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Saturday, December 29, 2007

Same topic, different book.

I am studying "Knapp, Basic Algebra", at first read, a well to do self-study book. Chapter I looks like this.
1. Division and Euclidean Algorithms 1
2. Unique Factorization of Integers 4
3. Unique Factorization of Polynomials 9
4. Permutations and Their Signs 15
5. Row Reduction 19
6. Matrix Operations 24
7. Problems 30

A manageable 14 pages on the Euclidean Algorithm for integers and polynomials, but dense. Too dense perhaps. Then I had a look at this other book. "Irving, Integers, Polynomials and Rings", have a look at the table of contents.

1 Introduction: The McNugget Problem
Part I Integers
2 Induction and the Division Theorem
3 The Euclidean Algorithm
4 Congruences
5 Prime Numbers
5.1 Prime Numbers and Generalized Induction
5.2 Uniqueness of Prime Factorizations
5.3 Greatest Common Divisors Revisited
6 Rings
7 Euler’s Theorem
8 Binomial Coefficients
Part II Polynomials
9 Polynomials and Roots
10 Polynomials with Real Coefficients
11 Polynomials with Rational Coefficients
12 Polynomial Rings
13 Quadratic Polynomials
14 Polynomial Congruence Rings
Part III All Together Now
15 Euclidean Rings
16 The Ring of Gaussian Integers
17 Finite Fields

I'll guess I stop for a while on my route and do a bit of fun-studying in Irving. If I don't study it now I probably never will. It is a beautiful book. I was almost forgotten that I had it.

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