Number Theory A Lively Introduction with Proofs, Applications, and Stories

ISBN-10: 0470424133
ISBN-13: 9780470424131
Edition: 2010
List price: $164.99 Buy it from $77.87 Rent it from $28.14
This item qualifies for FREE shipping

*A minimum purchase of $35 is required. Shipping is provided via FedEx SmartPost® and FedEx Express Saver®. Average delivery time is 1 – 5 business days, but is not guaranteed in that timeframe. Also allow 1 - 2 days for processing. Free shipping is eligible only in the continental United States and excludes Hawaii, Alaska and Puerto Rico. FedEx service marks used by permission."Marketplace" orders are not eligible for free or discounted shipping.

30 day, 100% satisfaction guarantee

If an item you ordered from TextbookRush does not meet your expectations due to an error on our part, simply fill out a return request and then return it by mail within 30 days of ordering it for a full refund of item cost.

Learn more about our returns policy

Description: Business professionals and engineers who need to gain a better understanding of mathematical reasoning will turn to Number Theory. This new book provides them with a rigorous yet accessible introduction to elementary number theory along with its  More...

Used Starting from $77.87
New Starting from $160.39
Rent Starting from $28.14
what's this?
Rush Rewards U
Members Receive:
coins
coins
You have reached 400 XP and carrot coins. That is the daily max!
You could win $10,000

Get an entry for every item you buy, rent, or sell.

Study Briefs

Limited time offer: Get the first one free! (?)

All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.

Add to cart
Study Briefs
Calculus 1 Online content $4.95 $1.99
Add to cart
Study Briefs
Algebra Online content $4.95 $1.99
Add to cart
Study Briefs
Introduction to Logic Online content $4.95 $1.99
Add to cart
Study Briefs
Business Math Formulas Online content $4.95 $1.99

Customers also bought

Loading
Loading
Loading
Loading
Loading
Loading
Loading
Loading
Loading
Loading

Book details

List price: $164.99
Copyright year: 2010
Publisher: John Wiley & Sons, Limited
Publication date: 3/19/2010
Binding: Hardcover
Pages: 784
Size: 7.50" wide x 9.25" long x 1.25" tall
Weight: 4.378
Language: English

Business professionals and engineers who need to gain a better understanding of mathematical reasoning will turn to Number Theory. This new book provides them with a rigorous yet accessible introduction to elementary number theory along with its relevant application. Every chapter includes a math myth, which is a fictional story that introduces an important number theory topic in a friendly, inviting manner. Many of the exercise sets include in-depth explorations, in which a series of exercises develop a topic that is related to the material in the section. Several theorems are preceded by Numerical Proof Previews, which are numerical examples that will help give business professionals and engineers a concrete understanding of both the statements of the theorems and the ideas behind their proofs, before formalizing the statement and proof in more abstract terms.

Preface
Structure of the Text
To the Student
To the Instructor
Acknowledgements
Prologue: Number Theory Through the Ages
Numbers, Rational and Irrational (Historical figures: Pythagoras and Hypatia)
Numbers and the Greeks
Numbers You Know
A First Look at Proofs
Irrationality of ?2
Using Quantifiers
Mathematical Induction (Historical figure: Noether)
The Principle of Mathematical Induction
Strong Induction and the Well-Ordering Principle
The Fibonacci Sequence and the Golden Ratio
The Legend of the Golden Ratio
Divisibility and Primes (Historical figure: Eratosthenes)
Basic Properties of Divisibility
Prime and Composite Numbers
Patterns in the Primes
Common Divisors and Common Multiples
The Division Theorem
Applications of god and 1cm
The Euclidean Algorithm (Historical figure: Euclid)
The Euclidean Algorithm
Finding the Greatest Common Divisor
A Greeker Argument that ?2 Is Irrational
Linear Diophantine Equations (Historical figure: Diophantus)
The Equation aX + bY= 1
Using the Euclidean Algorithm to Find a Solution
The Diophantine Equation aX + bY = n
Finding All Solutions to a Linear Diophantine Equation
The Fundamental Theorem of Arithmetic (Historical figure: Mersenne)
The Fundamental Theorem
Consequences of the Fundamental Theorem
Modular Arithmetic (Historical figure: Gauss)
Congruence Modulo n
Arithmetic with Congruences
Check-Digit Schemes
The Chinese Remainder Theorem
The Gregorian Calendar
The Mayan Calendar
Modular Number Systems (Historical figure: Turing)
The Number System Z<sub>n</sub>: An Informal View
The Number System Z<sub>n</sub>: Definition and Basic Properties
Multiplicative Inverses in Z<sub>n</sub>
Elementary Cryptography
Encryption Using Modular Multiplication
Exponents Modulo n (Historical figure: Fermat)
Fermat's Little Theorem
Reduced Residues and the Euler ?-Function
Euler's Theorem
Exponentiation Ciphers with a Prime Modulus
The RSA Encryption Algorithm
Primitive Roots (Historical figure: Lagrange)
The Order of an Element of Z<sub>n</sub>
Solving Polynomial Equations in Z<sub>n</sub>
Primitive Roots
Applications of Primitive Roots
Quadratic Residues (Historical figure: Eisenstein)
Squares Modulo n
Euler's Identity and the Quadratic Character of -1
The Law of Quadratic Reciprocity
Gauss's Lemma
Quadratic Residues and Lattice Points
Proof of Quadratic Reciprocity
Primality Testing (Historical figure: Erd�s)
Primality Testing
Continued Consideration of Charmichael Numbers
The Miller-Rabin Primality Test
Two Special Polynomial Equations in Z<sub>p</sub>
Proof that Miller-Rabin Is Effective
Prime Certificates
The AKS Deterministic Primality Test
Gaussian Integers (Historical figure: Euler)
Definition of the Gaussian Integers
Divisibility and Primes in Z[i]
The Division Theorem for the Gaussian Integers
Unique Factorization in Z[i]
Gaussian Primes
Fermat'sTwo Squares Theorem
Continued Fractions (Historical figure: Ramanujan)
Expressing Rational Numbers as Continued Fractions
Expressing Irrational Numbers as Continued Fractions
Approximating Irrational Numbers Using Continued Fractions
Proving That Convergents are Fantastic Approximations
Some Nonlinear Diophantine Equations (Historical figure: Germain)
Pell's Equation
Fermat's Last Theorem
Proof of Fermat's Last Theorem for n = 4
Germain's Contributions to Fermat's Last Theorem
A Geometric Look at the Equation x<sup>4</sup> + y<sup>4</sup> = z<sup>2</sup>
Index
Appendix: Axioms to Number Theory (online)

×
Free shipping on orders over $35*

*A minimum purchase of $35 is required. Shipping is provided via FedEx SmartPost® and FedEx Express Saver®. Average delivery time is 1 – 5 business days, but is not guaranteed in that timeframe. Also allow 1 - 2 days for processing. Free shipping is eligible only in the continental United States and excludes Hawaii, Alaska and Puerto Rico. FedEx service marks used by permission."Marketplace" orders are not eligible for free or discounted shipping.

Learn more about the TextbookRush Marketplace.

×