کتاب های موجود در دسته بندی نظریه مجموعه‌ها

Introduction to Modern Set Theory
Published on: 1990
Beginner Set Theory English

This is modern set theory from the ground up--from partial orderings and well-ordered sets to models, infinite cobinatorics and large …

Sets Functions Infinity Axioms Cardinality
Unifying Theories of Programming: 6th International Symposium, UTP 2016, Reykjavik, Iceland, June 4-5, 2016, Revised Selected Papers
Published on: 2017
Beginner Set Theory English

This book constitutes the refereed proceedings of the 6th International Symposium on Unifying Theories of Programming, UTP 2016, held in …

Software Theories Formalism Symposium Verification
Playing with Infinity. Mathematical Explorations and Excursions
Published on: 2010
Beginner Set Theory English

Popular account ranges from counting to mathematical logic and covers the many mathematical concepts that relate to infinity: graphic representation …

mathematics infinity exploration abstraction education
A Philosophical Companion to First-Order Logic
Published on: 1993
Beginner Set Theory English

This volume of recent writings, some previously unpublished, follows the sequence of a typical intermediate or upper-level logic course and …

Logic Philosophy Semantics Quantifiers Models
A Course in Functional Analysis
Published on: 1985
Beginner Set Theory English

This book is an introductory text in functional analysis. Unlike many modern treatments, it begins with the particular and works …

Hilbert spaces Banach spaces Linear operators Spectral theory Topology
Foundations of F#
Published on: 2007
Beginner Set Theory English

Functional programming (FP) is the future of .NET programming, and F# is much more than just an FP language. Every …

F# functional programming .NET foundations language
Advances in Applied Logics. Applications of Logic for Philosophy, Mathematics and Information Technology
Published on: 2023
Beginner Set Theory English

Logic Philosophy Mathematics Technology Applications
Computability Theory: An Introduction to Recursion Theory (Instructor's Solution Manual) (Solutions)
Published on: 2010
Beginner Set Theory English

Recursion Computability Solutions Theoretical Mathematics
Introduction to Axiomatic Set Theory
Published on: 1971
Beginner Set Theory English

This book presents the classic relative consistency proofs in set theory that are obtained by the device of 'inner models'. …

Axiomatic Set Theory Foundations Mathematics Logic
Introduction to Lattices and Order, Second Edition
Published on: 2002
Beginner Set Theory English

Ordered structures have been increasingly recognized in recent years due to an explosion of interest in theoretical computer science and …

Lattices Order Mathematics Algebra Structure
Descriptive set theory
Published on: 2009
Beginner Set Theory English

Descriptive Set Theory is the study of sets in separable, complete metric spaces that can be defined (or constructed), and …

Sets Topology Borel Cardinality Measurable
Philosophy of Logics
Published on: 1978
Beginner Set Theory English

The first systematic exposition of all the central topics in the philosophy of logic, Susan Haack's book has established an …

semantics truth inference propositions language
Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach (Encyclopedia of Mathematics and its Applications)
Published on: 2012
Beginner Set Theory English

The study of graph structure has advanced with great strides. This book unifies and synthesizes research over the last 25 …

Graph Theory Monadic Logic Automata Decidability Algorithms
An Introduction to Gödel's Theorems
Published on: 2007
Beginner Set Theory English

In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory …

Gödel Incompleteness Logic Theorems Mathematics
Nonstandard Analysis
Published on: 2006
Beginner Set Theory English

Elements of set theory
Published on: 1977
Beginner Set Theory English

This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge …

Sets Relations Functions Axioms Cardinality
Introduction to Lattices and Order
Published on: 2002
Beginner Set Theory English

Lattices Order Mathematics Structure Relations
Set Theory: Boolean-Valued Models and Independence Proofs
Published on: 2005
Beginner Set Theory English

Boolean-valued models Forcing Independence Set theory Continuum hypothesis
Zero to Infinity: The Foundations of Physics (WS 2007)
Published on: 2007
Beginner Set Theory English

Unique in its field, this book uses a methodology that is entirely new, creating the simplest and most abstract foundations …

Physics Foundations Concepts Theories WS2007
Combinatorial Set Theory: Partition Relations for Cardinals
Published on: 1984
Beginner Set Theory English

This work presents the most important combinatorial ideas in partition calculus and discusses ordinary partition relations for cardinals without the …

Combinatorics Set Theory Cardinals Partition Relations Mathematics
An Introduction to the Technique of Formative Processes in Set Theory
Published on: 2018
Beginner Set Theory English

Set Theory Formative Processes Mathematical Logic Foundations Abstract Structures
Axiomatic Set Theory: Theory Impredicative Theories of Classes
Published on: 1981
Beginner Set Theory English

Impredicative Classes Set Theory Axiomatic Mathematics
The Structure of Models of Peano Arithmetic
Published on: 2006
Beginner Set Theory English

Aimed at research logicians and mathematicians, this much-awaited monograph covers over forty years of work on relative classification theory for …

Model theory Peano Arithmetic mathematical logic nonstandard models set theory
Axiomatic Set Theory: Impredicative Theories of Classes
Published on: 1981
Beginner Set Theory English

Set Theory Impredicative Classes Mathematics Logic
Unifying Theories of Programming: 5th International Symposium, UTP 2014, Singapore, May 13, 2014, Revised Selected Papers
Published on: 2015
Beginner Set Theory English

This book constitutes the refereed proceedings of the 5th International Symposium on Unifying Theories of Programming, UTP 2014, held in …

Formal methods Programming theories Software design Mathematical models System behavior
First-Order Logic and Automated Theorem Proving
Published on: 1996
Beginner Set Theory English

There are many kinds of books on formal logic. Some have philosophers as their intended audience, some mathematicians, some computer …

Logic Theorem Automation Proof Computation
Set theory for the working mathematician
Published on: 1997
Beginner Set Theory English

This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. …

axioms cardinals ordinals paradoxes topology
An Introduction to Nonstandard Real Analysis (Pure and Applied Mathematics (Academic Press), Volume 118)
Published on: 1985
Beginner Set Theory English

The aim of this book is to make Robinson's discovery, and some of the subsequent research, available to students with …

Nonstandard Real Analysis Mathematics Pure Applied
Set Theory and Its Logic
Published on: 1969
Beginner Set Theory English

This is an extensively revised edition of Mr. Quine's introduction to abstract set theory and to various axiomatic systematizations of …

mathematics logic set-theory philosophy formalism
From Kant to Hilbert Volume 1: A Source Book in the Foundations of Mathematics
Published on: 2007
Beginner Set Theory English

Immanuel Kant's Critique of Pure Reason is widely taken to be the starting point of the modern period of mathematics …

logic philosophy mathematics foundational history
The Age of Alternative Logics: Assessing Philosophy of Logic and Mathematics Today (Logic, Epistemology, and the Unity of Science, 3)
Published on: 2006
Beginner Set Theory English

In the last century developments in mathematics, philosophy, physics, computer science, economics and linguistics have proven important for the development …

logic philosophy mathematics epistemology science
Nonstandard Analysis: Theory and Applications
Published on: 1997
Beginner Set Theory English

1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) …
Sets, Logic and Categories
Published on: 1998
Beginner Set Theory English

Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics …

Mathematics Set theory Logic Categories Foundations
Computational Quantum Chemistry: An Interactive Introduction to Basis Set Theory
Published on: 2002
Beginner Set Theory English

Computational Quantum Chemistry removes much of the mystery of modern computer programs for molecular orbital calculations by showing how to …

Quantum Chemistry Computational Basis Set Interactive Theory
Classic Set Theory: For Guided Independent Study
Published on: 1996
Beginner Set Theory English

Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg …

Set Theory Mathematics Textbook Independent Study Guide
Universal Algebra: Fundamentals and Selected Topics
Published on: 2011
Beginner Set Theory English

Starting with the most basic notions, Universal Algebra: Fundamentals and Selected Topics introduces all the key elements needed to read …

Algebras Lattices Homomorphisms Congruences Varieties
Introduction to Proof in Abstract Mathematics
Published on: 2014
Beginner Set Theory English

The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize …

Proof Abstract Mathematics Logic Theorems
Basic Category Theory for Computer Scientists
Published on: 1991
Beginner Set Theory English

Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially …
Ultrafilters Across Mathematics: International Congress Ultramath 2008: Applications of Ultrafilters and Ultraproducts in Mathematics, June 1-7, 2008, Pisa, Italy
Published on: 2010
Beginner Set Theory English

This volume originated from the International Congress ""ULTRAMATH: Applications of Ultrafilters and Ultraproducts in Mathematics"", which was held in Pisa, …
Forcing for Mathematicians
Published on: 2014
Beginner Set Theory English

Ever since Paul Cohen's spectacular use of the forcing concept to prove the independence of the continuum hypothesis from the …

Forcing Set Theory Logic Mathematics Independence

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تئوری مجموعه‌ها: مبانی و کاربردها

تئوری مجموعه‌ها یکی از موضوعات بنیادین در ریاضیات است که به مطالعه و درک مفهوم مجموعه‌ها، عناصر آنها و روابط بین مجموعه‌ها می‌پردازد. این شاخه از ریاضیات، پایه‌ریزی بسیاری از نظریه‌ها و ساختارهای ریاضی را فراهم می‌کند و به همین دلیل، اهمیت ویژه‌ای در آموزش و پژوهش‌های ریاضی دارد.

مبانی تئوری مجموعه‌ها

مبانی تئوری مجموعه‌ها شامل مفاهیم ابتدایی همچون مجموعه‌ها، زیرمجموعه‌ها، عضویت، و برابری مجموعه‌ها است. درک این مفاهیم اساسی به معناشناسی بیشتر تئوری مجموعه‌ها کمک می‌کند. این مباحث اولیه همچنین به موضوعاتی نظیر روابط دوتایی، توابع، و همبستگی بین مجموعه‌ها می‌پردازد که از علوم پایه در ریاضیات مدرن هستند.

اصول اکسیماتیک و نظریه مجموعه‌ها

در تئوری مجموعه‌ها، اصول اکسیماتیک نقشی کلیدی در تعریف دقیق و رسمی‌سازی مفاهیم دارد. سیستم‌های اکسیماتیک مانند نظریه مجموعه‌های زرملو-فرانکل (ZF) و افزودن اصل انتخاب (AC) به این سیستم، ساختاری مستحکم برای برخورد با ناهمگونی‌ها و تناقض‌های بالقوه فراهم می‌کنند. بسیاری از مسائل بنیادی در ریاضیات بر پایه این اصول بنا شده‌اند و به درک بهتر ما از جهان ریاضیات کمک می‌کنند.

کاربردهای تئوری مجموعه‌ها

تئوری مجموعه‌ها علاوه بر بکارگیری در ریاضیات خالص، در علوم مختلف نیز کاربرد دارد. از جمله این کاربردها می‌توان به علوم کامپیوتر، منطق ریاضی و حتی فلسفه اشاره کرد. در علوم کامپیوتر، تئوری مجموعه‌ها برای تحلیل الگوریتم‌ها و ساختار داده‌ها استفاده می‌شود. در منطق ریاضی، به عنوان اساسی برای تعریف منطق‌های مصنوعی و اثبات‌های منطقی به کار می‌رود.

کتاب‌های مرتبط و منابع مطالعاتی

در فروشگاه کتاب آنلاین ما، مجموعه‌ گسترده‌ای از کتاب‌های مرتبط با تئوری مجموعه‌ها در دسترس است که شامل کتاب‌های مقدماتی تا پیشرفته می‌شود. این کتاب‌ها توسط نویسندگان مطرح و اساتید برجسته تالیف شده و برای دانشجویان، محققین، و علاقه‌مندان به ریاضیات تهیه شده‌اند. مطالعه این منابع برای افرادی که به دنبال درک عمیق‌تر و دقیق‌تری از تئوری مجموعه‌ها هستند، بسیار مفید خواهد بود.

مزایای یادگیری تئوری مجموعه‌ها

آشنایی با تئوری مجموعه‌ها می‌تواند به توسعه تفکر منطقی و تحلیلی کمک کند و مهارت‌های حل مسئله را تقویت کند. این دانش اساس ریاضیات مدرن و بسیاری از علوم دیگر را تشکیل می‌دهد و به عنوان ابزاری قوی برای تحلیل و مدل‌سازی مفاهیم پیچیده به کار می‌رود. با یادگیری این نظریه، افراد می‌توانند به راحتی در مسائل مختلف علمی و حرفه‌ای خود به تحلیل و نتیجه‌گیری بپردازند.

در پایان، تئوری مجموعه‌ها نه تنها به عنوان یک موضوع درسی، بلکه به عنوان یک ابزار مفهومی برای حل مشکلات در زمینه‌های متنوعی از علم و مهندسی مطرح است. ما شما را به کاوش در این دنیای شگفت‌انگیز دعوت می‌کنیم و امیدواریم منابع ارائه شده، به شما در مسیر یادگیری و درک بهتر این حوزه کمک کند.