On Sets Not Belonging To Algebras Of Subsets

Author : Leonid Š. Grinblat
Publisher : American Mathematical Soc.
Page : 111 pages
File Size : 45,6 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821825419

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On Sets Not Belonging to Algebras of Subsets by Leonid Š. Grinblat Pdf

The main results of this work can be formulated in such an elementary way that it is likely to attract mathematicians from a broad spectrum of specialties, though its main audience will likely be combintorialists, set-theorists, and topologists. The central question is this: Suppose one is given an at most countable family of algebras of subsets of some fixed set such that, for each algebra, there exists at least one set that is not a member of that algebra. Can one then assert that there is a set that is not a member of any of the algebras? Although such a set clearly exists in the case of one or two algebras, it is very easy to construct an example of three algebras for which no such set can be found. Grinblat's principal concern is to determine conditions that, if imposed on the algebras, will insure the existence of a set not belonging to any of them. If the given family of algebras is finite, one arrives at a purely combinatorial problem for a finite set of ultrafilters. If the family is countably infinite, however, one needs not only combinatorics of ultrafilters but also set theory and general topology.

Author : MADHUMANGAL PAL
Publisher : PHI Learning Pvt. Ltd.
Page : 631 pages
File Size : 48,5 Mb
Release : 2013-04-02
Category : Mathematics
ISBN : 9788120347373

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ADVANCED ALGEBRA by MADHUMANGAL PAL Pdf

Intended for the undergraduate students of mathematics, this student-friendly text provides a complete coverage of all topics of Linear, Abstract and Boolean Algebra. The text discusses the matrix and determinants, Cramer’s rule, Vandermonde determinants, vector spaces, inner product space, Jacobi’s theorem, linear transformation, eigenvalues and eigenvectors. Besides, set theory, relations and functions, inclusion and exclusion principle, group, subgroup, semigroup, ring, integral domain, field theories, Boolean algebra and its applications have also been covered thoroughly. Each concept is supported by a large number of illustrations and 600 worked-out examples that help students understand the concepts in a clear way. Besides, MCQs and practice exercises are also provided at the end of each chapter with their answers to reinforce the students’ skill.

Author : Igor R. Shafarevich
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642563256

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Discourses on Algebra by Igor R. Shafarevich Pdf

Using various examples this monograph shows that algebra is one of the most beautiful forms of mathematics. In doing so, it explains the basics of algebra, number theory, set theory and probability. The text presupposes very limited knowledge of mathematics, making it an ideal read for anybody new to the subject. The author, I.R. Shafarevich, is well-known across the world as one of the most outstanding mathematicians of this century as well as one of the most respected mathematical writers.

Author : American Mathematical Society
Publisher : Unknown
Page : 852 pages
File Size : 55,8 Mb
Release : 1992
Category : Mathematics
ISBN : UCSD:31822015782311

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Notices of the American Mathematical Society by American Mathematical Society Pdf

Author : Nicholas Loehr
Publisher : CRC Press
Page : 619 pages
File Size : 43,7 Mb
Release : 2014-04-10
Category : Mathematics
ISBN : 9781466559028

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Advanced Linear Algebra by Nicholas Loehr Pdf

Designed for advanced undergraduate and beginning graduate students in linear or abstract algebra, Advanced Linear Algebra covers theoretical aspects of the subject, along with examples, computations, and proofs. It explores a variety of advanced topics in linear algebra that highlight the rich interconnections of the subject to geometry, algebra,

Author : Thierry Vialar
Publisher : BoD - Books on Demand
Page : 1134 pages
File Size : 42,5 Mb
Release : 2016-12-07
Category : Mathematics
ISBN : 9782955199046

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Handbook of Mathematics by Thierry Vialar Pdf

The book, revised, consists of XI Parts and 28 Chapters covering all areas of mathematics. It is a tool for students, scientists, engineers, students of many disciplines, teachers, professionals, writers and also for a general reader with an interest in mathematics and in science. It provides a wide range of mathematical concepts, definitions, propositions, theorems, proofs, examples, and numerous illustrations. The difficulty level can vary depending on chapters, and sustained attention will be required for some. The structure and list of Parts are quite classical: I. Foundations of Mathematics, II. Algebra, III. Number Theory, IV. Geometry, V. Analytic Geometry, VI. Topology, VII. Algebraic Topology, VIII. Analysis, IX. Category Theory, X. Probability and Statistics, XI. Applied Mathematics. Appendices provide useful lists of symbols and tables for ready reference. Extensive cross-references allow readers to find related terms, concepts and items (by page number, heading, and objet such as theorem, definition, example, etc.). The publisher’s hope is that this book, slightly revised and in a convenient format, will serve the needs of readers, be it for study, teaching, exploration, work, or research.

Author : Tsutomu Sasao,Jon T. Butler
Publisher : Morgan & Claypool Publishers
Page : 123 pages
File Size : 48,6 Mb
Release : 2014-11-01
Category : Technology & Engineering
ISBN : 9781627056502

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Applications of Zero-Suppressed Decision Diagrams by Tsutomu Sasao,Jon T. Butler Pdf

A zero-suppressed decision diagram (ZDD) is a data structure to represent objects that typically contain many zeros. Applications include combinatorial problems, such as graphs, circuits, faults, and data mining. This book consists of four chapters on the applications of ZDDs. The first chapter by Alan Mishchenko introduces the ZDD. It compares ZDDs to BDDs, showing why a more compact representation is usually achieved in a ZDD. The focus is on sets of subsets and on sum-of-products (SOP) expressions. Methods to generate all the prime implicants (PIs), and to generate irredundant SOPs are shown. A list of papers on the applications of ZDDs is also presented. In the appendix, ZDD procedures in the CUDD package are described. The second chapter by Tsutomu Sasao shows methods to generate PIs and irredundant SOPs using a divide and conquer method. This chapter helps the reader to understand the methods presented in the first chapter. The third chapter by Shin-Ichi Minato introduces the "frontier-based" method that efficiently enumerates certain subsets of a graph. The final chapter by Shinobu Nagayama shows a method to match strings of characters. This is important in routers, for example, where one must match the address information of an internet packet to the proprer output port. It shows that ZDDs are more compact than BDDs in solving this important problem. Each chapter contains exercises, and the appendix contains their solutions. Table of Contents: Preface / Acknowledgments / Introduction to Zero-Suppressed Decision Diagrams / Efficient Generation of Prime Implicants and Irredundant Sum-of-Products Expressions / The Power of Enumeration--BDD/ZDD-Based Algorithms for Tackling Combinatorial Explosion / Regular Expression Matching Using Zero-Suppressed Decision Diagrams / Authors' and Editors' Biographies / Index

Author : Vlastimil Dlab,Kenneth S Williams
Publisher : World Scientific
Page : 452 pages
File Size : 50,5 Mb
Release : 2020-06-09
Category : Mathematics
ISBN : 9789811219993

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Invitation To Algebra: A Resource Compendium For Teachers, Advanced Undergraduate Students And Graduate Students In Mathematics by Vlastimil Dlab,Kenneth S Williams Pdf

This book presents a compendium style account of a comprehensive mathematical journey from Arithmetic to Algebra. It contains material that is helpful to graduate and advanced undergraduate students in mathematics, university and college professors teaching mathematics, as well as some mathematics teachers teaching in the final year of high school. A successful teacher must know more than what a particular course curriculum asks for. A number of topics that are missing in present-day textbooks, and which may be attractive to students at the graduate or advanced undergraduate level in mathematics, for example, continued fractions, arithmetic progressions of higher order, complex numbers in plane geometry, differential schemes, path semigroups and path algebras, have been carefully presented. This reflects the aim of the book to attract students to mathematics.

Author : Luca Spadafora,Gennady P Berman
Publisher : World Scientific Publishing Company
Page : 224 pages
File Size : 52,7 Mb
Release : 2017-04-27
Category : Business & Economics
ISBN : 9789813202498

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Theoretical Foundations for Quantitative Finance by Luca Spadafora,Gennady P Berman Pdf

This book provides simple introduction to quantitative finance for students and junior quants who want to approach the typical industry problems with practical but rigorous ambition. It shows a simple link between theoretical technicalities and practical solutions. Mathematical aspects are discussed from a practitioner perspective, with a deep focus on practical implications, favoring the intuition and the imagination. In addition, the new post-crisis paradigms, like multi-curves, x-value adjustments (xVA) and Counterparty Credit Risk are also discussed in a very simple framework. Finally, real world data and numerical simulations are compared in order to provide a reader with a simple and handy insight on the actual model performances. Request Inspection Copy Contents:IntroductionAll the Financial Math You Need to Survive with Interesting ApplicationsThe Pricing of Financial Derivatives — The Replica ApproachRisk-Neutral PricingThe Black and Scholes Framework and Its ExtensionRisk ModelingThe New Post-Crisis Paradigms Readership: Students and researchers in the fields of quantitative finance, risk management and stochastic analysis.

Author : Paul Halmos,Steven Givant
Publisher : American Mathematical Soc.
Page : 141 pages
File Size : 44,8 Mb
Release : 2019-01-30
Category : Mathematics
ISBN : 9781470451660

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Logic as Algebra by Paul Halmos,Steven Givant Pdf

Here is an introduction to modern logic that differs from others by treating logic from an algebraic perspective. What this means is that notions and results from logic become much easier to understand when seen from a familiar standpoint of algebra. The presentation, written in the engaging and provocative style that is the hallmark of Paul Halmos, from whose course the book is taken, is aimed at a broad audience, students, teachers and amateurs in mathematics, philosophy, computer science, linguistics and engineering; they all have to get to grips with logic at some stage. All that is needed.

Author : Anthony N. Michel,Charles J. Herget
Publisher : Courier Corporation
Page : 514 pages
File Size : 40,7 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 9780486675985

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Applied Algebra and Functional Analysis by Anthony N. Michel,Charles J. Herget Pdf

"A valuable reference." — American Scientist. Excellent graduate-level treatment of set theory, algebra and analysis for applications in engineering and science. Fundamentals, algebraic structures, vector spaces and linear transformations, metric spaces, normed spaces and inner product spaces, linear operators, more. A generous number of exercises have been integrated into the text. 1981 edition.

Author : José M. Amigó,María J. Cánovas,Marco A. López-Cerdá,Manuel López-Pellicer
Publisher : Springer Nature
Page : 273 pages
File Size : 52,7 Mb
Release : 2023-07-01
Category : Mathematics
ISBN : 9783031300141

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Functional Analysis and Continuous Optimization by José M. Amigó,María J. Cánovas,Marco A. López-Cerdá,Manuel López-Pellicer Pdf

The book includes selected contributions presented at the "International Meeting on Functional Analysis and Continuous Optimization" held in Elche (Spain) on June 16–17, 2022. Its contents cover very recent results in functional analysis, continuous optimization and the interplay between these disciplines. Therefore, this book showcases current research on functional analysis and optimization with individual contributions, as well as new developments in both areas. As a result, the reader will find useful information and stimulating ideas.

Author : Stephan Foldes
Publisher : John Wiley & Sons
Page : 368 pages
File Size : 49,7 Mb
Release : 1994-03-31
Category : Mathematics
ISBN : 0471571806

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Fundamental Structures of Algebra and Discrete Mathematics by Stephan Foldes Pdf

Introduces and clarifies the basic theories of 12 structural concepts, offering a fundamental theory of groups, rings and other algebraic structures. Identifies essentials and describes interrelationships between particular theories. Selected classical theorems and results relevant to current research are proved rigorously within the theory of each structure. Throughout the text the reader is frequently prompted to perform integrated exercises of verification and to explore examples.

Author : Reena Garg
Publisher : KHANNA BOOK PUBLISHING CO. PVT. LTD.
Page : 596 pages
File Size : 50,9 Mb
Release : 2021-11-01
Category : Mathematics
ISBN : 9789391505172

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MATHEMATICS - I (Calculus and Linear Algebra) For Non-Computer Science Engineering Branches | AICTE Prescribed Textbook - English by Reena Garg Pdf

Calculus, Multivariable Calculus and Linear Algebra covers all the Modules prescribed by AICTE. Model curriculum to all the 1st year students (except CSE) studying in engineering institutions and universities of the country. It serves as both text book and / or useful reference work. It contains 5 units which include calculus, matrices, sequences & series and multivariable calculus along with their applications. This renowned and well respected title provides in one handy volume with the essential mathematical tools that helps in understanding the subject and problem solving techniques with many real life engineering applications. As per trademark of AICTE, this book is in student friendly style, author has endeavored enormous efforts in providing numerous solved examples and exercise under each topic to facilitate better understanding of the concepts to the students. Majority of Questions in this book have been designed to success the reader understands of the subject. Professionals or those who are preparing for competitive examinations will also find this book very useful. This book will give the students a complete grasp of the mathematical skills that are needed by engineers all over the country. Some Salient Features of the Book: · In depth coverage of all related, essential and mentioned topics as per AICTE in simple presentation with clarity and accuracy. · Emphasis on the applications of concepts and theorems. · Core concepts are presented through a large number of solved graded model examples in an innovative and lucid manner. · A good number of relatively competitive problems are given at the end of each unit in the form of short questions, HOTS, assignments, MCQs and know more for student’s practices purpose. Practical /Projects/ Activity also given in each unit for enhancing the student’s capability, to increase the feeling of team work. · To clarify the subject, the text has been supplemented through Notes, Observations and Remarks; an attempt has been made to explain the topic through maximum use of geometries wherever possible. · Some standard problems with sufficient hints have been included in each exercise to gauge the student’s visual understanding and for grasp the theory. · Video links, interesting facts, uses of ICT also included after each topic in every unit for easy understanding of the readers. Also included the pictorial representations of many topics for fast and permanent grasping of the content.

Author : Daniela Calvetti,Erkki Somersalo
Publisher : SIAM
Page : 181 pages
File Size : 45,8 Mb
Release : 2022-11-30
Category : Mathematics
ISBN : 9781611977400

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The Less Is More Linear Algebra of Vector Spaces and Matrices by Daniela Calvetti,Erkki Somersalo Pdf

Designed for a proof-based course on linear algebra, this rigorous and concise textbook intentionally introduces vector spaces, inner products, and vector and matrix norms before Gaussian elimination and eigenvalues so students can quickly discover the singular value decomposition (SVD)—arguably the most enlightening and useful of all matrix factorizations. Gaussian elimination is then introduced after the SVD and the four fundamental subspaces and is presented in the context of vector spaces rather than as a computational recipe. This allows the authors to use linear independence, spanning sets and bases, and the four fundamental subspaces to explain and exploit Gaussian elimination and the LU factorization, as well as the solution of overdetermined linear systems in the least squares sense and eigenvalues and eigenvectors. This unique textbook also includes examples and problems focused on concepts rather than the mechanics of linear algebra. The problems at the end of each chapter that and in an associated website encourage readers to explore how to use the notions introduced in the chapter in a variety of ways. Additional problems, quizzes, and exams will be posted on an accompanying website and updated regularly. The Less Is More Linear Algebra of Vector Spaces and Matrices is for students and researchers interested in learning linear algebra who have the mathematical maturity to appreciate abstract concepts that generalize intuitive ideas. The early introduction of the SVD makes the book particularly useful for those interested in using linear algebra in applications such as scientific computing and data science. It is appropriate for a first proof-based course in linear algebra.