Of Finance
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Author : R. J. Williams
language : en
Publisher: American Mathematical Society
Release Date : 2021-09-14
Introduction To The Mathematics Of Finance written by R. J. Williams and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-14 with Mathematics categories.
The modern subject of mathematical finance has undergone considerable development, both in theory and practice, since the seminal work of Black and Scholes appeared a third of a century ago. This book is intended as an introduction to some elements of the theory that will enable students and researchers to go on to read more advanced texts and research papers. The book begins with the development of the basic ideas of hedging and pricing of European and American derivatives in the discrete (i.e., discrete time and discrete state) setting of binomial tree models. Then a general discrete finite market model is introduced, and the fundamental theorems of asset pricing are proved in this setting. Tools from probability such as conditional expectation, filtration, (super)martingale, equivalent martingale measure, and martingale representation are all used first in this simple discrete framework. This provides a bridge to the continuous (time and state) setting, which requires the additional concepts of Brownian motion and stochastic calculus. The simplest model in the continuous setting is the famous Black-Scholes model, for which pricing and hedging of European and American derivatives are developed. The book concludes with a description of the fundamental theorems for a continuous market model that generalizes the simple Black-Scholes model in several directions.
Basic Set Theory
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Author : Nikolai Konstantinovich Vereshchagin
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Basic Set Theory written by Nikolai Konstantinovich Vereshchagin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
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.
A Modern Theory Of Integration
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Author : Robert G. Bartle
language : en
Publisher: American Mathematical Society
Release Date : 2024-10-25
A Modern Theory Of Integration written by Robert G. Bartle and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-25 with Mathematics categories.
The theory of integration is one of the twin pillars on which analysis is built. The first version of integration that students see is the Riemann integral. Later, graduate students learn that the Lebesgue integral is ?better? because it removes some restrictions on the integrands and the domains over which we integrate. However, there are still drawbacks to Lebesgue integration, for instance, dealing with the Fundamental Theorem of Calculus, or with ?improper? integrals. This book is an introduction to a relatively new theory of the integral (called the ?generalized Riemann integral? or the ?Henstock-Kurzweil integral?) that corrects the defects in the classical Riemann theory and both simplifies and extends the Lebesgue theory of integration. Although this integral includes that of Lebesgue, its definition is very close to the Riemann integral that is familiar to students from calculus. One virtue of the new approach is that no measure theory and virtually no topology is required. Indeed, the book includes a study of measure theory as an application of the integral. Part 1 fully develops the theory of the integral of functions defined on a compact interval. This restriction on the domain is not necessary, but it is the case of most interest and does not exhibit some of the technical problems that can impede the reader's understanding. Part 2 shows how this theory extends to functions defined on the whole real line. The theory of Lebesgue measure from the integral is then developed, and the author makes a connection with some of the traditional approaches to the Lebesgue integral. Thus, readers are given full exposure to the main classical results. The text is suitable for a first-year graduate course, although much of it can be readily mastered by advanced undergraduate students. Included are many examples and a very rich collection of exercises. There are partial solutions to approximately one-third of the exercises. A complete solutions manual is available separately.
A Course In Operator Theory
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Author : John B. Conway
language : en
Publisher: American Mathematical Society
Release Date : 2025-05-01
A Course In Operator Theory written by John B. Conway and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-01 with Mathematics categories.
Operator theory is a significant part of many important areas of modern mathematics: functional analysis, differential equations, index theory, representation theory, mathematical physics, and more. This text covers the central themes of operator theory, presented with the excellent clarity and style that readers have come to associate with Conway's writing. Early chapters introduce and review material on $C^*$-algebras, normal operators, compact operators, and non-normal operators. Some of the major topics covered are the spectral theorem, the functional calculus, and the Fredholm index. In addition, some deep connections between operator theory and analytic functions are presented. Later chapters cover more advanced topics, such as representations of $C^*$-algebras, compact perturbations, and von Neumann algebras. Major results, such as the Sz.–Nagy Dilation Theorem, the Weyl–von Neumann–Berg Theorem, and the classification of von Neumann algebras, are covered, as is a treatment of Fredholm theory. The last chapter gives an introduction to reflexive subspaces, which along with hyperreflexive spaces, are one of the more successful episodes in the modern study of asymmetric algebras. Professor Conway's authoritative treatment makes this a compelling and rigorous course text, suitable for graduate students who have had a standard course in functional analysis.