A Gateway to Abstract Mathematics

Dr Maxwell has written this short book to introduce students (and teachers) to the ideas involved in abstract mathematics.

E. A. Maxwell (Author)

9780521090285, Cambridge University Press

Paperback / softback, published 20 November 2008

140 pages
20.3 x 12.7 x 0.8 cm, 0.16 kg

Dr Maxwell has written this short book to introduce students (and teachers) to the ideas involved in abstract mathematics. In his preface he states, 'I have often felt that the present plunge into abstraction is too sudden and that there is a need for more elementary work to make the immersion less exhausting.' Dr Maxwell does this by taking various topics from elementary mathematics, and showing what happens when the rules are altered in quite simple ways. He first discusses digital arithmetic, then introduces the idea of a group and illustrates some properties of groups by examples from algebra and geometry.

Preface
Introduction
1. Digital arithmetic
2. Polynomials in digital arithmetic
3. The idea of a group
4. A group of 'product' operations in geometry
5. Groups within groups
6. Group structure on a circle
7. An abstract structure for angles
8. A very abstract algebra for angles
9. Some metrical analogies
Answers
Index.

Subject Areas: Mathematics [PB]