100 Best Number Theory Books of All Time

We've ranked the best number theory books using expert recommendations, sales data, and millions of reader ratings. At Shortform, we know books. Our book guides are the best in the world. Learn why.

Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem book cover1

Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem

Simon Singh

5.0
"I have discovered a truly marvelous proof, which this margin is too narrow to contain". With these tantalizing words the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations. What came to be known as Fermat's Last Theorem looked simple, yet the finest mathematical minds would be baffled for more than three and a half centuries.Fermat's Last Theor
Gödel, Escher, Bach: An Eternal Golden Braid book cover2

Gödel, Escher, Bach: An Eternal Golden Braid

Douglas R. Hofstadter

4.8
Douglas Hofstadter's book is concerned directly with the nature of “maps” or links between formal systems. However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers at
Zero: The Biography of a Dangerous Idea book cover3

Zero: The Biography of a Dangerous Idea

Charles Seife

4.6
The Babylonians invented it, the Greeks banned it, the Hindus worshipped it, and the Church used it to fend off heretics. For centuries, the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. Zero follows this number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe and its apotheosis as the mystery of t
Elementary Number Theory book cover4

Elementary Number Theory

David Burton

4.6
Written for the one-semester undergraduate number theory course, this text provides a simple account of classical number theory, set against a historical background that shows the subject's evolution from antiquity. It reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.
Number Theory book cover5

Number Theory

George E. Andrews

4.6
Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic.
In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elemen
An Introduction to the Theory of Numbers book cover6

An Introduction to the Theory of Numbers

H. W. Turnbull

4.5
The fifth edition of this classic reference work has been updated to give a reasonably accurate account of the present state of knowledge.
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics book cover7

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

John Derbyshire

4.4
In 1859, Bernhard Riemann, a little-known thirty-two year old mathematician, made a hypothesis while presenting a paper to the Berlin Academy titled “On the Number of Prime Numbers Less Than a Given Quantity.” Today, after 150 years of careful research and exhaustive study, the Riemann Hypothesis remains unsolved, with a one-million-dollar prize earmarked for the first person to conquer it. Altern
A History of π book cover8

A History of π

Petr Beckmann

4.4
The history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.
9

A Friendly Introduction to Number Theory

Joseph H. Silverman

4.4
Aimed at courses in Elementary Number Theory, this book is for math majors, for mathematics education students, and for Computer Science students. Starting from basic algebra, it takes the reader to mathematical research. It includes numerical examples, analyzed for patterns and used to make conjectures.
The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics book cover10

The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics

Marcus du Sautoy

4.4
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
11

Art of Problem Solving Introduction to Counting and Probability Textbook and Solutions Manual 2-Book Set

David Patrick

4.4
Art of Problem Solving Introduction to Counting and Probability Textbook and Solutions Manual 2-Book Set : Learn the basics of counting and probability from former USA Mathematical Olympiad winner David Patrick. Topics covered in the book include permutations, combinations, Pascal's Triangle, basic combinatorial identities, expected value, fundamentals of probability, geometric probability, the Bi
Euclid's Elements book cover12

Euclid's Elements

Euclid, Dana Densmore, T.L. Heath

4.4
Green Lion Press has prepared a new one-volume edition of T.L. Heath's translation of the thirteen books of Euclid's Elements. In keeping with Green Lion's design commitment, diagrams have been placed on every spread for convenient reference while working through the proofs; running heads on every page indicate both Euclid's book number and proposition numbers for that page; and adequate space for
Introduction to Analytic Number Theory book cover13

Introduction to Analytic Number Theory

Tom M. Apostol

4.3
"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enorm
The Golden Ratio: The Story of Phi, the World's Most Astonishing Number book cover14

The Golden Ratio: The Story of Phi, the World's Most Astonishing Number

Mario Livio

4.3
Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago
16

A Classical Introduction to Modern Number Theory (Graduate Texts in Mathematics) (v. 84)

Kenneth Ireland

4.3
This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress
The Book of Numbers book cover17

The Book of Numbers

John H. Conway

4.3
A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science book cover18

A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science

Michael S. Schneider

4.3
The Universe May Be a Mystery,But It's No Secret Michael Schneider leads us on a spectacular, lavishly illustrated journey along the numbers one through ten to explore the mathematical principles made visible in flowers, shells, crystals, plants, and the human body, expressed in the symbolic language of folk sayings and fairy tales, myth and religion, art and architecture. This is a new view of ma
A Mathematician's Apology book cover19

A Mathematician's Apology

G. H. Hardy, C. P. Snow

4.3
Written in 1940 as his mathematical powers were declining, G.H. Hardy's apology offers an engaging account of the thoughts of a man known for his eccentricities as well as his brilliance in mathematics.
20

Elementary Number Theory

Underwood Dudley

4.2
Ideal for a first course in number theory, this lively, engaging text requires only a familiarity with elementary algebra and the properties of real numbers. Author Underwood Dudley, who has written a series of popular mathematics books, maintains that the best way to learn mathematics is by solving problems. In keeping with this philosophy, the text includes nearly 1,000 exercises and problems—so
The Math Book (DK Big Ideas) book cover21

The Math Book (DK Big Ideas)

DK

4.2
Introduction to Number Theory book cover22

Introduction to Number Theory

Mathew Crawford

4.2
e: the Story of a Number book cover23

e: the Story of a Number

Eli Maor

4.2
The story of [pi] has been told many times, both in scholarly works and in popular books. But its close relative, the number e, has fared less well: despite the central role it plays in mathematics, its history has never before been written for a general audience. The present work fills this gap. Geared to the reader with only a modest background in mathematics, the book describes the story of e f
24

Basic Number Theory

Andre Weil

4.2
The first part of this volume is based on a course taught at Princeton University in 1961-62; at that time, an excellent set of notes was prepared by David Cantor, and it was originally my intention to make these notes available to the mathematical public with only quite minor changes. Then, among some old papers of mine, I accidentally came across a long-forgotten manuscript by Chevalley, of pre-
25

The Little Book of Bigger Primes

Paulo Ribenboim

4.2
A deep understanding of prime numbers is one of the great challenges in mathematics. In this new edition, fundamental theorems, challenging open problems, and the most recent computational records are presented in a language without secrets. The impressive wealth of material and references will make this book a favorite companion and a source of inspiration to all readers.

Paulo Ribenboim is Profes
A Course in Arithmetic book cover26

A Course in Arithmetic

J-P. Serre

4.2
Serre's A Course in Arithmetic is a concentrated, modern introduction to basically three areas of number theory, quadratic forms, Dirichlet's density theorem, and modular forms. The first edition was very well accepted and is now one of the leading introductory texts on the advanced undergraduate or beginning graduate level.
From the reviews: .,." The book is carefully written - in particular very
27

The Number Sense: How the Mind Creates Mathematics, Revised and Updated Edition

Stanislas Dehaene

4.2
The Number Sense is an enlightening exploration of the mathematical mind. Describing experiments that show that human infants have a rudimentary number sense, Stanislas Dehaene suggests that this sense is as basic as our perception of color, and that it is wired into the brain. Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematic
28

The Number Devil: A Mathematical Adventure

Hans Magnus Enzensberger, Rotraut Susanne Berner, Michael Henry Heim

4.2
The international best-seller that makes mathematics a thrilling exploration.

In twelve dreams, Robert, a boy who hates math, meets a Number Devil, who leads him to discover the amazing world of numbers: infinite numbers, prime numbers, Fibonacci numbers, numbers that magically appear in triangles, and numbers that expand without. As we dream with him, we are taken further and further into mathemat
29

The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth

Paul Hoffman

4.2
Based on a National Magazine Award-winning article, this masterful biography of Hungarian-born Paul Erdos is both a vivid portrait of an eccentric genius and a layman's guide to some of this century's most startling mathematical discoveries.
30

The Warrior's Apprentice (Vorkosigan Saga, #2)

Lois McMaster Bujold

4.2
Between the seemingly impossible tasks of living up to his warrior-father's legend and surmounting his own physical limitations, Miles Vorkosigan faces some truly daunting challenges.

Shortly after his arrival on Beta Colony, Miles unexpectedly finds himself the owner of an obsolete freighter and in more debt than he ever thought possible. Propelled by his manic "forward momentum," the ever-invent
31

Elementary Number Theory with Programming

Marty Lewinter, Jeanine Meyer

4.2
A highly successful presentation of the fundamental concepts of number theory and computer programming

Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts in the fields of computer science and mathematic
32

The Man Who Knew Infinity: A Life of the Genius Ramanujan

Robert Kanigel

4.2
The tale of a relationship between a young Indian mathematics genius, Ramanujan, and his tutor at Cambridge University, G.H. Hardy, in the years before World War I. Through their eyes the reader is taken on a journey through numbers theory. Ramanujan would regularly telescope 12 steps of logic into two - the effect is said to be like Dr Watson in the train of some argument by Sherlock Holmes. The
Fourier Analysis on Number Fields book cover33

Fourier Analysis on Number Fields

Dinakar Ramakrishnan, Robert J. Valenza

4.2
This book grew out of notes from several courses that the first author has taught over the past nine years at the California Institute of Technology, and earlier at the Johns Hopkins University, Cornell University, the University of Chicago, and the University of Crete. Our general aim is to provide a modern approach to number theory through a blending of complementary algebraic and analytic persp
34

Elements Of Number Theory (Undergraduate Texts In Mathematics)

John Stillwell

4.2
Solutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid the ad hoc proofs in favor of unifying ideas that work in many situations. There are exercises at the end of almost every section, so that each new idea or proof receives immediate reinforcement.
PHILOMATH: The Geometric Unification of Science & Art Through Number book cover35

PHILOMATH: The Geometric Unification of Science & Art Through Number

Robert Edward Grant, Talal Ghannam

4.2

Unifying the various scientific disciplines under one consistent theory is neither an impossible endeavor nor the Holy Grail, as it is often referred to. Since the dawn of history, scientists, philosophers, and sages have always pursued knowledge with an holistic instinct, believing staunchly in its universality and interconnectedness; it cannot nor should it be fragmented. Unfortunately, for abou

A Course in Number Theory and Cryptography book cover36

A Course in Number Theory and Cryptography

Neal Koblitz

4.2
. . . both Gauss and lesser mathematicians may be justified in rejoic- ing that there is one science [number theory] at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean. - G. H. Hardy, A Mathematician's Apology, 1940 G. H. Hardy would have been surprised and probably displeased with the increasing interest in number theory for appli
37

A Conversational Introduction to Algebraic Number Theory: Arithmetic Beyond Z

Paul Pollack

4.2
Multiplicative Number Theory book cover38

Multiplicative Number Theory

Harold Davenport, H.L. Montgomery

4.2
The new edition of this thorough examination of the distribution of prime numbers in arithmetic progressions offers many revisions and corrections as well as a new section recounting recent works in the field. The book covers many classical results, including the Dirichlet theorem on the existence of prime numbers in arithmetical progressions and the theorem of Siegel. It also presents a simplifie
The Arithmetic of Elliptic Curves book cover39

The Arithmetic of Elliptic Curves

Joseph H. Silverman

4.2
Treats the arithmetic theory of elliptic curves in its modern formulation through the use of basic algebraic number theory and algebraic geometry. This book outlines necessary algebro-geometric results and offers an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, and elliptic curves over finite fields.
40

Classroom-Ready Number Talks for Kindergarten, First and Second Grade Teachers: 1000 Interactive Activities and Strategies that Teach Number Sense and Math Facts

Nancy Hughes

4.2
A wide variety of ready-to-use number talks that help kindergarten through second-grade students learn math concepts in fun and easy ways

Bringing the exciting teaching method of number talks into your classroom has never been easier. Simply choose from the hundreds of great ideas in this book and get going, with no extra time wasted!

From activities on addition and subtraction to fractions and dec
41

Prime Numbers and the Riemann Hypothesis

Barry Mazur

4.2
Prime numbers are beautiful, mysterious, and beguiling mathematical objects. The mathematician Bernhard Riemann made a celebrated conjecture about primes in 1859, the so-called Riemann Hypothesis, which remains to be one of the most important unsolved problems in mathematics. Through the deep insights of the authors, this book introduces primes and explains the Riemann Hypothesis. Students with mi
42

Surreal Numbers

Donald E. Knuth

4.2
Shows how a young couple turned on to pure mathematics and found total happiness. This title is intended for those who might enjoy an engaging dialogue on abstract mathematical ideas, and those who might wish to experience how new mathematics is created.
43

Spectral Methods of Automorphic Forms

Henryk Iwaniec

4.1
Automorphic forms are one of the central topics of analytic number theory. In fact, they sit at the confluence of analysis, algebra, geometry, and number theory. The first edition of this volume was respected, both as a textbook and as a source for results, ideas, and references. It helped to spark a growing interest in the mathematical community to bring it back into print. In this second edition
The Higher Arithmetic: An Introduction to the Theory of Numbers book cover44

The Higher Arithmetic: An Introduction to the Theory of Numbers

H. Davenport

4.1
Updated in a seventh edition, The Higher Arithmetic introduces concepts and theorems in a way that does not require the reader to have an in-depth knowledge of the theory of numbers, and also touches on matters of deep mathematical significance. This new edition includes state of the art material on the use of computers in number theory, as well as taking full account of the proving of Fermat's la
45

The Queen of Mathematics: An Introduction to Number Theory

W.S. Anglin

4.1
Like other introductions to number theory, this one includes the usual curtsy to divisibility theory, the bow to congruence, and the little chat with quadratic reciprocity. It also includes proofs of results such as Lagrange's Four Square Theorem, the theorem behind Lucas's test for perfect numbers, the theorem that a regular n-gon is constructible just in case phi(n) is a power of 2, the fact tha
46

Basic Quadratic Forms

Larry J. Gerstein

4.1
47

Topics in the Theory of Numbers

Paul Erdos, Janos Suranyi, Barry Guiduli

4.1
Number theory, the branch of mathematics that studies the properties of the integers, is a repository of interesting and quite varied problems, sometimes impossibly difficult ones. In this book, the authors have gathered together a collection of problems from various topics in number theory that they find beautiful, intriguing, and from a certain point of view instructive.
48

Number Theory: Structures, Examples, and Problems

Titu Andreescu, Dorin Andrica

4.1
This introductory textbook takes a problem-solving approach to number theory, situating each concept within the framework of an example or a problem for solving. Starting with the essentials, the text covers divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, binomial coefficients, Fermat and Mersenne primes and other special numbers, an
The Trachtenberg Speed System of Basic Mathematics book cover49

The Trachtenberg Speed System of Basic Mathematics

Rudolph McShane, Jakow Trachtenberg, Ann Cutler, Sam Sloan

4.1
The Trachtenberg Speed System of Basic Mathematics is a revolutionary system for calculating and teaching basic math. Children, who had repeatedly failed in arithmetic until their parents sent them to learn this method, were able to perform amazing calculations within seconds. In one demonstration, a ten year old kid when asked to multiply 5132437201 times 452736502785 simply wrote on the blackboa
The Mathematical Theory of Communication book cover50

The Mathematical Theory of Communication

Claude E. Shannon, Warren Weaver

4.1
Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory in the Bell System Technical Journal more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and si
51

The Lost Notebook and Other Unpublished Papers of Srinivasa Ramanujan

S. Ramanujan

4.1
The so-called "Lost Notebook" of S.R. Ramanujan was brought to light in 1976 as part of the Watson bequest, by G.E. Andrews with whose introduction this collection of unpublished manuscripts opens. A major portion of the "Lost Notebook" - really just 90 unpaginated sheets of work on "q"-series and other topics - is reproduced here in facsimile. Letters from Ramanujan to Hardy as well as various ot
Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being book cover52

Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being

George Lakoff, Rafael Nuñez

4.1
53

Algebraic Number Theory

Frazer Jarvis

4.1
This undergraduate textbook provides an approachable and thorough introduction to the topic of algebraic number theory, taking the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the
54

Problems in Analytic Number Theory

M. Ram Murty

4.1
This book gives a problem-solving approach to the difficult subject of analytic number theory. It is primarily aimed at graduate students and senior undergraduates. The goal is to give a rapid introduction of how analytic methods are used to study the distribution of prime numbers. The book also includes an introduction to p-adic analytic methods. It is ideal for a first course in analytic number
How Did You Count?: Picture Book book cover55

How Did You Count?: Picture Book

Christopher Danielson

4.1

Winner of the 2026 Mathical Book Prize!From the author of the award-winning Which One Doesn’t Belong? and How Many? comes How Did You Count?, the latest title in Christopher Danielson’s collection that is sure to spark conversation, questioning and wondering amongst both younger and older students alike.This listing is for a hard cover copy of the children's picture book. There is also a Teacher's

56

Trolling Euclid: An Irreverent Guide to Nine of Mathematics' Most Important Problems

Tom Wrigh

4.1
Proofs from THE BOOK book cover57

Proofs from THE BOOK

Martin Aigner, Günter M. Ziegler, Karl H. Hofmann

4.1
This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden's permanent conjecture, as well as additional, highly original and delightful proofs in other chapters.

From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition"

"... It is almost impossible to write a mathematics book that can be read and enjoyed by peop
58

Elementary Number Theory and Its Applications

Kenneth H. Rosen

4.1
The fourth edition of Kenneth Rosen's widely used and successful text, Elementary Number Theory and Its Applications, preserves the strengths of the previous editions, while enhancing the book's flexibility and depth of content coverage.The blending of classical theory with modern applications is a hallmark feature of the text. The Fourth Edition builds on this strength with new examples, addition
59

Number Theory: An Approach Through History from Hammurapi to Legendre

André Weil

4.1
This book presents a historical overview of number theory. It examines texts that span some thirty-six centuries of arithmetical work, from an Old Babylonian tablet to Legendre's Essai sur la Th�orie des Nombres, written in 1798. Coverage employs a historical approach in the analysis of problems and evolving methods of number theory and their significance within mathematics. The book also takes th
60

Unsolved Problems in Number Theory

Richard Guy

4.1
Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane's Online Encyclopedia of Integer Sequences, at the end of several of the se
61

Here's Looking at Euclid: A Surprising Excursion Through the Astonishing World of Math

Alex Bellos

4.1
Too often math gets a bad rap, characterized as dry and difficult. But, Alex Bellos says, "math can be inspiring and brilliantly creative. Mathematical thought is one of the great achievements of the human race, and arguably the foundation of all human progress. The world of mathematics is a remarkable place."Bellos has traveled all around the globe and has plunged into history to uncover fascinat
62

Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis

Hugh L. Montgomery

4.1
This volume contains lectures presented by Hugh L. Montgomery at the NSF-CBMS Regional Conference held at Kansas State University in May 1990. The book focuses on important topics in analytic number theory that involve ideas from harmonic analysis. One particularly valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literat
63

An Illustrated Theory of Numbers

Martin H. Weissman

4.1
An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history.

Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and all
Love and Math: The Heart of Hidden Reality book cover64

Love and Math: The Heart of Hidden Reality

Edward Frenkel

4.1
A New York Times Science Bestseller

What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren’t even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry.

In Love and Math, renowned mathematician Edward Frenkel re
65

Pure Mathematics for Beginners: A Rigorous Introduction to Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra

Steve Warner

4.1
Pure Mathematics for BeginnersPure Mathematics for Beginners consists of a series of lessons in Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra.The 16 lessons in this book cover basic through intermediate material from each of these 8 topics. In addition, all the proofwriting skills that are essential for advanced study in mathemati
66

Additive Combinatorics

Terence Tao, Van H. Vu

4.1
Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring togeth
67

A First Course in Modular Forms

Fred Diamond, Jerry Shurman

4.1
This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular curves an
68

Computational Number Theory

Abhijit Das

4.1
Developed from the author's popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also suitable for researchers new to the field and practitioners of cryptography in industry.



Requiring no
Elementary Number Theory book cover69

Elementary Number Theory

Gareth A. Jones

4.1
70

Rational Points on Elliptic Curves

Joseph H. Silverman, John Tate

4.1
The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book's accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Di
71

Recreations in the Theory of Numbers

Albert H. Beiler

4.0
Number theory, the Queen of Mathematics, is an almost purely theoretical science. Yet it can be the source of endlessly intriguing puzzle problems, as this remarkable book demonstrates. This is the first book to deal exclusively with the recreational aspects of the subject and it is certain to be a delightful surprise to all devotees of the mathematical puzzle, from the rawest beginner to the most
72

Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law

Peter Woit

4.0
At what point does theory depart the realm of testable hypothesis and come to resemble something like aesthetic speculation, or even theology? The legendary physicist Wolfgang Pauli had a phrase for such ideas: He would describe them as "not even wrong," meaning that they were so incomplete that they could not even be used to make predictions to compare with observations to see whether they were w
73

Man vs. Math: Understanding the curious mathematics that power our world

Timothy Revell

4.0
What is the mathematics behind a twitter trend? Does my food really have an equation? And, is there really an algorithm for Love?

Mathematics is inescapable. Wherever you go, whatever you do, however you live your life, mathematics plays a role. From searching for love to donating a kidney, the mathematics governing our world is fascinating, and far reaching. Using interesting anecdotes, simple ana
74

PI in the Sky: Counting, Thinking, and Being

John D. Barrow

4.0
John D. Barrow's Pi in the Sky is a profound -- and profoundly different -- exploration of the world of mathematics: where it comes from, what it is, and where it's going to take us if we follow it to the limit in our search for the ultimate meaning of the universe. Barrow begins by investigating whether math is a purely human invention inspired by our practical needs. Or is it something inherent
75

Riemann's Zeta Function

Harold M. Edwards

4.0
76

A Concise Introduction to the Theory of Numbers

Alan Baker

4.0
Number theory has a long and distinguished history and the concepts and problems relating to the subject have been instrumental in the foundation of much of mathematics. In this book, Professor Baker describes the rudiments of number theory in a concise, simple and direct manner. Though most of the text is classical in content, he includes many guides to further study which will stimulate the read
The New Ambidextrous Universe book cover77

The New Ambidextrous Universe

Martin Gardner

4.0
"What makes Gardner so appealing is his ease in exploring deep ideas . . . and making them accessible to the interested but nontechnical reader. This is a special talent and no one has ever displayed it quite as well as he does." — Los Angeles Times
"Absorbing; enlightening; lucid; witty; inventive. An exemplar of science writing at its very best." — American Mathematical Monthly
A substantial revis
78

Analytic Number Theory (Colloquium Publications, Vol. 53) (Colloquium Publications (Amer Mathematical Soc))

Henryk Iwaniec, Emmanuel Kowalski

4.0
79

Number theory through exercises

Hayk Sedrakyan

4.0
Does God Play Dice?: The New Mathematics of Chaos book cover80

Does God Play Dice?: The New Mathematics of Chaos

Ian Stewart

4.0
The revised and updated edition includes three completely new chapters on the prediction and control of chaotic systems. It also incorporates new information regarding the solar system and an account of complexity theory. This witty, lucid and engaging book makes the complex mathematics of chaos accessible and entertaining. Presents complex mathematics in an accessible style. Includes three new ch
The Transcendental Tangle: Untying the Enigmatic Knots of the Infinite: A Playful Exploration and Guide to the Enigmatic Worl book cover81

The Transcendental Tangle: Untying the Enigmatic Knots of the Infinite: A Playful Exploration and Guide to the Enigmatic Worl

Matthew Weinberg

4.0
The Magic of Math: Solving for x and Figuring Out Why book cover82

The Magic of Math: Solving for x and Figuring Out Why

Arthur Benjamin

4.0
The world's greatest mental mathematical magician takes us on a spellbinding journey through the wonders of numbers (and more)

"Arthur Benjamin ... joyfully shows you how to make nature's numbers dance."--Bill Nye (the science guy)


The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples-from ice-cream scoops and poker hands to measuring mountains and
Everything and More: A Compact History of Infinity book cover83

Everything and More: A Compact History of Infinity

David Foster Wallace

4.0
One of the outstanding voices of his generation, David Foster Wallace has won a large and devoted following for the intellectual ambition and bravura style of his fiction and essays. Now he brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity.


Is infinity a valid mathematical property or a meaningless abstraction? The ni
84

An Imaginary Tale: The Story of the Square Root of Minus One

Paul J. Nahin

4.0
In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i, re-creating the baffling mathematical problems that conjured it up and the colorful characters who tried to solve them. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining
85

Prime Numbers: A Computational Perspective

Richard Crandall, Carl B. Pomerance

4.0
Bridges the gap between theoretical and computational aspects of prime numbers

Exercise sections are a goldmine of interesting examples, pointers to the literature and potential research projects

Authors are well-known and highly-regarded in the field
86

Advanced Topics in Computational Number Theory

Henri Cohen

4.0
The computation of invariants of algebraic number fields such as integral bases, discriminants, prime decompositions, ideal class groups, and unit groups is important both for its own sake and for its numerous applications, for example, to the solution of Diophantine equations. The practical com- pletion of this task (sometimes known as the Dedekind program) has been one of the major achievements
87

Three Pearls of Number Theory

A. Y. Khinchin

4.0
These 3 puzzles involve the proof of a basic law governing the world of numbers known to be correct in all tested cases — the problem is to prove that the law is always correct. Includes van der Waerden's theorem on arithmetic progressions, the Landau-Schnirelmann hypothesis and Mann's theorem, and a solution to Waring's problem.
88

A Computational Introduction to Number Theory and Algebra

Victor Shoup

4.0
Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The mathematical prerequisites are minimal
On Numbers and Games book cover89

On Numbers and Games

John H. Conway

4.0
90

Algebraic Number Theory

Jürgen Neukirch, Norbert Schappacher

4.0
From the review: "The present book has as its aim to resolve a discrepancy in the textbook literature and ... to provide a comprehensive introduction to algebraic number theory which is largely based on the modern, unifying conception of (one-dimensional) arithmetic algebraic geometry. ... Despite this exacting program, the book remains an introduction to algebraic number theory for the beginner..
91

104 Number Theory Problems: From the Training of the USA IMO Team

Titu Andreescu, Dorin Andrica, et al.

4.0
This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and in mathematical research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive pr
92

Statistical Independence in Probability, Analysis and Number Theory

Mark Kac

4.0
This concise monograph in probability by Mark Kac, a well-known mathematician, presumes a familiarity with Lebesgue's theory of measure and integration, the elementary theory of Fourier integrals, and the rudiments of number theory. Readers may then follow Dr. Kac's attempt "to rescue statistical independence from the fate of abstract oblivion by showing how in its simplest form it arises in vario
93

p-adic Numbers, p-adic Analysis, and Zeta-Functions (Graduate Texts in Mathematics) (v. 58)

Neal Koblitz

4.0
The first edition of this work has become the standard introduction to the theory of p-adic numbers at both the advanced undergraduate and beginning graduate level. This second edition includes a deeper treatment of p-adic functions in Ch. 4 to include the Iwasawa logarithm and the p-adic gamma-function, the rearrangement and addition of some exercises, the inclusion of an extensive appendix of an
94

An Introduction to Number Theory

Harold M. Stark

4.0
The majority of students who take courses in number theory are mathematics majors who will not become number theorists. Many of them will, however, teach mathematics at the high school or junior college level, and this book is intended for those students learning to teach, in addition to a careful presentation of the standard material usually taught in a first course in elementary number theory, t
Galois Theory Through Exercises (Springer Undergraduate Mathematics Series) book cover95

Galois Theory Through Exercises (Springer Undergraduate Mathematics Series)

Juliusz Brzeziński

4.0

This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises). In addition to covering standard material, the book explores topics related to classical problems such as Galois’ theorem on solvable groups of polynomial equations of prime degrees, Nagell's proof of non-solvability by ra

Elliptic Tales: Curves, Counting, and Number Theory book cover96

Elliptic Tales: Curves, Counting, and Number Theory

Avner Ash, Robert Gross

4.0
"Elliptic Tales" describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematic
97

Algebraic Number Theory

John William Scott Cassels and Albrecht Frhlich

4.0
First printed in 1967, this book has been essential reading for aspiring algebraic number theorists for more than forty years. It contains the lecture notes from an instructional conference held in Brighton in 1965, which was a milestone event that introduced class field theory as a standard tool of mathematics. There are landmark contributions from Serre and Tate. The book is a standard text for
Algebraic Geometry book cover98

Algebraic Geometry

Robin Hartshorne

4.0
Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. After receiving his Ph.D. from Princeton in 1963, Hartshorne became a Junior Fellow at Harvard, then taught there for several years. In 1972 he moved to California where he is now Professor at the University of California at Berkeley. He is the author of "
Algebra 1: An Incremental Development - Test Forms, 3rd Edition book cover99

Algebra 1: An Incremental Development - Test Forms, 3rd Edition

John H. Saxon

4.0

Homeschooling Algebra 1, test forms only. 30 test forms Grade Level 9.

100

Hilbert's Tenth Problem: An Introduction to Logic, Number Theory, and Computability

M. Ram Murty and Brandon Fodden

4.0