The Banach-Tarski Paradox is a most striking mathematical construction: it asserts that a solid ball can be taken apart into finitely many pieces that can be rearranged using rigid motions to form a ball twice as large. This volume explores the cons…
Proofs play a central role in advanced mathematics and theoretical computer science, yet many students struggle the first time they take a course in which proofs play a significant role. This bestselling text's third edition helps students transitio…
The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic,…
The breathtakingly rapid pace of change in computing makes it easy to overlook the pioneers who began it all. The Universal Computer: The Road from Leibniz to Turing explores the fascinating lives, ideas, and discoveries of seven remarkable mathemat…
The authors have written an introduction to logic taking Goedel's incompleteness theorem as a starting point. The book should interest everyone from mathematicians to philosophers and readers who wish to understand the foundations and limitations of…
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…
Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, Third Edition, offers an overview of the basic ideas and results of Hilbert space theory and functional analysis. It acquaints students with the…
"Among the many expositions of Goedel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzen gives careful, non-technical explanations both of what those theorems say and, more importantly, w…
Accessible to all students with a sound background in high school mathematics, A Concise Introduction to Pure Mathematics, Fourth Edition presents some of the most fundamental and beautiful ideas in pure mathematics. It covers not only standard mate…
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart.Potter offers a thorough account of cardinal a…
A comprehensive philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and…
Take an apple and cut it into five pieces. Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as…
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 applica…
'Rings, Fields and Groups' gives a stimulating and unusual introduction to the results, methods and ideas now commonly studied on abstract algebra courses at undergraduate level. The author provides a mixture of informal and formal material which he…
Few mathematical results capture the imagination like Georg Cantor's groundbreaking work on infinity in the late nineteenth century. This opened the door to an intricate axiomatic theory of sets which was born in the decades that followed. Written f…
This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory,. It provides an exposition of some of the most important results in set theory obtained in the 20th c…
One of the greatest revolutions in mathematics occurred when Georg Cantor (1845-1918) promulgated his theory of transfinite sets. This revolution is the subject of Joseph Dauben's important studythe most thorough yet writtenof the philosopher and ma…
The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and t…
In this innovative approach to the practice of social science, Charles Ragin explores the use of fuzzy sets to bridge the divide between quantitative and qualitative methods. Paradoxically, the fuzzy set is a powerful tool because it replaces an unw…
This classic by one of the twentieth century's most prominent mathematicians offers a concise introduction to set theory. Suitable for advanced undergraduates and graduate students in mathematics, it employs the language and notation of informal mat…
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 an…
Probability and Measure Theory, Second Edition, is a text for a graduate-level course in probability that includes essential background topics in analysis. It provides extensive coverage of conditional probability and expectation, strong laws of lar…
Proofs 101: An Introduction to Formal Mathematics serves as an introduction to proofs for mathematics majors who have completed the calculus sequence (at least Calculus I and II) and a first course in linear algebra. The book prepares students for t…
For propositional logic it can be decided whether a formula has a deduction from a finite set of other formulas. This volume begins with a method to decide this for the quantified formulas of those fragments of arithmetic which express the propertie…
At the beginning of the 1990s research started in how to combine soft comput ing with reconfigurable hardware in a quite unique way. One of the methods that was developed has been called evolvable hardware. Thanks to evolution ary algorithms researc…
Presents Results from a Very Active Area of Research Exploring an active area of mathematics that studies the complexity of equivalence relations and classification problems, Invariant Descriptive Set Theory presents an introduction to the basic con…
Fuzzy hardware developments have been a major force driving the applications of fuzzy set theory and fuzzy logic in both science and engineering. This volume provides the reader with a comprehensive up-to-date look at recent works describing new inn…
Defines the class of cycle-free partial orders (CFPOs), and analyzes the CFPOs fulfilling a natural transitivity assumption, called $k$-connected set transitivity ($k$-$CS$-transitivity). This work generalizes Droste's classification of the countabl…
Over the years, this book has become a standard reference and guide in the set theory community. It provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of c…
This is a revised and expanded edition of a successful graduate and reference text. The book is designed for a standard graduate course on probability theory, including some important applications. The new edition offers a detailed treatment of the…
A superb text on the fundamentals of Lebesgue measure and integration. This book is designed to give the reader a solid understanding of Lebesgue measure and integration. It focuses on only the most fundamental concepts, namely Lebesgue measure for…
Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance for many applications in computer science or engineering. This book gives a comprehensive…
This volume presents the lecture notes of short courses given by three leading experts in mathematical logic at the 2012 Asian Initiative for Infinity Logic Summer School. The major topics cover set-theoretic forcing, higher recursion theory, and ap…
Software reuse approaches are known to enable considerable effort and cost savings during the development of a group of software systems with a significant overlap in functionality. In practice, however, the need for systematic reuse often becomes a…
The Elements of Advanced Mathematics, Fourth Edition is the latest edition of the author's bestselling series of texts. Expanding on previous editions, the new Edition continues to provide students with a better understanding of proofs, a core conce…
This volume, which ten years ago appeared as the first in the acclaimed series Lecture Notes in Logic, serves as an introduction to recursion theory. The fundamental concept of recursion makes the idea of computability accessible to a mathematical a…
This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating ho…
In this monograph, questions of extensions and relaxations are consid ered. These questions arise in many applied problems in connection with the operation of perturbations. In some cases, the operation of "small" per turbations generates "small" de…
This collection of articles, originating from a short course held at the University of Manchester, explores the ideas behind Pila's proof of the Andre-Oort conjecture for products of modular curves. The basic strategy has three main ingredients: the…
Fuzzy Sets in Decision Analysis, Operations Research and Statistics includes chapters on fuzzy preference modeling, multiple criteria analysis, ranking and sorting methods, group decision-making and fuzzy game theory. It also presents optimization t…
This book constitutes the thoroughly refereed post-proceedings of the Second International Conference on Rough Sets and Current Trends in Computing, RSCTC 2000, held in Banff, Canada in October 2000. The 80 revised papers presented together with an…
In this book the authors present their research into the foundations of the theory of Polish groups and the associated orbit equivalence relations. The particular case of locally compact groups has long been studied in many areas of mathematics. Non…
This monograph includes expanded selected papers presented in the "Workshop on the Future Directions of Fuzzy Theory and Systems". It contains many recent developments in the field and provides valuable insights into the future direction and applica…
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. Thi…
A Concrete Introduction to Analysis, Second Edition offers a major reorganization of the previous edition with the goal of making it a much more comprehensive and accessible for students. The standard, austere approach to teaching modern mathematics…
Designed to work as a reference and as a supplement to an advanced course on dynamical systems, this book presents a self-contained and comprehensive account of modern smooth ergodic theory. Among other things, this provides a rigorous mathematical…
This monograph covers the recent major advances in various areas of set theory. From the reviews:"One of the classical textbooks and reference books in set theory....The present 'Third Millennium' edition...is a whole new book. In three parts the au…
This introduction to fuzzy set theory and its multitude of applications seeks to balance the character of the book with the dynamic nature of the research. This edition includes new chapters on possibility theory, fuzzy logic and approximate reasoni…