## Basic Set Theory

**Author**: Nikolai Konstantinovich Vereshchagin,Alexander Shen

**Publisher:**American Mathematical Soc.

**ISBN:**0821827316

**Category:**Mathematics

**Page:**116

**View:**7812

**DOWNLOAD NOW »**

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 dedicated treatment. This book provides just that in the form of 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.

## The Discrete Math Workbook

*A Companion Manual for Practical Study*

**Author**: Sergei Kurgalin,Sergei Borzunov

**Publisher:**Springer

**ISBN:**3319926454

**Category:**Computers

**Page:**485

**View:**1461

**DOWNLOAD NOW »**

This practically-oriented textbook presents an accessible introduction to discrete mathematics through a substantial collection of classroom-tested exercises. Each chapter opens with concise coverage of the theory underlying the topic, reviewing the basic concepts and establishing the terminology, as well as providing the key formulae and instructions on their use. This is then followed by a detailed account of the most common problems in the area, before the reader is invited to practice solving such problems for themselves through a varied series of questions and assignments. Topics and features: provides an extensive set of exercises and examples of varying levels of complexity, suitable for both laboratory practical training and self-study; offers detailed solutions to many problems, applying commonly-used methods and computational schemes; introduces the fundamentals of mathematical logic, the theory of algorithms, Boolean algebra, graph theory, sets, relations, functions, and combinatorics; presents more advanced material on the design and analysis of algorithms, including asymptotic analysis, and parallel algorithms; includes reference lists of trigonometric and finite summation formulae in an appendix, together with basic rules for differential and integral calculus. This hands-on study guide is designed to address the core needs of undergraduate students training in computer science, informatics, and electronic engineering, emphasizing the skills required to develop and implement an algorithm in a specific programming language.

## Moscow Mathematical Olympiads, 1993-1999

**Author**: Roman Mikhaĭlovich Fedorov,Silvio Levy

**Publisher:**American Mathematical Soc.

**ISBN:**0821853635

**Category:**Mathematics

**Page:**220

**View:**718

**DOWNLOAD NOW »**

The Moscow Mathematical Olympiad has been challenging high school students with stimulating, original problems of different degrees of difficulty for over 75 years. The problems are nonstandard; solving them takes wit, thinking outside the box, and, sometimes, hours of contemplation. Some are within the reach of most mathematically competent high school students, while others are difficult even for a mathematics professor. Many mathematically inclined students have found that tackling these problems, or even just reading their solutions, is a great way to develop mathematical insight. In 2006 the Moscow Center for Continuous Mathematical Education began publishing a collection of problems from the Moscow Mathematical Olympiads, providing for each an answer (and sometimes a hint) as well as one or more detailed solutions. This volume represents the years 1993-1999. The problems and the accompanying material are well suited for math circles. They are also appropriate for problem-solving classes and practice for regional and national mathematics competitions. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

## Moscow Mathematical Olympiads, 2000-2005

**Author**: Roman Vasilʹevich Fedorov,Silvio Levy,Alexander Kovaldzhi,Ivan Yashchenko

**Publisher:**American Mathematical Soc.

**ISBN:**082186906X

**Category:**Mathematics

**Page:**176

**View:**9377

**DOWNLOAD NOW »**

The Moscow Mathematical Olympiad has been challenging high school students with stimulating, original problems of different degrees of difficulty for over 75 years. The problems are nonstandard; solving them takes wit, thinking outside the box, and, sometimes, hours of contemplation. Some are within the reach of most mathematically competent high school students, while others are difficult even for a mathematics professor. Many mathematically inclined students have found that tackling these problems, or even just reading their solutions, is a great way to develop mathematical insight. In 2006 the Moscow Center for Continuous Mathematical Education began publishing a collection of problems from the Moscow Mathematical Olympiads, providing for each an answer (and sometimes a hint) as well as one or more detailed solutions. This volume represents the years 2000-2005. The problems and the accompanying material are well suited for math circles. They are also appropriate for problem-solving classes and practice for regional and national mathematics competitions. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

## Infinite Dimensional Analysis

*A Hitchhiker's Guide*

**Author**: Charalambos D. Aliprantis,Kim C. Border

**Publisher:**Springer Science & Business Media

**ISBN:**3540295879

**Category:**Business & Economics

**Page:**704

**View:**8718

**DOWNLOAD NOW »**

What you’ll find in this monograph is nothing less than a complete and rigorous study of modern functional analysis. It is intended for the student or researcher who could benefit from functional analytic methods, but who does not have an extensive background in the subject and does not plan to make a career as a functional analyst. It develops the topological structures in connection with a number of topic areas such as measure theory, convexity, and Banach lattices, as well as covering the analytic approach to Markov processes. Many of the results were previously available only in works scattered throughout the literature.

## Naive Mengenlehre

**Author**: Paul R. Halmos

**Publisher:**Vandenhoeck & Ruprecht

**ISBN:**9783525405277

**Category:**Arithmetic

**Page:**132

**View:**1594

**DOWNLOAD NOW »**

## Naive Set Theory

**Author**: P. R. Halmos

**Publisher:**Springer Science & Business Media

**ISBN:**1475716451

**Category:**Mathematics

**Page:**104

**View:**4891

**DOWNLOAD NOW »**

Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book contains my answer to that question. The purpose of the book is to tell the beginning student of advanced mathematics the basic set theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds. From this point of view the concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here. Scholarly bibliographical credits and references are out of place in a purely expository book such as this one. The student who gets interested in set theory for its own sake should know, however, that there is much more to the subject than there is in this book. One of the most beautiful sources of set-theoretic wisdom is still Hausdorff's Set theory. A recent and highly readable addition to the literature, with an extensive and up-to-date bibliography, is Axiomatic set theory by Suppes.

## Basic Set Theory

**Author**: Azriel Levy

**Publisher:**Courier Corporation

**ISBN:**0486150739

**Category:**Mathematics

**Page:**416

**View:**2818

**DOWNLOAD NOW »**

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.

## The Joy of Sets

*Fundamentals of Contemporary Set Theory*

**Author**: Keith Devlin

**Publisher:**Springer Science & Business Media

**ISBN:**9780387940946

**Category:**Mathematics

**Page:**194

**View:**3415

**DOWNLOAD NOW »**

This text covers the parts of contemporary set theory relevant to other areas of pure mathematics. After a review of "naïve" set theory, it develops the Zermelo-Fraenkel axioms of the theory before discussing the ordinal and cardinal numbers. It then delves into contemporary set theory, covering such topics as the Borel hierarchy and Lebesgue measure. A final chapter presents an alternative conception of set theory useful in computer science.

## Basic Discrete Mathematics

*Logic, Set Theory, and Probability*

**Author**: Richard Kohar

**Publisher:**World Scientific Publishing Company

**ISBN:**9814730416

**Category:**Mathematics

**Page:**732

**View:**8502

**DOWNLOAD NOW »**

This lively introductory text exposes the student in the humanities to the world of discrete mathematics. A problem-solving based approach grounded in the ideas of George Pólya are at the heart of this book. Students learn to handle and solve new problems on their own. A straightforward, clear writing style and well-crafted examples with diagrams invite the students to develop into precise and critical thinkers. Particular attention has been given to the material that some students find challenging, such as proofs. This book illustrates how to spot invalid arguments, to enumerate possibilities, and to construct probabilities. It also presents case studies to students about the possible detrimental effects of ignoring these basic principles. The book is invaluable for a discrete and finite mathematics course at the freshman undergraduate level or for self-study since there are full solutions to the exercises in an appendix. "Written with clarity, humor and relevant real-world examples, Basic Discrete Mathematics is a wonderful introduction to discrete mathematical reasoning."- Arthur Benjamin, Professor of Mathematics at Harvey Mudd College, and author of The Magic of Math

## Set Theory for the Working Mathematician

**Author**: Krzysztof Ciesielski,None

**Publisher:**Cambridge University Press

**ISBN:**9780521594653

**Category:**Mathematics

**Page:**236

**View:**4933

**DOWNLOAD NOW »**

Presents those methods of modern set theory most applicable to other areas of pure mathematics.

## Differentialgeometrie

*Kurven - Flächen - Mannigfaltigkeiten*

**Author**: Wolfgang Kühnel

**Publisher:**Springer-Verlag

**ISBN:**3834896551

**Category:**Mathematics

**Page:**280

**View:**5413

**DOWNLOAD NOW »**

Dieses Buch ist eine Einführung in die Differentialgeometrie. Zunächst geht es um die klassischen Aspekte wie die Geometrie von Kurven und Flächen, bevor dann höherdimensionale Flächen sowie abstrakte Mannigfaltigkeiten betrachtet werden. Die Nahtstelle ist dabei das zentrale Kapitel "Die innere Geometrie von Flächen". Dieses führt den Leser bis hin zu dem berühmten Satz von Gauß-Bonnet, der ein entscheidendes Bindeglied zwischen lokaler und globaler Geometrie darstellt. Die zweite Hälfte des Buches ist der Riemannschen Geometrie gewidmet. Den Abschluss bildet ein Kapitel über "Einstein-Räume", die eine große Bedeutung sowohl in der "Reinen Mathematik" als auch in der Allgemeinen Relativitätstheorie von A. Einstein haben. Es wird großer Wert auf Anschaulichkeit gelegt, was durch zahlreiche Abbildungen unterstützt wird. Im Laufe der Neuauflagen wurde der Text erweitert, neue Aufgaben wurden hinzugefügt und am Ende des Buches wurden zusätzliche Hinweise zur Lösung der Übungsaufgaben ergänzt. Der Text wurde für die fünfte Auflage gründlich durchgesehen und an einigen Stellen verbessert.

## Axiomatic Set Theory

**Author**: Patrick Suppes

**Publisher:**Courier Corporation

**ISBN:**0486136876

**Category:**Mathematics

**Page:**265

**View:**329

**DOWNLOAD NOW »**

Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.

## Elementary Set Theory, Part I

**Author**: K.T. Leung,Doris Lai-chue Chen

**Publisher:**Hong Kong University Press

**ISBN:**9789622090132

**Category:**Mathematics

**Page:**80

**View:**2931

**DOWNLOAD NOW »**

This book provides students of mathematics with the minimum amount of knowledge in logic and set theory needed for a profitable continuation of their studies. There is a chapter on statement calculus, followed by eight chapters on set theory.

## Set Theory, Logic and Their Limitations

**Author**: Moshe Machover

**Publisher:**Cambridge University Press

**ISBN:**9780521479981

**Category:**Mathematics

**Page:**288

**View:**5311

**DOWNLOAD NOW »**

Rigorous coverage of logic and set theory for students of mathematics and philosophy.

## A Course on Set Theory

**Author**: Ernest Schimmerling

**Publisher:**Cambridge University Press

**ISBN:**1139501488

**Category:**Mathematics

**Page:**N.A

**View:**4059

**DOWNLOAD NOW »**

Set theory is the mathematics of infinity and part of the core curriculum for mathematics majors. This book blends theory and connections with other parts of mathematics so that readers can understand the place of set theory within the wider context. Beginning with the theoretical fundamentals, the author proceeds to illustrate applications to topology, analysis and combinatorics, as well as to pure set theory. Concepts such as Boolean algebras, trees, games, dense linear orderings, ideals, filters and club and stationary sets are also developed. Pitched specifically at undergraduate students, the approach is neither esoteric nor encyclopedic. The author, an experienced instructor, includes motivating examples and over 100 exercises designed for homework assignments, reviews and exams. It is appropriate for undergraduates as a course textbook or for self-study. Graduate students and researchers will also find it useful as a refresher or to solidify their understanding of basic set theory.

## A First Course in Mathematical Logic and Set Theory

**Author**: Michael L. O'Leary

**Publisher:**John Wiley & Sons

**ISBN:**0470905883

**Category:**Mathematics

**Page:**464

**View:**6109

**DOWNLOAD NOW »**

Rather than teach mathematics and the structure of proofssimultaneously, this book first introduces logic as the foundationof proofs and then demonstrates how logic applies to mathematicaltopics. This method ensures that readers gain a firmunderstanding of how logic interacts with mathematics and empowersthem to solve more complex problems. The study of logic andapplications is used throughout to prepare readers for further workin proof writing. Readers are first introduced tomathematical proof-writing, and then the book provides anoverview of symbolic logic that includes two-column logicproofs. Readers are then transitioned to set theory andinduction, and applications of number theory, relations, functions,groups, and topology are provided to further aid incomprehension. Topical coverage includes propositional logic,predicate logic, set theory, mathematical induction, number theory,relations, functions, group theory, and topology.

## Principia Mathematica.

**Author**: Alfred North Whitehead,Bertrand Russell

**Publisher:**N.A

**ISBN:**N.A

**Category:**Logic, Symbolic and mathematical

**Page:**167

**View:**421

**DOWNLOAD NOW »**

## Mathematical Methods in Linguistics

**Author**: Barbara B.H. Partee,A.G. ter Meulen,R. Wall

**Publisher:**Springer Science & Business Media

**ISBN:**9789027722454

**Category:**Language Arts & Disciplines

**Page:**666

**View:**3176

**DOWNLOAD NOW »**

Elementary set theory accustoms the students to mathematical abstraction, includes the standard constructions of relations, functions, and orderings, and leads to a discussion of the various orders of infinity. The material on logic covers not only the standard statement logic and first-order predicate logic but includes an introduction to formal systems, axiomatization, and model theory. The section on algebra is presented with an emphasis on lattices as well as Boolean and Heyting algebras. Background for recent research in natural language semantics includes sections on lambda-abstraction and generalized quantifiers. Chapters on automata theory and formal languages contain a discussion of languages between context-free and context-sensitive and form the background for much current work in syntactic theory and computational linguistics. The many exercises not only reinforce basic skills but offer an entry to linguistic applications of mathematical concepts. For upper-level undergraduate students and graduate students in theoretical linguistics, computer-science students with interests in computational linguistics, logic programming and artificial intelligence, mathematicians and logicians with interests in linguistics and the semantics of natural language.

## The Geometry of Moduli Spaces of Sheaves

*A Publication of the Max-Planck-Institut für Mathematik, Bonn*

**Author**: Daniel Huybrechts,Manfred Lehn

**Publisher:**Vieweg+Teubner Verlag

**ISBN:**9783663116257

**Category:**Technology & Engineering

**Page:**270

**View:**7872

**DOWNLOAD NOW »**

This book is intended to serve as an introduction to the theory of semistable sheaves and at the same time to provide a survey of recent research results on the geometry of moduli spaces. The first part introduces the basic concepts in the theory: Hilbert polynomial, slope, stability, Harder-Narasimhan filtration, Grothendieck's Quot-scheme. It presents detailed proofs of the Grauert-Mülich Theorem, the Bogomolov Inequality, the semistability of tensor products, and the boundedness of the family of semistable sheaves. It also gives a self-contained account of the construction of moduli spaces of semistable sheaves on a projective variety à la Gieseker, Maruyama, and Simpson. The second part presents some of the recent results of the geometry of moduli spaces of sheaves on an algebraic surface, following work of Mukai, O'Grady, Gieseker, Li and many others. In particular, moduli spaces of sheaves on K3 surfaces and determinant line bundles on the moduli spaces are treated in some detail. Other topics include the Serre correspondence, restriction of stable bundles to curves, symplectic structures, irreducibility and Kodaira-dimension of moduli spaces.