Set theory Books

Random sets as models for set-valued observations, are a new type of data proving useful in areas such as survey sampling, biostatistics, and intelligent systems. This is the first text to explore the topic in depth, using extended probability theory to...

This text unites logical and philosophical aspects of set theory in a manner intelligible to mathematicians without training in formal logic and to logicians without a mathematical background. 1961 edition.

As the systems which form the fabric of modern society become more complex and more interdependent, the need for the understanding of the behavior of such systems becomes increasingly more essential. What are the causes and...

Internal logic is the logic of content. The content is here arithmetic and the emphasis is on a constructive logic of arithmetic (arithmetical logic). Kronecker's general arithmetic of forms (polynomials) together with Fermat's...

The first edition of this book, which was the first English Diophantus, appeared in 1885 and has long been out of print. It is with this in mind that the author endeavored to make accessible again the teachings contained within this rare tome. This...

Category theory abstractions are very challenging to apprehend correctly, require a steep learning curve for non-mathematicians, and, for people with traditional naïve set theory education, a paradigm shift in thinking. The book utilizes a novel approach...

An up-to-date and comprehensive account of set-oriented symbolic manipulation and automated reasoning methods. This book is of interest to graduates and researchers in theoretical computer science and computational logic and...

This CoPart is a dual complement to Visual Category Theory Brick by Brick, Part 2. The original series translated abstract categorical concepts into the language of LEGO® bricks, and the CoPart series implement the opposite way of translating brick...

Sur Les Fondements De La Theorie Des Ensembles Transfinis (1899) est un livre �����crit par Georg Cantor, math�����maticien allemand. Le livre traite de la th�����orie des ensembles et explore les concepts de nombres transfinis, d'infini et de...

Combinatory logic is a versatile field that is connected to philosophical, mathematical, and computational logic. This comprehensive reference on combinatory logic covers results in the field from the last four decades along with classical information on...

Captivate your audience and enhance your storytelling with this tutorial based 4-color cookbook, featuring dozens of solutions to your titling needs. Each chapter includes case studies and interviews with the pros, lending cutting insight and lessons...

Problems in decision making and in other areas such as pattern recogni­ tion, control, structural engineering etc. involve numerous aspects of uncertainty. Additional vagueness is introduced as models become more complex but...

The rapid development of set theory in the last fifty years, mainly by obtaining plenty of independence results, strongly influenced an understanding of the structure of the real line. This book is devoted to the study of the...

Problems in Set Theory, Mathematical Logic and the Theory of Algorithms by I. Lavrov & L. Maksimova is an English translation of the fourth edition of the most popular student problem book in mathematical logic in Russian...

This monograph, for the first time in book form, considers the large structure of metric spaces as captured by bornologies: families of subsets that contain the singletons, that are stable under finite unions, and that are stable under taking subsets of...

This introduction to mathematical logic takes Gödel's incompleteness theorem as a starting point. It goes beyond a standard text book and should interest everyone from mathematicians to philosophers and general readers who wish to understand the...

Esse livro apresenta a hist ria dos n meros complexos seguida por sua estrutura alg brica de grupo, anel e corpo, destacando o fato de n o ser um corp

Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application...

This text for advanced undergraduates and graduate students examines problems concerning convex sets in real Euclidean spaces of two or three dimensions. It illustrates the different ways in which convexity can enter into the formulation as the solution...

While intuitionistic (or constructive) set theory IST has received a certain attention from mathematical logicians, so far as I am aware no book providing a systematic introduction to the subject has yet been published. This may be the case in part...

The interactive process of sharing can be represented by the arithmetic operation commonlycalled division. It involves the separation of an object into two or more parts. When subjected toquantitative and qualitative analysis under a condition of equity...

The Art of Proving Binomial Identities accomplishes two goals: (1) It provides a unified treatment of the binomial coefficients, and (2) Brings together much of the undergraduate mathematics curriculum via one theme (the binomial coefficients). The...

A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of...

The theoretical assumptions of the following mathematical topics are presented in this book:mathematical logicset theoryfunction theoryliteral calculusproperties of powers and radicalsmonomial and polynomial calculusEach topic is covered by emphasizing...

Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein's general relativity, as he...

Set theory can be rigorously and profitably studied through an intuitive approach, thus independently of formal logic. This book is addressed to all mathematicians and tries to convince them that this intuitive approach to axiomatic set theory is not...

An Elementary Transition to Abstract Mathematics will help students move from introductory courses to those where rigor and proof play a much greater role. The text is organized into five basic parts: the first looks back on selected topics from...

Grigori Mints is one the most distinguished proof theorists ofour time. He has contributed significantly not only to thesubject in general but also to most of its applications.This collection of papers by a number of Mints' colleaguesworldwide are both a...

Fundamentals of Fuzzy Sets covers the basic elements of fuzzy set theory. Its four-part organization provides easy referencing of recent as well as older results in the field. The first part discusses the historical...

Fuzzy differential functions are applicable to real-world problems in engineering, computer science, and social science. That relevance makes for rapid development of new ideas and theories. This volume is a timely introduction to the subject that...

Först och främst är detta en vacker berättelse om en flicka som lär sig att räkna. Det visar sig dock vara så att de flesta av oss har glömt hur vi blev skickliga räknare. Få vet om att vi då...

Datenqualität, Genauigkeit bzw. Ungenauigkeit von Daten und anderen Informationen sind grundlegende Aspekte von Messungen und Beobachtungen, die quantitativ beschrieben werden müssen, um unrealistische Resultate von Analysen zu...

Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to...

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...

The concept of infinity is one of the most important, and at the same time, one of the most mysterious concepts of science. Already in antiquity many philosophers and mathematicians pondered over its contradictory nature. In...

The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. It is also viewed as a foundation of mathematics so that "to make a notion precise"...

Architecture of Mathematics describes the logical structure of Mathematics from its foundations to its real-world applications. It describes the many interweaving relationships between different areas of mathematics and its practical applications, and as...

Model theory investigates mathematical structures by means of formal languages. So-called first-order languages have proved particularly useful in this respect.This text introduces the model theory of first-order logic, avoiding syntactical issues not...

The first part of this advanced-level text covers pure set theory, and the second deals with applications and advanced topics (point set topology, real spaces, Boolean algebras, infinite combinatorics and large cardinals). 1979 edition.

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...

Introduction to Modern Set Theory is designed for aone-semester course in set theory at the advanced undergraduate or beginning graduate level. Three features are the full integration into the text of the study of models of set theory, the use of...

An Introduction to Fuzzy Logic Applications in Intelligent Systems consists of a collection of chapters written by leading experts in the field of fuzzy sets. Each chapter addresses an area where fuzzy sets have been applied...

Originally published in 1973. This book is directed to the student of philosophy whose background in mathematics is very limited. The author strikes a balance between material of a philosophical and a formal kind, and does this in a way that will bring...

Beyond calculus, the world of mathematics grows increasingly abstract and places new and challenging demands on those venturing into that realm. As the focus of calculus instruction has become increasingly computational, it leaves many students ill...

This book has a fundamental relationship to the International Seminar on Fuzzy Set Theory held each September in Linz, Austria. First, this volume is an extended account of the eleventh Seminar of 1989. Second, and more...

Classical and Fuzzy Concepts in Mathematical Logic and Applications provides a broad, thorough coverage of the fundamentals of two-valued logic, multivalued logic, and fuzzy logic.Exploring the parallels between classical and fuzzy mathematical logic,...