Algebra Mathematical Logic Number Theory Topology

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Algebra Mathematical Logic Number Theory Topology

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Author : Ivan Matveevich Vinogradov
language : en
Publisher: American Mathematical Soc.
Release Date : 1986

Algebra Mathematical Logic Number Theory Topology written by Ivan Matveevich Vinogradov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Algebra categories.

Collection of papers on the current research in algebra, mathematical logic, number theory and topology.

Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume I Set Theory Second Edition

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Author : Douglas Cenzer
language : en
Publisher: World Scientific
Release Date : 2025-01-10

Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume I Set Theory Second Edition written by Douglas Cenzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-10 with Mathematics categories.

This book presents both axiomatic and descriptive set theory, targeting upper-level undergraduate and beginning graduate students. It aims to equip them for advanced studies in set theory, mathematical logic, and other mathematical fields, including analysis, topology, and algebra.The book is designed as a flexible and accessible text for a one-semester introductory in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered through the text.This new edition includes additional topics on trees, ordinal functions, and sets, along with numerous new exercises. The presentation has been improved, and several typographical errors have been corrected.

Pure Mathematics For Beginners

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Author : Steve Warner
language : en
Publisher:
Release Date : 2018-09-25

Pure Mathematics For Beginners written by Steve Warner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-25 with categories.

Pure Mathematics for Beginners Pure Mathematics for Beginners consists of a series of lessons in Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra. The 16 lessons in this book cover basic through intermediate material from each of these 8 topics. In addition, all the proofwriting skills that are essential for advanced study in mathematics are covered and reviewed extensively. Pure Mathematics for Beginners is perfect for professors teaching an introductory college course in higher mathematics high school teachers working with advanced math students students wishing to see the type of mathematics they would be exposed to as a math major. The material in this pure math book includes: 16 lessons in 8 subject areas. A problem set after each lesson arranged by difficulty level. A complete solution guide is included as a downloadable PDF file. Pure Math Book Table Of Contents (Selected) Here's a selection from the table of contents: Introduction Lesson 1 - Logic: Statements and Truth Lesson 2 - Set Theory: Sets and Subsets Lesson 3 - Abstract Algebra: Semigroups, Monoids, and Groups Lesson 4 - Number Theory: Ring of Integers Lesson 5 - Real Analysis: The Complete Ordered Field of Reals Lesson 6 - Topology: The Topology of R Lesson 7 - Complex Analysis: The field of Complex Numbers Lesson 8 - Linear Algebra: Vector Spaces Lesson 9 - Logic: Logical Arguments Lesson 10 - Set Theory: Relations and Functions Lesson 11 - Abstract Algebra: Structures and Homomorphisms Lesson 12 - Number Theory: Primes, GCD, and LCM Lesson 13 - Real Analysis: Limits and Continuity Lesson 14 - Topology: Spaces and Homeomorphisms Lesson 15 - Complex Analysis: Complex Valued Functions Lesson 16 - Linear Algebra: Linear Transformations

Basic Category Theory

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Author : Tom Leinster
language : en
Publisher: Cambridge University Press
Release Date : 2014-07-24

Basic Category Theory written by Tom Leinster and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-24 with Mathematics categories.

A short introduction ideal for students learning category theory for the first time.

Categorical Foundations

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Author : Maria Cristina Pedicchio
language : en
Publisher: Cambridge University Press
Release Date : 2004

Categorical Foundations written by Maria Cristina Pedicchio and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

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The Mathematics Of Logic

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Author : Richard W. Kaye
language : en
Publisher: Cambridge University Press
Release Date : 2007-07-12

The Mathematics Of Logic written by Richard W. Kaye and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-12 with Mathematics categories.

This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with König's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theory and nonstandard analysis.

Algorithmic Algebraic Number Theory

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Author : M. Pohst
language : en
Publisher: Cambridge University Press
Release Date : 1997-09-25

Algorithmic Algebraic Number Theory written by M. Pohst and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-09-25 with Mathematics categories.

Now in paperback, this classic book is addresssed to all lovers of number theory. On the one hand, it gives a comprehensive introduction to constructive algebraic number theory, and is therefore especially suited as a textbook for a course on that subject. On the other hand many parts go beyond an introduction an make the user familliar with recent research in the field. For experimental number theoreticians new methods are developed and new results are obtained which are of great importance for them. Both computer scientists interested in higher arithmetic and those teaching algebraic number theory will find the book of value.

Mathematics Of Fuzzy Sets

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Author : Ulrich Höhle
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Mathematics Of Fuzzy Sets written by Ulrich Höhle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory is a major attempt to provide much-needed coherence for the mathematics of fuzzy sets. Much of this book is new material required to standardize this mathematics, making this volume a reference tool with broad appeal as well as a platform for future research. Fourteen chapters are organized into three parts: mathematical logic and foundations (Chapters 1-2), general topology (Chapters 3-10), and measure and probability theory (Chapters 11-14). Chapter 1 deals with non-classical logics and their syntactic and semantic foundations. Chapter 2 details the lattice-theoretic foundations of image and preimage powerset operators. Chapters 3 and 4 lay down the axiomatic and categorical foundations of general topology using lattice-valued mappings as a fundamental tool. Chapter 3 focuses on the fixed-basis case, including a convergence theory demonstrating the utility of the underlying axioms. Chapter 4 focuses on the more general variable-basis case, providing a categorical unification of locales, fixed-basis topological spaces, and variable-basis compactifications. Chapter 5 relates lattice-valued topologies to probabilistic topological spaces and fuzzy neighborhood spaces. Chapter 6 investigates the important role of separation axioms in lattice-valued topology from the perspective of space embedding and mapping extension problems, while Chapter 7 examines separation axioms from the perspective of Stone-Cech-compactification and Stone-representation theorems. Chapters 8 and 9 introduce the most important concepts and properties of uniformities, including the covering and entourage approaches and the basic theory of precompact or complete [0,1]-valued uniform spaces. Chapter 10 sets out the algebraic, topological, and uniform structures of the fundamentally important fuzzy real line and fuzzy unit interval. Chapter 11 lays the foundations of generalized measure theory and representation by Markov kernels. Chapter 12 develops the important theory of conditioning operators with applications to measure-free conditioning. Chapter 13 presents elements of pseudo-analysis with applications to the Hamilton–Jacobi equation and optimization problems. Chapter 14 surveys briefly the fundamentals of fuzzy random variables which are [0,1]-valued interpretations of random sets.

Elements Of Point Set Topology

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Author : John D. Baum
language : en
Publisher: Courier Corporation
Release Date : 1991-01-01

Elements Of Point Set Topology written by John D. Baum and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-01 with Mathematics categories.

Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.

Algebra Mathematical Logic Number Theory Topology

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Author : I.M.. Vinogradov
language : en
Publisher:
Release Date : 1986

Algebra Mathematical Logic Number Theory Topology written by I.M.. Vinogradov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Algebra categories.