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کتاب های موجود در دسته بندی نظریه اعداد

Elementary Number Theory. Primes, Congruences and Secrets
Published on: 2008
Beginner Number Theory English

Primes Congruences Cryptography Modular Arithmetic Number Theory
An Invitation to Modern Number Theory
Published on: 2006
Beginner Number Theory English

NumberTheory Modern Mathematics Undergraduate Theory
Algebraic K-theory of Number Fields
Published on: 2014
Beginner Number Theory English

K-theory Number Fields Algebraic Geometry Class Groups Euler Characteristics
The Theory of Algebraic Numbers (1st edition)
Published on: 1961
Beginner Number Theory English

Number theory Algebra Mathematics Abstract Polynomial
Elliptic functions
Published on: 2006
Beginner Number Theory English

A beginning graduate level treatment of elliptic functions with a huge array of examples.

Elliptic Functions Mathematics Algebra Analysis
Arithmetic on Elliptic Curves with Complex Multiplication
Published on: 1980
Beginner Number Theory English

Elliptic Curves Arithmetic Mathematics Multiplication
Introduction to Analytic Number Theory
Published on: 1976
Beginner Number Theory English

This introductory textbook is designed to teach undergraduates the basic ideas and techniques of number theory, with special consideration to …

NumberTheory PrimeNumbers ArithmeticFunctions Divisors Congruences
Modular Forms and Fermat’s Last Theorem
Published on: 1997
Beginner Number Theory English

This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August …

Elliptic Modular Theorem Fermat Mathematics
A Classical Introduction to Modern Number Theory
Published on: 1982
Beginner Number Theory English

Bridging the gap between elementary number theory and the systematic study of advanced topics, A CLASSICAL INTRODUCTION TO MODERN NUMBER …

Number Theory Algebra Prime Problems
Representation theory and automorphic forms
Published on: 2008
Beginner Number Theory English

This volume uses a unified approach to representation theory and automorphic forms. The invited papers, written by leading mathematicians, track …

Lie groups Number theory Modular forms Harmonic analysis Langlands program
Advanced Number Theory with Applications
Published on: 2010
Beginner Number Theory English

Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, …

NumberTheory Applications Mathematics Theorems Analysis
Algebraic Number Fields
Published on: 1973
Beginner Number Theory English

The book is directed toward students with a minimal background who want to learn class field theory for number fields. …

Algebraic Number Fields Theory Mathematics
Elementary number theory, cryptography and codes
Published on: 2008
Beginner Number Theory English

In this volume one finds basic techniques from algebra and number theory (e.g. congruences, unique factorization domains, finite fields, quadratic …

NumberTheory Cryptography Codes Mathematics Algorithms
Transcendental Number Theory
Published on: 1975
Beginner Number Theory English

First published in 1975, this classic book gives a systematic account of transcendental number theory, that is those numbers which …
Eisenstein series and the Selberg trace formula I by Don Zagier from Automorphic Forms, Representation Theory and Arithmetic: Papers, Presented at the Bombay Colloquium 1979 (Tata Institute Studies in Mathematics)
Published on: 1982
Beginner Number Theory English

The Book of Numbers
Published on: 1996
Beginner Number Theory English

Journey through the world of numbers with the foremost authorities and writers in the field. John Horton Conway and Richard …

Mathematics Identity Technology Religion Apocalypse
Algebraic number fields: (L-functions and Galois properties) : proceedings of a symposium
Published on: 1977
Beginner Number Theory English

Algebraic Number Fields L-functions Galois
Coding Theory and Number Theory
Published on: 2003
Beginner Number Theory English

This book grew out of our lectures given in the Oberseminar on 'Cod­ ing Theory and Number Theory' at the …

coding cryptography algorithms modularity primes
Computational number theory
Published on: 1996
Beginner Number Theory English

Diophantine Equations and Inequalities in Algebraic Number Fields
Published on: 1991
Beginner Number Theory English

Diophantine Equations Algebraic Number Fields Inequalities
Elementary number theory, group theory, and Ramanujan graphs
Published on: 2003
Beginner Number Theory English

This text is a self-contained study of expander graphs, specifically, their explicit construction. Expander graphs are highly connected but sparse, …

Number theory Group theory Ramanujan graphs Mathematics Combinatorics
Lewis Carroll in Numberland: His Fantastical Mathematical Logical Life
Published on: 2008
Beginner Number Theory English

I liked this book because it is a bio of Lewis Carroll from a mathematical standpoint. Yes, it does touch …

Mathematics Logic Creativity Biography Wonderland
Rational Points on Elliptic Curves
Published on: 2015
Beginner Number Theory English

Written by leading experts in the field Presents a technically difficult field which is readable by the average undergraduate mathematics …

Elliptic Curves Rational Points Number Theory Algebra Geometry
Modular Functions and Dirichlet Series in Number Theory
Published on: 1976
Beginner Number Theory English

ModularForms DirichletSeries NumberTheory ComplexAnalysis Ramanujan
Advanced Number Theory with Applications (Solutions, Instructor Solutions Manual)
Published on: 2009
Beginner Number Theory English

Number-Theory Applications Solutions Mathematics Advanced
Elementary Number Theory: Primes, Congruences, and Secrets [book draft]
Published on: 2017
Beginner Number Theory English

primes congruences cryptography modularity mathematics
Elementary Number Theory: Primes, Congruences, and Secrets: A Computational Approach (Undergraduate Texts in Mathematics)
Published on: 2008
Beginner Number Theory English

This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. …

primes congruences secrets computational mathematics
Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics)
Published on:
Beginner Number Theory English

The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay …

Elliptic Curves Rational Points Mathematics
Complex multiplication
Published on: 2010
Beginner Number Theory English

This is a self-contained account of the state of the art in classical complex multiplication that includes recent results on …

Elliptic Curves Algebraic Number Theory
Elliptic curves: number theory and cryptography
Published on: 2008
Beginner Number Theory English

Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide …

Elliptic Curves Number Theory Cryptography
Algebraic Number Theory and Fermat's Last Theorem
Published on: 2002
Beginner Number Theory English

This new, completely revised edition of a classic text introduces all elements necessary for understanding The Proof (Title of a …

Algebraic Number Theory Fermat Theorem
The arithmetic of elliptic curves
Published on: 2009
Beginner Number Theory English

The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have …

Elliptic Curves Arithmetic Theory Applications
Proofs from the Book
Published on: 2009
Beginner Number Theory English

"... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas …

Mathematics Elegance Theorems Beauty Erdős
Algebraic number theory and Fermat’s last theorem
Published on: 2002
Beginner Number Theory English

Number theory Algebraic integers Fermat's Last Theorem Galois theory Modular forms
Number Theory: A Very Short Introduction (Very Short Introductions)
Published on: 2020
Beginner Number Theory English

Mathematics Number Theory Primes Diophantine Cryptography
Algebraic number fields: (L-functions and Galois properties) proceedings of a symposium (2 to 12 September 1975 in the University of Durham
Published on: 1977
Beginner Number Theory English

Algebraic Number L-functions Galois Symposium
Number theory: an introduction via the distribution of primes
Published on: 2007
Beginner Number Theory English

This book provides an introduction and overview of number theory based on the distribution and properties of primes. This unique …

Primes Distribution Number Theory Introduction Mathematics
Algebraic geometry and arithmetic curves
Published on: 2006
Beginner Number Theory English

Introduction; 1. Some topics in commutative algebra; 2. General Properties of schemes; 3. Morphisms and base change; 4. Some local …

Algebraic Geometry Arithmetic Curves Schemes Cohomology Morphisms
Algebraic Number Theory and Fermat’s Last Theorem [4th ed.]
Published on: 2016
Beginner Number Theory English

Number theory Algebra Fermat's theorem Elliptic curves Modular forms
A course in arithmetic
Published on: 1996
Beginner Number Theory English


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نظریه اعداد: دریچه‌ای به دنیای شگفت‌انگیز اعداد

نظریه اعداد یکی از شاخه‌های باستانی و اساسی ریاضیات است که به مطالعه اعداد صحیح و ویژگی‌های آنان می‌پردازد. این شاخه از ریاضیات با مسائلی سر و کار دارد که اغلب به ظاهر ساده اما عمیقاً جذاب و پیچیده‌اند.

تاریخچه و اهمیت

نظریه اعداد از زمان‌های باستان مورد توجه ریاضی‌دانان بوده است. این شاخه ابتدا با مسائل پایه‌ای مانند یافتن اعداد اول یا حل معادلات دیوفانتی آغاز شد. اهمیت این شاخه از ریاضیات نه تنها در کشف و شناخت اعداد بلکه در کاربردهای فراوانی که در علوم کامپیوتر، رمزنگاری و دیگر شاخه‌های علمی ایفا می‌کند، نهفته است.

موضوعات مهم در نظریه اعداد

نظریه اعداد شامل موضوعات و بخش‌های بسیار متنوعی است که هر یک به نوبه خود به بررسی ویژگی‌ها و رفتارهای منحصربه‌فرد اعداد می‌پردازند. از جمله این موضوعات می‌توان به عبارات زیر اشاره کرد:

  • اعداد اول و توزیع آن‌ها: پژوهش در خصوص یافتن اعداد اول و بررسی چگونگی توزیع آن‌ها در میان اعداد صحیح.
  • معادلات دیوفانتی: حل معادلاتی که دارای مقادیر صحیح هستند و اغلب راه حل‌های ساده‌ای ندارند.
  • توابع شمارشی: مطالعه تابع شمارش اعداد اول و تحلیل رفتار آن.

کاربردهای نظریه اعداد

با وجود آنکه نظریه اعداد در ابتدا شاخه‌ای تئوریک محسوب می‌شود، اما کاربردهای عملی متعددی دارد. برای مثال، در رمزنگاری مدرن نقش بسیار مهمی دارد. الگوریتم‌های رمزنگاری مانند RSA پایه‌ای در نظریه اعداد دارند و استفاده از اعداد اول بزرگ برای ایجاد کلیدهای رمزنگاری امن به کار می‌رود.

علاوه بر این، نظریه اعداد در الگوریتم‌های محاسباتی، تحلیل پیچیدگی الگوریتم‌ها، و حتی در هوش مصنوعی کاربرد دارد. استفاده از ویژگی‌های خاص اعداد و ویژگی‌ها، بهینه‌سازی و سرعت بخشی به فرآیندهای محاسباتی را ممکن می‌سازد.

کتاب‌های پیشنهادی در نظریه اعداد

در بین کتاب‌های موجود در دسته نظریه اعداد، برخی از آثار کلاسیک و مدرن وجود دارند که می‌توانند برای علاقه‌مندان به این حوزه بسیار مفید باشند. این کتاب‌ها معمولاً به ارائه توضیحات و مثال‌هایی از مفاهیم نظریه اعداد می‌پردازند و شامل تمرینات مختلفی برای فهم بهتر مطالب هستند. از جمله این کتب می‌توان به موارد زیر اشاره کرد:

  • «مقدمه‌ای بر نظریه اعداد» ـ کتابی جامع و کاربردی که اصول پایه‌ای و معاصر نظریه اعداد را توضیح می‌دهد.
  • «مسائل حل نشده در نظریه اعداد» ـ کتابی که به بررسی مشکلات و مسائلی می‌پردازد که هنوز به طور کامل حل نشده‌اند.
  • «نظریه اعداد: راهنمایی برای مبتدیان» ـ کتابی مناسب برای شروع مطالعه نظریه اعداد همراه با تمرین‌ها و مثال‌های کاربردی.

چرا نظریه اعداد را مطالعه کنیم؟

مطالعه نظریه اعداد تنها برای علاقه‌مندان و دانشجویان ریاضی نیست، بلکه برای هر کسی که به دنبال فهم عمیق‌تر مفاهیم ریاضی و علوم محاسباتی است، مفید خواهد بود. این شاخه از ریاضیات نه تنها به درک بهتری از جهان اعداد کمک می‌کند، بلکه مهارت‌های حل مسئله و تفکر انتقادی را نیز تقویت می‌نماید.

علاقه‌مندان به این حوزه می‌توانند با مطالعه موضوعات نظریه اعداد به اکتشافات جدیدی در زمینه رایانه و سایر علوم دست یابند و در توسعه دانش و فناوری مؤثر باشند.