|
|
| book details |
The Foundations of Mathematics
By (author) Ian Stewart, By (author) David Tall
|
| on special |
normal price: R 4,495.95
Price: R 4,045.95
|
| book description |
The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas. This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups. While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward. This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.
| product details |
Normally shipped |
Publisher | Oxford University Press
Published date | 12 Mar 2015
Language |
Format | Hardback
Pages | 408
Dimensions | 217 x 145 x 27mm (L x W x H)
Weight | 600g
ISBN | 978-0-1987-0644-1
Readership Age |
BISAC | mathematics / number systems
| other options |
|
|
|
To view the items in your trolley please sign in.
| sign in |
|
|
|
| specials |
|
Our moment has seen the resurgence of an anarchist sensibility, from the uprisings in Seattle in 1999 to the Occupy movement of 2011.
|
|
André Alexis
Paperback / softback
176 pages
was: R 315.95
now: R 283.95
|
A pack of dogs are granted the power of human thought - but what will it do to them? A surprising and insightful look at the beauty and perils of consciousness.
|
|
|
Dete Meserve
Paperback / softback
320 pages
was: R 666.95
now: R 599.95
|
|
|
|
|
