The Best Number Theory Books 2025

1. Elementary Theory of Numbers [Paperback - Used]

CONDITION - USED - Pages can include limited notes and highlighting, and the copy can include "From the library of" labels or previous owner inscriptions. Accessories such as CD, codes, toys, may not be included. Superb introduction to Euclidean algorithm and its consequences, congruences, continued fractions, powers of an integer modulo m, Gaussian integers, Diophantine equations, more. Problems, with answers. Bibliography.

Elementary Theory of Numbers, Used [Paperback]

2. Elementary Number Theory, Used [Paperback]

An undergraduate-level introduction to number theory, with the emphasis on fully explained proofs and examples. Exercises, together with their solutions are integrated into the text, and the first few chapters assume only basic school algebra. Elementary ideas about groups and rings are then used to study groups of units, quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part, suitable for third-year students, uses ideas from algebra, analysis, calculus and geometry to study Dirichlet series and sums of squares. In particular, the last chapter gives a concise account of Fermat's Last Theorem, from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles.

Elementary Number Theory, Used [Paperback]

3. Primality and Cryptography, Used [Hardcover]

A comprehensive account of recent algorithms developed in computational number theory and primality testing. Provides a general framework for the theoretical study of public key cryptography and pseudorandom generators. Unique in its approach, the book will be a valuable addition to computer literature.

Primality and Cryptography, Used [Hardcover]

4. Introduction to Number Theory, Used [Hardcover]

On historical and mathematical ground alike, number theory has earned a place in the curriculum of every mathematics student. This clear presentation covers the elements of number theory, with stress on the basic topics concerning prime numbers and Diophantine equations (especially quadratic equations in two variables). Topics covered include distribution of primes, unique factorization, reduction of positive definite quadratic forms, the Kronecker symbol, continued fractions, and what Gauss did.

Introduction to Number Theory, Used [Hardcover]

5. Prime Numbers, Friends Who Give Problems: A Trialogue with Papa Paulo, Used [Paperback]

Prime Numbers, Friends Who Give Problems is written as a trialogue, with two persons who are interested in prime numbers asking the author, Papa Paulo, intelligent questions. Starting at a very elementary level, the book advances steadily, covering all important topics of the theory of prime numbers, up to the most famous problems. The humorous conversations and the inclusion of a back-story add to the uniqueness of the book. Concepts and results are also explained with great care, making the book accessible to a wide audience.

Prime Numbers, Friends Who Give Problems: a Trialogue with Papa Paulo, Used [Paperback]

6. Unsolved Problems in Number Theory, Used [Hardcover]

Mathematics is kept alive by the appearance of new unsolved problems, problems posed from within mathematics itself, and also from the increasing number of disciplines where mathematics is applied. This book provides a steady supply of easily understood, if not easily solved, problems which can be considered in varying depths by mathematicians at all levels of mathematical maturity. For this new edition, the author has included new problems on symmetric and asymmetric primes, sums of higher powers, Diophantine m-tuples, and Conway's RATS and palindromes. The author has also included a useful new feature at the end of several of the sections: lists of references to OEIS, Neil Sloane's Online Encyclopedia of Integer Sequences. About the first Edition: "...many talented young mathematicians will write their first papers starting out from problems found in this book." Andr s S rk zi, MathSciNet

Unsolved Problems in Number Theory, Used [Hardcover]

7. The Nature and Power of Mathematics [Paperback - Used]

CONDITION - USED - Pages can include limited notes and highlighting, and the copy can include "From the library of" labels or previous owner inscriptions. Accessories such as CD, codes, toys, may not be included. In this engaging book, Donald Davis explains some of the most fascinating ideas in mathematics to the nonspecialist, highlighting their philosophical and historical interest, their often surprising applicability, and their beauty. The three main topics discussed are non-Euclidean geometry, with its application to the theory of relativity; number theory, with its application to cryptography; and fractals, which are an application in art, among other areas, of early mathematical work on iteration. Other topics include the influence of Greek mathematics on Kepler's laws of planetary motion, and the theoretical work that led to the development of computers. Assuming the reader has some background in basic algebra and geometry, Davis relies on exercises to develop some of the important concepts. These exercises are designed to improve the reader's ability in logic, and enable him or her actually to experience mathematics at increasingly advanced levels.

The Nature and Power of Mathematics, Used [Paperback]

8. Music of the Primes, The, Used [Paperback]

In 1859, German mathematician Bernhard Riemann presented a paper to the Berlin Academy that would forever change the history of mathematics. The subject was the mystery of prime numbers. At the heart of the presentation was an idea that Riemann had not yet proved but one that baffles mathematicians to this day. Solving the Riemann Hypothesis could change the way we do business, since prime numbers are the lynchpin for security in banking and e-commerce. It would also have a profound impact on the cutting-edge of science, affecting quantum mechanics, chaos theory, and the future of computing. Leaders in math and science are trying to crack the elusive code, and a prize of $1 million has been offered to the winner. In this engaging book, Marcus du Sautoy reveals the extraordinary history behind the holy grail of mathematics and the ongoing quest to capture it.

The Music of the Primes : Searching to Solve the Greatest Mystery in Mathematics, Used [Paperback]

9. Calculus, Early Transcendentals, Student Resource Manual [Paperback - Used]

CONDITION - USED - Pages can include limited notes and highlighting, and the copy can include "From the library of" labels or previous owner inscriptions. Accessories such as CD, codes, toys, may not be included. Designed for the Calculus I-II-III sequence, the seventh edition continues to evolve to fulfill the needs of a changing market by providing flexible solutions to teaching and learning needs of all kinds. The new edition retains the strengths of earlier editions--its trademark clarity of exposition, sound mathematics, excellent exercises and examples, and appropriate level--while incorporating new ideas that have withstood the objective scrutiny of many skilled and thoughtful instructors. For the first time, the Seventh Edition is available in both Late Transcendentals and Early Transcendentals versions.

Calculus, Early Transcendentals, Student Resource Manual, Used [Paperback]

10. The Nature and Power of Mathematics (Dover Books on Mathematics), Used [Paperback]

In this engaging book, Donald Davis explains some of the most fascinating ideas in mathematics to the nonspecialist, highlighting their philosophical and historical interest, their often surprising applicability, and their beauty. The three main topics discussed are non- Euclidean geometry, with its application to the theory of relativity; number theory, with its application to cryptography; and fractals, which are an application in art, among other areas, of early mathematical work on iteration. Other topics include the influence of Greek mathematics on Kepler's laws of planetary motion, and the theoretical work that led to the development of computers. Assuming the reader has some background in basic algebra and geometry, Davis relies on exercises to develop some of the important concepts. These exercises are designed to improve the reader's ability in logic, and enable him or her actually to experience mathematics at increasingly advanced levels.

The Nature and Power of Mathematics, Used [Paperback]