کتاب های موجود در دسته بندی نظریه مجموعه‌ها

Nonstandard methods in stochastic analysis and mathematical physics
Published on: 1986
Beginner Set Theory English

The Bulletin of the American Mathematical Society acclaimed this text as "a welcome addition" to the literature of nonstandard analysis, …

stochastic analysis nonstandard physics mathematics
Descriptive Set Theory 2nd Edition (Mathematical Surveys and Monographs)
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 …

Borel Hierarchies Polish Analytic Cardinals
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
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
Unifying Theories of Programming: 4th International Symposium, UTP 2012, Paris, France, August 27-28, 2012, Revised Selected Papers
Published on: 2013
Beginner Set Theory English

This book constitutes the refereed proceedings of the 4th International Symposium on Unifying Theories of Programming, UTP 2012, held in …

Formal Methods Software Engineering Program Semantics Theoretical Computer Science Verification
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
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
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, …
Notes on set theory
Published on: 2006
Unordered Set Theory English

The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and …

Set Theory Cardinality Ordinals Axioms
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
Set Theory: An Introduction to Large Cardinals
Published on: 1974
Beginner Set Theory English

cardinals hierarchy ordinals axioms consistency
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
Handbook of Set Theory
Published on: 2010
Beginner Set Theory English

This handbook is the definitive compendium of the methods, results, and current initiatives in modern set theory in all its …

Set Theory Mathematics Logic Foundations Analysis
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
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
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
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
Nonstandard methods in functional analysis: Lectures and notes
Published on: 2010
Beginner Set Theory English

In the early 1960s, by using techniques from the model theory of first-order logic, Robinson gave a rigorous formulation and …
The Axiom of Choice
Published on: 1973
Beginner Set Theory English

Comprehensive in its selection of topics and results, this self-contained text examines the relative strengths and the consequences of the …

Mathematics Logic Philosophy SetTheory Choice
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 …
Set Theory: Boolean-Valued Models and Independence Proofs
Published on: 2005
Beginner Set Theory English

Boolean-valued models Forcing Independence Set theory Continuum hypothesis
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
Set Theory and the Continuum Problem
Published on: 1996
Beginner Set Theory English

Set Theory and the Continuum Problem is a novel introduction to set theory, including axiomatic development, consistency, and independence results. …

Set theory Continuum Cantor Cardinality Mathematics
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
Descriptive Set Theory and Forcing: How to prove theorems about Borel sets the hard way
Published on: 1995
Beginner Set Theory English

An advanced graduate course. Some knowledge of forcing is assumed, and some elementary Mathematical Logic, e.g. the Lowenheim-Skolem Theorem. A …

Set theory Forcing Borel sets Theorems Mathematical analysis
Computability: An Introduction to Recursive Function Theory
Published on: 1980
Beginner Set Theory English

Recursive Functions Computability Theory Decidability Turing Machines Mathematical Logic
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
Lectures on the hyperreals: an introduction to nonstandard analysis
Published on: 1998
Beginner Set Theory English

This is an introduction to nonstandard analysis based on a course of lectures given several times by the author. It …

hyperreals nonstandard analysis mathematics logic
Philosophical Perspectives on Infinity
Published on: 2009
Beginner Set Theory English

Exploring philosophical questions about infinity, Graham Oppy examines how the infinite lurks everywhere, both in science and in our ordinary …

Infinity Philosophy Mathematics Metaphysics Paradoxes
Unifying Theories of Programming and Formal Engineering Methods: International Training School on Software Engineering, Held at ICTAC
Published on: 2013
Beginner Set Theory English

This book presents 5 tutorial lectures by leading researchers given at the ICTAC 2013 Software Engineering School on Unifying Theories …

Programming Theories Engineering ICTAC Software
Computability Theory: An Introduction to Recursion Theory (Instructor's Solution Manual) (Solutions)
Published on: 2010
Beginner Set Theory English

Recursion Computability Solutions Theoretical Mathematics
Analysis with ultrasmall numbers
Published on: 2014
Beginner Set Theory English

Analysis with Ultrasmall Numbers presents an intuitive treatment of mathematics using ultrasmall numbers. With this modern approach to infinitesimals, proofs …

ultrasmall analysis mathematics numbers calculus
The search for mathematical roots, 1870-1940: logics, set theories and the foundations of mathematics from Cantor through Russell to Godel
Published on: 2000
Beginner Set Theory English

While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the …

Cantor Russell Gödel logic set theory
A Course on Set Theory
Published on: 2011
Beginner Set Theory English

Set theory is the mathematics of infinity and part of the core curriculum for mathematics majors. This book blends theory …

Set Theory Mathematics Foundations Logic Proofs
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: Naïve, Axiomatic and Applied. A Basic Compendium with Exercises for Use in Set Theory for Non Logicians, Working and Teaching Mathematicians and Students
Published on: 1978
Beginner Set Theory English

Set Theory Naïve Axiomatic Applied Exercises
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
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
Popular Lectures on Mathematical Logic
Published on: 1993
Beginner Set Theory English

A noted logician and philosopher addresses various forms of mathematical logic, discussing both theoretical underpinnings and practical applications. Author Hao …
Axiomatic Set Theory
Published on: 1960
Beginner Set Theory English

Set Theory Axioms Mathematics Logic

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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.