Introduction to Set Theory, Third Edition, Revised and Expanded

Author: Karel Hrbacek,Thomas Jech

Publisher: CRC Press

ISBN: 9780824779153

Category: Mathematics

Page: 310

View: 8337

Thoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, Introduction to Set Theory, Third Edition covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It also provides five additional self-contained chapters, consolidates the material on real numbers into a single updated chapter affording flexibility in course design, supplies end-of-section problems, with hints, of varying degrees of difficulty, includes new material on normal forms and Goodstein sequences, and adds important recent ideas including filters, ultrafilters, closed unbounded and stationary sets, and partitions.
Posted in Mathematics

A Concise Introduction to Pure Mathematics, Second Edition

Author: Martin Liebeck

Publisher: CRC Press

ISBN: 9781584885474

Category: Mathematics

Page: 224

View: 6940

A Concise Introduction to Pure Mathematics, Second Edition provides a robust bridge between high school and university mathematics, expanding upon basic topics in ways that will interest first-year students in mathematics and related fields and stimulate further study. Divided into 22 short chapters, this textbook offers a selection of exercises ranging from routine calculations to quite challenging problems. The author discusses real and complex numbers and explains how these concepts are applied in solving natural problems. He introduces topics in analysis, geometry, number theory, and combinatorics. What's New in the Second Edition: Contains extra material concerning prime numbers, forming the basis for data encryption Explores "Secret Codes" - one of today's most spectacular applications of pure mathematics Discusses Permutations and their importance in many topics in discrete mathematics The textbook allows for the design of courses with various points of emphasis, because it can be divided into four fairly independent sections related to: an introduction to number systems and analysis; theory of the integers; an introduction to discrete mathematics; and functions, relations, and countability.
Posted in Mathematics

The Shape of Space

Author: Jeffrey R. Weeks

Publisher: CRC Press

ISBN: 9780824707095

Category: Mathematics

Page: 408

View: 7310

Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.
Posted in Mathematics

Introduction to the Theory of Sets

Author: Joseph Breuer

Publisher: Courier Corporation

ISBN: 0486154874

Category: Mathematics

Page: 128

View: 8107

This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.
Posted in Mathematics

Elements of Set Theory

Author: Herbert B. Enderton

Publisher: Academic Press

ISBN: 0080570429

Category: Mathematics

Page: 279

View: 7368

This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.
Posted in Mathematics

Differential equations

introduction and qualitative theory

Author: Jane Cronin

Publisher: Marcel Dekker Inc

ISBN: 9780824768195

Category: Mathematics

Page: 372

View: 6040

Existence theorems; Linear systems; Autonomous systems; Stability; The lyapunov second method; Periodic solutions; Bifurcation and branching of periodic solutions.
Posted in Mathematics

Set Theory for the Working Mathematician

Author: Krzysztof Ciesielski

Publisher: Cambridge University Press

ISBN: 9780521594653

Category: Mathematics

Page: 236

View: 3753

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

Classical Descriptive Set Theory

Author: Alexander Kechris

Publisher: Springer Science & Business Media

ISBN: 1461241901

Category: Mathematics

Page: 404

View: 6532

Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.
Posted in Mathematics

Discovering Modern Set Theory: The basics

Author: Winfried Just,Martin Weese

Publisher: American Mathematical Soc.

ISBN: 0821802666

Category: Mathematics

Page: 210

View: 6817

This book is an introduction to set theory for beginning graduate students who want to get a sound grounding in those aspects of set theory used extensively throughout other areas of mathematics. Topics covered include formal languages and models, the power and limitation of the Axiomatic Method, the Axiom of Choice, including the fascinating Banach-Tarski Paradox, applications of Zorn's Lemma, ordinal arithmetic, including transfinite induction, and cardinal arithmetic. The style of writing, more a dialogue with the reader than that of the Master indoctrinating the pupil, makes this also very suitable for self-study.
Posted in Mathematics

Introduction to Modern Cryptography, Second Edition

Author: Jonathan Katz,Yehuda Lindell

Publisher: CRC Press

ISBN: 146657027X

Category: Computers

Page: 603

View: 6503

Cryptography is ubiquitous and plays a key role in ensuring data secrecy and integrity as well as in securing computer systems more broadly. Introduction to Modern Cryptography provides a rigorous yet accessible treatment of this fascinating subject. The authors introduce the core principles of modern cryptography, with an emphasis on formal definitions, clear assumptions, and rigorous proofs of security. The book begins by focusing on private-key cryptography, including an extensive treatment of private-key encryption, message authentication codes, and hash functions. The authors also present design principles for widely used stream ciphers and block ciphers including RC4, DES, and AES, plus provide provable constructions of stream ciphers and block ciphers from lower-level primitives. The second half of the book covers public-key cryptography, beginning with a self-contained introduction to the number theory needed to understand the RSA, Diffie-Hellman, and El Gamal cryptosystems (and others), followed by a thorough treatment of several standardized public-key encryption and digital signature schemes. Integrating a more practical perspective without sacrificing rigor, this widely anticipated Second Edition offers improved treatment of: Stream ciphers and block ciphers, including modes of operation and design principles Authenticated encryption and secure communication sessions Hash functions, including hash-function applications and design principles Attacks on poorly implemented cryptography, including attacks on chained-CBC encryption, padding-oracle attacks, and timing attacks The random-oracle model and its application to several standardized, widely used public-key encryption and signature schemes Elliptic-curve cryptography and associated standards such as DSA/ECDSA and DHIES/ECIES Containing updated exercises and worked examples, Introduction to Modern Cryptography, Second Edition can serve as a textbook for undergraduate- or graduate-level courses in cryptography, a valuable reference for researchers and practitioners, or a general introduction suitable for self-study.
Posted in Computers

Intermediate set theory

Author: Frank Robert Drake,Dasharath Singh

Publisher: John Wiley & Sons Inc

ISBN: 9780471964940

Category: Mathematics

Page: 234

View: 4896

The authors cover first order logic and the main topics of set theory in a clear mathematical style with sensible philosophical discussion. The emphasis is on presenting the use of set theory in various areas of mathematics, with particular attention paid to introducing axiomatic set theory, showing how the axioms are needed in mathematical practice and how they arise. Other areas introduced include the axiom of choice, filters and ideals. Exercises are provided which are suitable for both beginning students and degree-level students.
Posted in Mathematics

Mathematical Models in Population Biology and Epidemiology

Author: Fred Brauer,Dawn Bies

Publisher: Springer Science & Business Media

ISBN: 1475735162

Category: Science

Page: 417

View: 3649

The goal of this book is to search for a balance between simple and analyzable models and unsolvable models which are capable of addressing important questions on population biology. Part I focusses on single species simple models including those which have been used to predict the growth of human and animal population in the past. Single population models are, in some sense, the building blocks of more realistic models -- the subject of Part II. Their role is fundamental to the study of ecological and demographic processes including the role of population structure and spatial heterogeneity -- the subject of Part III. This book, which will include both examples and exercises, is of use to practitioners, graduate students, and scientists working in the field.
Posted in Science

Introduction to Modern Set Theory

Author: Judith Roitman

Publisher: John Wiley & Sons

ISBN: 9780471635192

Category: Mathematics

Page: 156

View: 1352

This is modern set theory from the ground up--from partial orderings and well-ordered sets to models, infinite cobinatorics and large cardinals. The approach is unique, providing rigorous treatment of basic set-theoretic methods, while integrating advanced material such as independence results, throughout. The presentation incorporates much interesting historical material and no background in mathematical logic is assumed. Treatment is self-contained, featuring theorem proofs supported by diagrams, examples and exercises. Includes applications of set theory to other branches of mathematics.
Posted in Mathematics

Introduction to Mathematical Logic, Fourth Edition

Author: Elliott Mendelson

Publisher: CRC Press

ISBN: 9780412808302

Category: Mathematics

Page: 440

View: 8191

The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them. Introduction to Mathematical Logic includes: propositional logic first-order logic first-order number theory and the incompleteness and undecidability theorems of Gödel, Rosser, Church, and Tarski axiomatic set theory theory of computability The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.
Posted in Mathematics

Invariant Descriptive Set Theory

Author: Su Gao

Publisher: CRC Press

ISBN: 9781584887942

Category: Mathematics

Page: 392

View: 2388

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 concepts, methods, and results of this theory. It brings together techniques from various areas of mathematics, such as algebra, topology, and logic, which have diverse applications to other fields. After reviewing classical and effective descriptive set theory, the text studies Polish groups and their actions. It then covers Borel reducibility results on Borel, orbit, and general definable equivalence relations. The author also provides proofs for numerous fundamental results, such as the Glimm–Effros dichotomy, the Burgess trichotomy theorem, and the Hjorth turbulence theorem. The next part describes connections with the countable model theory of infinitary logic, along with Scott analysis and the isomorphism relation on natural classes of countable models, such as graphs, trees, and groups. The book concludes with applications to classification problems and many benchmark equivalence relations. By illustrating the relevance of invariant descriptive set theory to other fields of mathematics, this self-contained book encourages readers to further explore this very active area of research.
Posted in Mathematics

Ordinary Differential Equations

Introduction and Qualitative Theory, Third Edition

Author: Jane Cronin

Publisher: CRC Press

ISBN: 1420014935

Category: Mathematics

Page: 408

View: 7054

Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of nonlinear equations. Requiring only a background in advanced calculus and linear algebra, the text is appropriate for advanced undergraduate and graduate students in mathematics, engineering, physics, chemistry, or biology. This third edition of a highly acclaimed textbook provides a detailed account of the Bendixson theory of solutions of two-dimensional nonlinear autonomous equations, which is a classical subject that has become more prominent in recent biological applications. By using the Poincaré method, it gives a unified treatment of the periodic solutions of perturbed equations. This includes the existence and stability of periodic solutions of perturbed nonautonomous and autonomous equations (bifurcation theory). The text shows how topological degree can be applied to extend the results. It also explains that using the averaging method to seek such periodic solutions is a special case of the use of the Poincaré method.
Posted in Mathematics

Stochastic Processes

From Applications to Theory

Author: Pierre Del Moral,Spiridon Penev

Publisher: CRC Press

ISBN: 1498701841

Category: Mathematics

Page: 916

View: 2184

Unlike traditional books presenting stochastic processes in an academic way, this book includes concrete applications that students will find interesting such as gambling, finance, physics, signal processing, statistics, fractals, and biology. Written with an important illustrated guide in the beginning, it contains many illustrations, photos and pictures, along with several website links. Computational tools such as simulation and Monte Carlo methods are included as well as complete toolboxes for both traditional and new computational techniques.
Posted in Mathematics

Financial Modelling with Jump Processes

Author: Peter Tankov

Publisher: CRC Press

ISBN: 1135437947

Category: Mathematics

Page: 552

View: 8489

WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematical tools required for applications can be intimidating. Potential users often get the impression that jump and Lévy processes are beyond their reach. Financial Modelling with Jump Processes shows that this is not so. It provides a self-contained overview of the theoretical, numerical, and empirical aspects involved in using jump processes in financial modelling, and it does so in terms within the grasp of nonspecialists. The introduction of new mathematical tools is motivated by their use in the modelling process, and precise mathematical statements of results are accompanied by intuitive explanations. Topics covered in this book include: jump-diffusion models, Lévy processes, stochastic calculus for jump processes, pricing and hedging in incomplete markets, implied volatility smiles, time-inhomogeneous jump processes and stochastic volatility models with jumps. The authors illustrate the mathematical concepts with many numerical and empirical examples and provide the details of numerical implementation of pricing and calibration algorithms. This book demonstrates that the concepts and tools necessary for understanding and implementing models with jumps can be more intuitive that those involved in the Black Scholes and diffusion models. If you have even a basic familiarity with quantitative methods in finance, Financial Modelling with Jump Processes will give you a valuable new set of tools for modelling market fluctuations.
Posted in Mathematics

Phase Transformations in Metals and Alloys, Third Edition (Revised Reprint)

Author: David A. Porter,Kenneth E. Easterling

Publisher: CRC Press

ISBN: 9780748757411

Category: Technology & Engineering

Page: 528

View: 6957

In the decade since the first edition of this popular text was published, the metallurgical field has undergone rapid developments in many sectors. Nonetheless, the underlying principles governing these developments remain the same. A textbook that presents these advances within the context of the fundamentals is greatly needed by instructors in the field Phase Transformations in Metals and Alloys, Second Edition maintains the simplicity that undergraduate instructors and students have come to appreciate while updating and expanding coverage of recently developed methods and materials. The book is effectively divided into two parts. The beginning chapters contain the background material necessary for understanding phase transformations - thermodynamics, kinetics, diffusion theory and the structure and properties of interfaces. The following chapters deal with specific transformations - solidification, diffusional transformation in solids and diffusionless transformation. Case studies of engineering alloys are incorporated to provide a link between theory and practice. New additions include an extended list of further reading at the end of each chapter and a section containing complete solutions to all exercises in the book Designed for final year undergraduate and postgraduate students of metallurgy, materials science, or engineering materials, this is an ideal textbook for both students and instructors.
Posted in Technology & Engineering

Sets, Functions, and Logic

An Introduction to Abstract Mathematics, Third Edition

Author: Keith Devlin

Publisher: CRC Press

ISBN: 1482286025

Category: Mathematics

Page: 160

View: 4435

Keith Devlin. You know him. You've read his columns in MAA Online, you've heard him on the radio, and you've seen his popular mathematics books. In between all those activities and his own research, he's been hard at work revising Sets, Functions and Logic, his standard-setting text that has smoothed the road to pure mathematics for legions of undergraduate students. Now in its third edition, Devlin has fully reworked the book to reflect a new generation. The narrative is more lively and less textbook-like. Remarks and asides link the topics presented to the real world of students' experience. The chapter on complex numbers and the discussion of formal symbolic logic are gone in favor of more exercises, and a new introductory chapter on the nature of mathematics--one that motivates readers and sets the stage for the challenges that lie ahead. Students crossing the bridge from calculus to higher mathematics need and deserve all the help they can get. Sets, Functions, and Logic, Third Edition is an affordable little book that all of your transition-course students not only can afford, but will actually read...and enjoy...and learn from. About the Author Dr. Keith Devlin is Executive Director of Stanford University's Center for the Study of Language and Information and a Consulting Professor of Mathematics at Stanford. He has written 23 books, one interactive book on CD-ROM, and over 70 published research articles. He is a Fellow of the American Association for the Advancement of Science, a World Economic Forum Fellow, and a former member of the Mathematical Sciences Education Board of the National Academy of Sciences,. Dr. Devlin is also one of the world's leading popularizers of mathematics. Known as "The Math Guy" on NPR's Weekend Edition, he is a frequent contributor to other local and national radio and TV shows in the US and Britain, writes a monthly column for the Web journal MAA Online, and regularly writes on mathematics and computers for the British newspaper The Guardian.
Posted in Mathematics