A Concrete Introduction to Higher Algebra : Undergraduate Texts in Mathematics - Lindsay N. Childs

Instant online reading.
Don't wait for delivery!
Go digital and save!

A Concrete Introduction to Higher Algebra

By: Lindsay N. Childs

Write A Review

Paperback | 14 January 2000 | Edition Number 2

At a Glance

Paperback
544 Pages

Edition Type
Revised

Dimensions(cm)
23.39 x 15.6 x 2.79

Paperback

$139.00

or 4 interest-free payments of $34.75 with

Aims to ship in 7 to 10 business days

This book is an informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. A strong emphasis on congruence classes leads in a natural way to finite groups and finite fields. The new examples and theory are built in a well-motivated fashion and made relevant by many applications--to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises, ranging from routine examples to extensions of theory, are found throughout the book; hints and answers for many of them are included in an appendix.

Industry Reviews

From the reviews:

"The user-friendly exposition is appropriate for the intended audience. Exercises often appear in the text at the point they are relevant, as well as at the end of the section or chapter. Hints for selected exercises are given at the end of the book. There is sufficient material for a two-semester course and various suggestions for one-semester courses are provided. Although the overall organization remains the same in the second edition?Changes include the following: greater emphasis on finite groups, more explicit use of homomorphisms, increased use of the Chinese remainder theorem, coverage of cubic and quartic polynomial equations, and applications which use the discrete Fourier transform." MATHEMATICAL REVIEWS

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Mathematics Algebra

This product is categorised by

Non-Fiction Mathematics Algebra

Introduction	p. vii
Numbers	p. 1
Induction	p. 8
Induction	p. 8
Another Form of Induction	p. 13
Well-Ordering	p. 16
Division Theorem	p. 18
Bases	p. 20
Operations in Base a	p. 23
Euclid's Algorithm	p. 25
Greatest Common Divisors	p. 25
Euclid's Algorithm	p. 27
Bezout's Identity	p. 29
The Efficiency of Euclid's Algorithm	p. 36
Euclid's Algorithm and Incommensurability	p. 40
Unique Factorization	p. 47
The Fundamental Theorem of Arithmetic	p. 47
Exponential Notation	p. 50
Primes	p. 55
Primes in an Interval	p. 59
Congruences	p. 63
Congruence Modulo m	p. 63
Basic Properties	p. 65
Divisibility Tricks	p. 68
More Properties of Congruence	p. 71
Linear Congruences and Bezout's Identity	p. 72
Congruence Classes	p. 76
Congruence Classes (mod m): Examples	p. 76
Congruence Classes and Z/mZ	p. 80
Arithmetic Modulo m	p. 82
Complete Sets of Representatives	p. 86
Units	p. 88
Applications of Congruences	p. 91
Round Robin Tournaments	p. 91
Pseudorandom Numbers	p. 92
Factoring Large Numbers by Trial Division	p. 100
Sieves	p. 103
Factoring by the Pollard Rho Method	p. 105
Knapsack Cryptosystems	p. 111
Rings and Fields	p. 118
Axioms	p. 118
Z/mZ	p. 124
Homomorphisms	p. 127
Fermat's and Euler's Theorems	p. 134
Orders of Elements	p. 134
Fermat's Theorem	p. 138
Euler's Theorem	p. 141
Finding High Powers Modulo m	p. 145
Groups of Units and Euler's Theorem	p. 147
The Exponent of an Abelian Group	p. 152
Applications of Fermat's and Euler's Theorems	p. 155
Fractions in Base a	p. 155
RSA Codes	p. 164
2-Pseudoprimes	p. 169
Trial a-Pseudoprime Testing	p. 175
The Pollard p - 1 Algorithm	p. 177
On Groups	p. 180
Subgroups	p. 180
Lagrange's Theorem	p. 182
A Probabilistic Primality Test	p. 185
Homomorphisms	p. 186
Some Nonabelian Groups	p. 189
The Chinese Remainder Theorem	p. 194
The Theorem	p. 194
Products of Rings and Euler's [phi]-Function	p. 202
Square Roots of 1 Modulo m	p. 205
Matrices and Codes	p. 208
Matrix Multiplication	p. 209
Linear Equations	p. 212
Determinants and Inverses	p. 214
M[subscript n](R)	p. 215
Error-Correcting Codes, I	p. 217
Hill Codes	p. 224
Polynomials	p. 231
Unique Factorization	p. 239
Division Theorem	p. 239
Primitive Roots	p. 243
Greatest Common Divisors	p. 245
Factorization into Irreducible Polynomials	p. 249
The Fundamental Theorem of Algebra	p. 253
Rational Functions	p. 254
Partial Fractions	p. 255
Irreducible Polynomials over R	p. 258
The Complex Numbers	p. 260
Root Formulas	p. 263
The Fundamental Theorem	p. 269
Integrating	p. 273
Derivatives	p. 277
The Derivative of a Polynomial	p. 277
Sturm's Algorithm	p. 280
Factoring in Q[x], I	p. 286
Gauss's Lemma	p. 286
Finding Roots	p. 289
Testing for Irreducibility	p. 291
The Binomial Theorem in Characteristic p	p. 293
The Binomial Theorem	p. 293
Fermat's Theorem Revisited	p. 297
Multiple Roots	p. 300
Congruences and the Chinese Remainder Theorem	p. 302
Congruences Modulo a Polynomial	p. 302
The Chinese Remainder Theorem	p. 308
Applications of the Chinese Remainder Theorem	p. 310
The Method of Lagrange Interpolation	p. 310
Fast Polynomial Multiplication	p. 313
Factoring in F[subscript p][x] and in Z[x]	p. 323
Berlekamp's Algorithm	p. 323
Factoring in Z[x] by Factoring mod M	p. 333
Bounding the Coefficients of Factors of a Polynomial	p. 334
Factoring Modulo High Powers of Primes	p. 338
Primitive Roots	p. 346
Primitive Roots Modulo m	p. 346
Polynomials Which Factor Modulo Every Prime	p. 351
Cyclic Groups and Primitive Roots	p. 353
Cyclic Groups	p. 353
Primitive Roots Modulo p[superscript e]	p. 356
Pseudoprimes	p. 363
Lots of Carmichael Numbers	p. 363
Strong a-Pseudoprimes	p. 368
Rabin's Theorem	p. 372
Roots of Unity in Z/mZ	p. 378
For Which a Is m an a-Pseudoprime?	p. 378
Square Roots of -1 in Z/pZ	p. 381
Roots of -1 in Z/mZ	p. 382
False Witnesses	p. 385
Proof of Rabin's Theorem	p. 388
RSA Codes and Carmichael Numbers	p. 392
Quadratic Residues	p. 397
Reduction to the Odd Prime Case	p. 397
The Legendre Symbol	p. 399
Proof of Quadratic Reciprocity	p. 405
Applications of Quadratic Reciprocity	p. 407
Congruence Classes Modulo a Polynomial	p. 414
The Ring F[x]/m(x)	p. 414
Representing Congruence Classes mod m(x)	p. 418
Orders of Elements	p. 422
Inventing Roots of Polynomials	p. 426
Finding Polynomials with Given Roots	p. 428
Some Applications of Finite Fields	p. 432
Latin Squares	p. 432
Error Correcting Codes	p. 438
Reed-Solomon Codes	p. 450
Classifying Finite Fields	p. 464
More Homomorphisms	p. 464
On Berlekamp's Algorithm	p. 468
Finite Fields Are Simple	p. 469
Factoring x[superscript pn] - x in F[subscript p][x]	p. 471
Counting Irreducible Polynomials	p. 474
Finite Fields	p. 477
Most Polynomials in Z[x] Are Irreducible	p. 479
Hints to Selected Exercises	p. 483
References	p. 509
Index	p. 513
Table of Contents provided by Syndetics. All Rights Reserved.

A Concrete Introduction to Higher Algebra

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Algebra

The Maths Book

Big Ideas Simply Explained

Linear Algebra and Its Applications

6th Global Edition

Elementary Linear Algebra

8th Edition - International Metric Edition

A Mind for Numbers

How to Excel at Math and Science (Even If You Flunked Algebra)

Essential Math for Data Science

Take Control of Your Data with Fundamental Linear Algebra, Probability, and Statistics

Linear Algebra: A Modern Introduction

4th Edition

Essential Calculus

2nd Edition

Mechanical Engineering for Makers

A Hands-on Guide to Designing and Making Physical Things

The Cartoon Guide to Algebra

Cartoon Guide Series

Statistics

5th Edition - The Art and Science of Learning from Data, Global Edition

Number Systems

A Path into Rigorous Mathematics

The Analystâs Gambit

A Second Course in Functional Analysis

Saturated Fusion Systems on $p$-Groups of Maximal Class

$G$-Global Homotopy Theory and Algebraic $K$-Theory

Arithmetic Quotients of the Bruhat-Tits Building for Projective GeneralLinear Groups in Positive Characteristic

I Wish They'd Taught Me That

Overlooked and Omitted Topics in Mathematics

Topology at Infinity of Discrete Groups

Geometry, Groups and Mathematical Philosophy

Introduction to Lie Algebras

Finite and Infinite Dimension

The Practice of Algebraic Curves

A Second Course in Algebraic Geometry