**Best Reference Books on Number Theory**, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of

**Number Theory Books**with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on Number Theory below.

- Basic Number Theory
- Analytic Number Theory
- Computational Number Theory
- Algebraic Number Theory
- Number Theory and Cryptography

## 1. Basic Number Theory

1."Introduction to the Theory of Numbers" by W W Adams and L J Goldstein | |

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2."A Concise Introduction to the Theory of Numbers" by A Baker
“A Concise Introduction to the Theory of Numbers” Book Review: This reader-friendly book provides an introduction to the rudiments of number theory, a subject with a long and significant history. The comprehensive and easy-to-understand chapters cover major topics such as visibility, arithmetic functions, congruences, quadratic residues, quadratic forms, Diophantine approximation, quadratic fields, and Diophantine equations. Each chapter includes exercises for practice. Despite its old-fashioned style, the book incorporates study guides that encourage readers to explore the vast resources of the subject. Based on Professor Baker’s lectures at the University of Cambridge, this book is ideal for undergraduate mathematics students seeking a concise and direct introduction to number theory.
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3."An Introduction to the Theory of Numbers" by I Niven and H S Zuckerman
“An Introduction to the Theory of Numbers” book review: This revised edition of the book on number theory covers the latest developments in the subject. The book is organized into chapters covering a broad range of topics, including visibility, congruences, quadratic reciprocity, quadratic forms, functions of number theory, Diophantine equations, farey fractions, simple continued fractions, prime and multiplicative number theory, irrational and algebraic numbers, partition function, and sequences of integers. The text emphasizes the binomial theorem and techniques of numerical calculation, and offers several self-study problems for readers. This fifth edition, written by renowned mathematicians, provides maximum flexibility with self-explanatory chapters. It also includes new features such as extended coverage of the binomial theorem, techniques of numerical calculation, and a section on public key cryptography.
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4."Basic College Mathematics with Early Integers" by Elayn Martin-Gay
“Basic College Mathematics with Early Integers” Book Review: The book focuses on developing conceptual understanding, featuring numerous applications and exercises to aid readers. It includes a textbook and access kit for MyMathLab/MyStatLab. The Bittinger Worktext Series has revolutionized developmental education by introducing worktexts that provide math concepts one at a time. The book features objective-based worktexts, presenting one math concept per chapter in a well-structured and easy-to-follow manner. This approach helps students grasp the basics of each concept before moving on to more advanced topics. The book emphasizes cognitive comprehension and offers support with advanced applications, tests, and additional resources to help students apply and retain their knowledge. MyMathLab provides a variety of online homework tools, tutorials, and tests.
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5."The Trachtenberg Speed System of Basic Mathematics" by Rudolph McShane and Jakow Trachtenberg
“The Trachtenberg Speed System of Basic Mathematics” Book Review: The aim of this book is to introduce ‘The Trachtenberg Speed System’ which provides techniques for dealing with basic math and large sums. This book is designed to be helpful for children struggling with mathematics as well as their teachers. It provides a course for basic mathematical skills, enabling the reader to deal with large sums and improve their focus and ability with everyday math. The book introduces the shorthand of mathematics, which requires only the ability to count from one to eleven. It allows anyone to know numbers and calculations that provide greater speed, ease of use, and accuracy. The chapters cover topics such as table or no tables, multiplication by the direct method, speed multiplication, addition and the right answer, division, squares and square roots, and an algebraic description of the method. The book uses fundamental mathematical skills and principles for performing various operations and illustrates a set of rules that enable every child to perform multiplication, division, insertion, subtraction, and square roots with consistent accuracy and remarkable speed. It provides a good starting point for gaining confidence in numbers.
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6."Basic Algebra" by Anthony W Knapp
“Basic Algebra” Book Review: This book offers a comprehensive treatment of algebraic concepts and tools that are fundamental to all mathematicians. It covers a range of topics, including groups, rings, fields, modules, and Galois groups, with numerous examples and computation methods. The book is well-balanced between basic and advanced algebraic concepts, and it includes applications to science and engineering. The chapters are structured around integers, polynomials, matrices, vector spaces, group theory, multilinear algebra, commutative rings, and Galois theory. It is suitable as a textbook for undergraduate students and requires only a basic familiarity with matrix algebra, geometry, and proof techniques. The book includes many problems and examples with hints and complete solutions. It is a valuable resource for mathematicians and practitioners.
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7."Basic Essentials of Mathematics" by James T Shea
“Basic Essentials of Mathematics” Book Review: This book is an ideal introductory guide to mathematics. The book covers a wide range of topics, including arithmetic, algebra, geometry, trigonometry, and calculus. Shea’s writing style is clear and concise, making it easy for readers to understand even complex concepts. Each chapter includes examples and practice problems, making it an ideal textbook for students. This book is a useful resource for anyone looking to gain a solid understanding of mathematics fundamentals.
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8."Number Theory" by George E Andrews
“Number Theory” Book Review: This book provides a comprehensive coverage of the basic principles, key concepts, and major aspects of number theory. It presents a combinational approach to basic number theory, catering to the interests of both mathematics majors and other students. The book covers topics such as the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots, and prime numbers. Recent chapters offer a good treatment of quadratic congruences, additions (including partition theory), and geometric number theory. The book includes numerous exercises that allow students to build number tables and find themes in them. The book is enriched with several numerical examples and will be helpful for students seeking a strong foundation in dealing with more advanced issues in number theory.
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9."An Introduction to the Theory of Numbers" by G H Hardy and Edward M Wright
“An Introduction to the Theory of Numbers” Book Review: This updated and revised edition of a classic textbook serves as a comprehensive introduction to basic number theory. Written in clear language, the book covers important topics such as primes, congruences, irrational numbers, and more. The chapters are well-structured and self-contained, making it an accessible resource for undergraduate students of mathematics and a valuable reference for number theorists. The new edition includes a chapter by J.H. Silverman on modular elliptic curves and their role in the proof of Fermat’s theorem. Each chapter concludes with notes featuring major developments in number theory and suggestions for further study.
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10."An Adventurer's Guide to Number Theory" by Richard Friedberg
“An Adventurer’s Guide to Number Theory” Book Review: This book serves as a solid introduction to number theory, presenting an intelligent approach that delves into the history of the subject, framing numbers and numerical properties as abstract concepts. It is written for students who possess a foundational understanding of mathematics and algebra. The text explores the earliest discoveries in number theory, from the works of Pythagoras and Euclid to those of Diophantus, Fermat, Euler, Lagrange, and Gauss. Students are challenged to think creatively about imaginary and playful numbers as they study topics such as primes and divisions, quadratic forms and arithmetic, and quadratic reciprocity and related theorems. The book also includes unusual elements to inspire readers, including original problems from Diophantus’ Arithmetica, evidence of Fermat’s Last Theorem 3 and 4, and two testimonials of Wilson’s Theorem. Professionals and students alike will find value in this book.
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11."Number Theory and Its Applications (Developments in Mathematics)" by imusti
“Number Theory and Its Applications 1999th Edition” Book Review: This book is a comprehensive textbook written for advanced undergraduate and graduate students in mathematics. The book provides an introduction to the basic concepts of number theory and their applications, with a focus on algebraic and analytic number theory. It covers topics such as prime numbers, congruences, Diophantine equations, quadratic forms, elliptic curves, and modular forms. The book also includes a chapter on cryptography and coding theory. Each chapter contains numerous exercises, making it an excellent resource for self-study or as a textbook for a course in number theory.
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## 2. Analytic Number Theory

1."Algebraic Number Theory" by S Lang
“Algebraic Number Theory” Book Review: This book presents a comprehensive overview of classical algebraic and analytic number theory, as well as algebraic numbers. It is a valuable resource for those pursuing research in algebraic number theory, as it is self-contained and theoretically sound. The latest developments in the field are included, providing readers with up-to-date knowledge. The book approaches cyclotomic fields as analogues of constant field extensions in algebraic geometry, offering a global perspective on number fields. Topics covered include Algebraic Integers, Completions, The Different and Discriminant, Cyclotomic Fields, Parallelotopes, The Ideal Function, Adele and Adeles, Elementary Properties of the Zeta Function and L-series, Norm Index Computations, The Artin Symbol, Reciprocity Law, and Class Field Theory, Hecke’s Proof, Functional Equation, Tate’s Thesis, Density of Primes and Tauberian Theorem, The Brauer-Siegel Theorem, Explicit Formulas, among others.
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2."A Course in Arithmetic" by J P Serre
“A Course in Arithmetic” Book Review: The book is a valuable resource, written in simple language and with a purely algebraic approach. It offers a classification of quadratic forms over the rational numbers field. The book covers a range of topics including Finite Fields, p-Adic Fields, Hilbert Symbol, Quadratic Forms over Q p and over Q, Integral Quadratic Forms with Discriminant ± 1, The Theorem on Arithmetic Progressions, Modular Forms, and more.
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3."Introduction to Analytic Number Theory" by T Apostol
“Introduction to Analytic Number Theory” Book Review: This book is a comprehensive guide to the topic of number theory, designed to be accessible to undergraduates regardless of their prior knowledge of the subject. The book starts by introducing the basic properties of natural numbers and progresses to cover more advanced topics. The text is presented in a clear and concise manner, with a wealth of information that is easy to read and understand. Each chapter includes exercises to reinforce the material covered. The book covers a broad range of topics including the Fundamental Theorem of Arithmetic, arithmetical functions and Dirichlet multiplication, prime numbers and their distribution, congruences, finite abelian groups and their characters, Dirichlet’s Theorem on primes in arithmetic progressions, periodic arithmetical functions and Gauss sums, quadratic residues and the quadratic reciprocity law, primitive roots, Dirichlet series and Euler products, and an analytic proof of the Prime Number Theorem.
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4."Analytic Number Theory" by Henryk Iwaniec and Emmanuel Kowalski
“Analytic Number Theory” Book Review: This graduate-level book provides a comprehensive overview of number theory and its diverse concepts and methods. The book aims to showcase the theory’s scope, including classical and modern directions, beautiful theorems, and powerful techniques. It balances clarity, completeness, and generality and includes exercises and examples to enhance understanding and provide additional information. Readers should have a basic understanding of the topic. Topics covered include arithmetic functions, prime numbers, L-functions, sieve methods, exponential sums, modular forms, automorphic forms, Kloosterman sums, primes in arithmetic progressions, the Goldbach problem, and effective bounds for the class number.
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5."A Primer of Analytic Number Theory: From Pythagoras to Riemann" by Jeffrey Stopple
“A Primer of Analytic Number Theory: From Pythagoras to Riemann” Book Review: This book provides a comprehensive understanding of the subject matter through easy-to-understand language and covers all the essential topics. Its primary goal is to improve the reader’s analytical skills while exploring ancient problems related to polygonal numbers, perfect numbers, and amicable pairs. The book emphasizes the importance of the Riemann zeta function and its connection to the Riemann Hypothesis. It offers a solid foundation in elementary number theory, with a range of exercises and advanced concepts that are suitable for undergraduates. Topics covered include Sums and Differences, Products and Divisibility, Order of Magnitude, Averages, Primes, Basel Problem, Euler’s Product, The Riemann Zeta Function, Stirling’s Formula, Explicit Formula, Pell’s Equation, Elliptic Curves, and Analytic Theory of Algebraic Numbers.
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6."Analytic Number Theory: Exploring the Anatomy of Integers" by Jean-marie De Koninck and Florian Luca
“Analytic Number Theory: Exploring the Anatomy of Integers” Book Review: This book offers a unique approach to analytic number theory, focusing on the multiplicative structure of integers. It provides a clear introduction to the subject with carefully chosen problems at the end of each chapter. The book also includes solved numericals and solutions to every problem, making it ideal for readers looking to test their understanding of the topic. The book covers topics such as prime numbers, the Riemann zeta function, the prime number theorem, arithmetic functions, smooth numbers, sieve methods, characters and the Dirichlet theorem, and more.
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7."Analytic Number Theory: An Introductory Course" by Paul Trevier Bateman and Harold G Diamond
“Analytic Number Theory: An Introductory Course” Book Review: This graduate-level book provides a thorough introduction to the topic and offers a wealth of resources for readers. The text assumes prior knowledge of real analysis, complex analysis, number theory, and abstract algebra. The book contains numerous exercises throughout each chapter, as well as development of particular subjects and theorems with references. The author focuses on a collection of powerful methods of analysis that provide deep number theoretical estimates. Topics covered include Calculus of Arithmetic Functions, Summatory Functions, The Distribution of Prime Numbers, An Elementary Proof of the P.N.T., Dirichlet Series and Mellin Transforms, Inversion Formulas, The Riemann Zeta Function, Primes in Arithmetic Progressions, Applications of Characters, Oscillation Theorems, Sieves, Application of Sieves, and appendices.
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8."Geometric and Analytic Number Theory" by Edmund Hlawka and Johannes Schoißengeier
“Geometric and Analytic Number Theory” Book Review: This book provides a unique approach to understanding number theory, focusing not only on how to solve problems but also why they are solved. It includes essential findings, examples, and exercises. The target audience is beginners with a background in analytic geometry, differential and integral calculus, and the elements of complex variable theory. The book introduces basic results from areas such as the geometry of numbers, diophantine approximation, prime number theory, and asymptotic calculation of number-theoretic functions. Topics covered include The Dirichlet Approximation Theorem, The Kronecker Approximation Theorem, Geometry of Numbers, Number-Theoretic Functions, The Prime Number Theorem, Characters of Groups of Residues, The Algorithm of Lenstra, Lenstra, and Lovász, etc.
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9."Abstract Analytic Number Theory" by John Knopfmacher
“Abstract Analytic Number Theory” Book Review: This well-written book applies classical analytic number theory to various mathematical subjects in an arithmetical manner. It focuses on arithmetical semigroups and algebraic enumeration problems, exploring their analytical properties in depth. The book carefully treats fundamental concepts and theorems, covering topics such as Arithmetical Asymptotic Enumeration, Functions, Enumeration Problems, Arithmetical Semigroups, Arithmetical Semigroups with Analytical Properties of Classical Type, Further Statistical Properties of Arithmetical Functions, The Abstract Prime Number Theorem, Fourier Analysis of Arithmetical Functions, Additive Arithmetical Semigroups, Arithmetical Formations, and more. The book also includes appendices and a bibliography.
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## 3. Computational Number Theory

1."Computational Number Theory (Discrete Mathematics and Its Applications)" by Abhijit Das
“Computational Number Theory (Discrete Mathematics and Its Applications) 1st Edition” Book Review: This book is designed for advanced undergraduate and early graduate engineering students as well as researchers new to the field. It covers major topics of computational number theory, such as arithmetic of integers and polynomials, elliptic curves, and primality testing. The book also includes applications in cryptography and provides complete coverage of number-theoretic algorithms with explanations of all computational aspects. Theoretical tools used in cryptography and cryptanalysis are explored, and examples and exercises are provided. The book offers detailed explanations with numerous examples and is suitable for graduate engineering students. Additional topics covered include public key cryptography, cryptography, and cryptanalysis.
Other topics mentioned are cryptography, cryptanalysis, public key cryptography. | |

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2."Elementary Number Theory: Primes, Congruences, and Secrets: A Computational Approach (Undergraduate Texts in Mathematics)" by William Stein
“Elementary Number Theory: Primes, Congruences, and Secrets: A Computational Approach (Undergraduate Texts in Mathematics) 2009th Edition” Book Review: This undergraduate textbook aims to introduce readers to active research in number theory and provide a deeper understanding of prime numbers. The book is accompanied by Sage mathematical software, which is used to solve problems throughout the text. The book contains numerous exercises and examples to aid in understanding the material. The reader is expected to have basic knowledge of reading and writing mathematical proofs. The focus of the book is on resolving the congruent number problem.
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3."Computational Algebra and Number Theory (Mathematics and Its Applications)" by Wieb Bosma and Alf van der Poorten
“Computational Algebra and Number Theory (Mathematics and Its Applications (325)” Book Review: This book examines the interplay between mathematics and computer science, delving into the powerful synergy between these two fields. Numerous examples are presented to aid comprehension. Various theories, such as graph theory, are thoroughly explained. The book focuses on fundamental principles and frequently utilized techniques.
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4."C++ Toolbox for Verified Computing I: Basic Numerical Problems Theory, Algorithms, and Programs" by Ulrich Kulisch and Matthias Hocks
“C++ Toolbox for Verified Computing I: Basic Numerical Problems Theory, Algorithms, and Programs” Book Review: This book offers a collection of C++ programs that can be utilized to tackle various numeric problems. The accuracy of the results obtained from these programs is also validated. The C-XSC library is utilized throughout the text. The book is written in a way that does not require an extensive knowledge of C++ programming.
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5."Cryptography and Computational Number Theory (Progress in Computer Science and Applied Logic)" by Kwok Y Lam and Igor Shparlinski | |

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6."Advanced Topics in Computational Number Theory (Graduate Texts in Mathematics)" by Henri Cohen
“Advanced Topics in Computational Number Theory (Graduate Texts in Mathematics (193)” Book Review: This book is a comprehensive reference book for graduate students and researchers in the field of number theory. The book covers various advanced topics such as computational algebraic number theory, elliptic curves, algorithmic aspects of number theory and much more. The author also provides an introduction to the computational methods and techniques used in number theory, including basic algorithms and complexity analysis. The book also includes examples, problems and exercises to enhance understanding of the subject matter.
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7."Numerical Methods for Scientists and Engineers (Dover Books on Mathematics)" by Richard W Hamming
“Numerical Methods for Scientists and Engineers (Dover Books on Mathematics)” Book Review: This book is a classic textbook that covers a broad range of numerical methods used in scientific and engineering computations. It is organized into three main parts: interpolation, approximation, and numerical integration and differentiation. The book also covers topics such as solutions to linear systems, matrix inversion, numerical solutions to differential equations, Fourier analysis, and Monte Carlo methods. The author presents the material in a clear and concise manner and includes many examples and exercises throughout the book, making it an excellent resource for students and practitioners alike.
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8."The Mathematical Theory of Communication" by Claude E Shannon and Warren Weaver | |

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9."The Mathematical Theory of Finite Element Methods (Texts in Applied Mathematics)" by Susanne Brenner and Ridgway Scott
“The Mathematical Theory of Finite Element Methods (Texts in Applied Mathematics Book 15) 3rd Edition” Book Review: The target audience of this book includes mathematicians, engineers, and physical scientists. It covers the fundamental mathematical theories of finite methods and emphasizes the most commonly used tools in research in this field. The book presents a basic understanding of theories, functional and numeral analysis, and approximation. Each chapter is accompanied by additional exercises for practice.
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## 4. Algebraic Number Theory

1."A Classical Introduction to Modern Number Theory" by K Ireland and M Rosen
“A Classical Introduction to Modern Number Theory” Book Review: This book serves as a connection between basic number theory and the advanced study of the subject. It offers a traditional introduction to Modern Number Theory and requires the reader to have prior knowledge of basic abstract algebra. The book features an extensive bibliography and a variety of challenging exercises to enhance the reader’s understanding of number theory. It covers a wide range of important results with elementary proofs. The second edition of the book has been updated, and it includes two new chapters that showcase Mordell-Weil’s conviction in elliptic curves.
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2."Number Fields" by D A Marcus
“Number Fields” Book Review: The fundamental concepts of algebraic number theory are presented in a clear and concise manner in this textbook, which does not assume any prior knowledge of abstract algebra. Key ideas of each chapter are emphasized through the use of various proofs. The book is filled with exercises and appendices to help summarize the necessary background information on algebra. It strikes a balance between computational and theoretical aspects of the subject. The latest edition of this book is widely recognized as an excellent resource for students learning number theory.
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3."Algebraic Number Theory" by Jürgen Neukirch and Norbert Schappacher
“Algebraic Number Theory” Book Review: The main aim of this book is to fill the gap in the content of existing textbooks and provide a comprehensive introduction to algebraic number theory for beginners. It presents basic concepts from the viewpoint of Arakelov theory and elaborates on the content of class field theory. The book contains various examples and hints for further study to enhance the reader’s knowledge. A significant advantage of the new edition is the concluding chapter on zeta-functions and L-series. The book is known for its simplicity, systematic approach, and theoretical balance, making it a highly recommended textbook for studying algebraic number field theory.
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4."Algebraic Number Theory" by John William Scott Cassels and Albrecht Frhlich
“Algebraic Number Theory” Book Review: This book is a classic textbook on algebraic number theory. It covers the basic concepts of algebraic number theory, such as rings of integers, ideal theory, and class groups. The book also discusses more advanced topics like Galois representations, zeta functions, and Iwasawa theory. It includes numerous examples, exercises, and historical notes to aid the reader’s understanding. This book is intended for graduate students and researchers in mathematics who have a strong foundation in algebra and number theory.
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5."Algebraic Number Theory" by Frazer Jarvis
“Algebraic Number Theory” Book Review: The book begins with an introduction to number fields, rings of integers, and Dedekind domains. It covers a wide range of topics such as ideal class groups, Dirichlet’s Unit Theorem, cyclotomic fields, and the Minkowski bound. The later chapters delve into more advanced topics like Galois cohomology and Iwasawa theory. The author provides many examples, exercises and applications throughout the text. This book is a valuable resource for graduate students and researchers in algebraic number theory.
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6."Algebraic Number Theory and Fermat's Last Theorem" by Ian Stewart and David Tall
“Algebraic Number Theory and Fermat’s Last Theorem” Book Review: This book offers an introduction to the fundamental concepts of algebraic numbers while also delving into one of the most captivating stories in mathematical history – the pursuit of a proof for Fermat’s Last Theorem. It aims to inspire a comprehensive study of algebraic number theory by providing a unique perspective. The latest edition of the book presents current information on the unique prime factorization of real quadratic number fields, including Harper’s proof that Z(√14) is Euclidean. Additionally, it expands one chapter into two, exploring fundamental ideas related to modular functions and highlighting the groundbreaking contributions of Frey, Wiles, and others. The book enhances and updates the index, figures, bibliography, and further reading list to provide a richer learning experience. It also demonstrates how fundamental algebraic number concepts can be used to solve problems from a numerical standpoint.
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7."Algebraic Number Theory" by Richard A Mollin
“Algebraic Number Theory” Book Review: In the latest edition of this book, the primary focus of the first chapter is on integral domains, ideals, and unique factorization, while the second chapter delves into field extensions, and the third chapter discusses class groups. Applications are now compiled in chapter four and are also highlighted towards the end of chapter five, with a particular emphasis on Kronecker-Weber thought application for quantitative testing. The sections on ideal decomposition in number fields are now distributed in chapter five. The final chapter provides a thorough explanation of the reciprocity laws. The book includes mini-biographies of notable mathematicians, easily readable formatting, a comprehensive index, and numerous exercises. It is an ideal resource for a first-semester course, as it is both accessible and self-contained, providing a comprehensive and in-depth understanding of numerous applications.
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8."Algebraic Number Theory and Fermat's Last Theorem" by Ian Stewart and David Tall | |

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9."A Course in Algebraic Number Theory" by Robert B Ash | |

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## 5. Number Theory and Cryptography

1."A Course in Number Theory and cryptography" by Neal Koblitz
“A Course in Number Theory and cryptography” Book Review: This book serves as an introduction to both modern and ancient arithmetic topics. The main chapters cover elementary number theory, finite fields, quadratic residues, cryptography, and public key systems. Other topics discussed include primality and factoring, as well as elliptic curves. The book offers numerous exercises and problems for students to practice their skills. It is an excellent resource for mathematics and engineering students alike.
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2."Elliptic Curves: Number Theory and Cryptography" by Lawrence C Washington
“Elliptic Curves: Number Theory and Cryptography” Book Review: This book presents an overview of the essential principles of elliptic curves in numerical analysis. The chapters cover the basics of the theory, torsion points, elliptic curves, and the discrete logarithm problem. Other topics include elliptic curve cryptography, elliptic curves over Q, and isogenies. The book discusses equations and problems in detail, providing a thorough understanding of the material. It is a valuable resource for both mathematics and engineering students.
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3."Computational Number Theory and Modern Cryptography" by Song Y Yan
“Computational Number Theory and Modern Cryptography” Book Review: This book provides an in-depth exploration of the fundamental principles of computational number theory and cryptography. The chapters cover topics such as primality testing, integer factorization, secret-key cryptography, and discrete logarithm-based cryptography. The book also includes discussions on quantum computational number theory, quantum-resistant cryptography, and elliptic curves. Bibliographic notes and references are provided for further reading, while equations and diagrams are presented in detail. The book is an ideal resource for computer engineering and mathematics students.
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4."Number Theory: Structures, Examples, and Problems" by Titu Andreescu and Dorin Andrica
“Number Theory: Structures, Examples, and Problems” Book Review: This book explores essential topics in number theory. The main chapters cover divisibility, the powers of integers, the floor function, and the fractional part, as well as the digits of numbers. Other topics discussed include arithmetic functions, Diophantine equations, and binomial coefficients. The book provides a detailed description of problems and examples, and includes additional problems to test the understanding of students. It is a valuable resource for both engineering and mathematics students.
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5."Number Theory Cryptography and Its Applications to GNU/Linux Software" by Giovanni A Orlando | |

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6."Number Theory for Computing" by M E Hellmann and Song Y Yan
“Number Theory for Computing” Book Review: This book serves as an introduction to classical number theory and its applications. The main chapters cover elementary number theory, algorithmic number theory, primality testing, and integer factorization. Other topics discussed include quantum number-theoretic algorithms, computer systems design, cryptography, and information security. Bibliographic notes are included at the end of every chapter to facilitate further reading and review. The book is suitable for undergraduate students studying computing and information technology, as well as electrical and electronics engineering.
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7."Elementary Number Theory, Cryptography and Codes" by M Welleda Baldoni and Ciro Ciliberto
“Elementary Number Theory, Cryptography and Codes” Book Review: This book presents the fundamental methods of algebra and number theory. The main chapters cover a review of numbers, computational complexity, factoring integers, and continued fractions. Other topics discussed include congruences, unique factorization domains, finite fields, quadratic residues, and primality tests. The book includes multiple-choice questions and computational exercises for students to practice, as well as programming exercises with program questions to test their knowledge. This resource is suitable for advanced mathematical and computational engineering students.
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8."Number Theory in Science and Communication" by Manfred Schroeder
“Number Theory in Science and Communication” Book Review: This comprehensive book provides an in-depth understanding of number theory and its practical applications. It covers various major chapters, such as the natural numbers, primes, the distribution of primes, and various fractions like continued, Egyptian, and farey. The book also covers topics like linear congruences, Diophantine equations, and theorems of Fermat, Wilson, and Euler. It presents a detailed discussion of equations and graphs. This book covers a total of 30 chapters to provide a thorough understanding of the subject matter. It is an ideal resource for undergraduate students of computer science and IT engineering.
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9."Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories (Encyclopaedia of Mathematical Sciences)" by Yu I Manin and Alexei A Panchishkin
“Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories (Encyclopaedia of Mathematical Sciences)” Book Review: This book presents the fundamentals of number theory alongside contemporary and cutting-edge problems. The book covers topics such as non-Abelian generalizations of class field theory, recursive computability, and Diophantine equations. It also includes discussions on zeta- and L-functions, Wiles’ proof of Fermat’s last theorem, and relevant techniques that come from the synthesis of various theories. The book provides numerous problems and solutions to enhance the reader’s understanding. It is an ideal resource for graduate-level students of computational engineering and applied mathematics.
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