Advanced Algebra, Part 1

The book contains many 'drill' examples, which the author considers essential.

E. A. Maxwell (Author)

9780521102674, Cambridge University Press

Paperback / softback, published 12 March 2009

324 pages
21.6 x 14 x 1.8 cm, 0.41 kg

The scope and treatment of Dr Maxwell's two-volume course covering the transition from school to university is directed towards training students in algebraic thinking, so that processes do not become too mechanical. The explanations are full, the difficulties of the beginner are foreseen and overcome. Indeed, the course should prove excellent for the lone student as well as for the supervised class. Topics in part one include polynomial theory, equations, inequalities, partial fractions, permutations and combinations, the binomial theorem and series and determinants. The 'feel' of the book may be illustrated by reference to the treatment of partial fractions, which is novel in several ways. A theoretical exposition is given in some detail and varies from standard treatments in leading to a method of calculation that arises directly from it. The book contains many 'drill' examples, which the author considers essential.

Preface
Introduction
1. Some fundamental ideas and notations
2. The linear polynomial
3. The quadratic polynomial
4. Complex numbers
5. The transformation of equations
synthetic division and the remainder theorem
6. Introduction to the general polynomial
7. Solutions of equations
8. Solution of simultaneous equations
9. The graph of a polynomial
10. Partial fractions
11. Inequalities
12. The graph of a rational function
13. Permutations and combinations
14. The binomial theorem
15. The summation of series
16. Infinite series
17. The binomial series
18. The exponential series
19. The logarithmic series
20. Elementary properties of determinants
Answers to examples.

Subject Areas: Mathematics [PB]