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The Foundations of Mathematics
By Ian Stewart
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Description
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
Binding:
Paperback
Edition:
2
Number of Pages:
416
Release Date:
2015-05-01
Publication Date:
2015-03-12
Publisher:
Oxford University Press
Languages:
Original:
English
ISBN10:
019870643X
ISBN13:
9780198706434
GPSR Manufacturer Reference:
Minimum Reading Age:
10
Maximum Reading Age:
80
Weight:
508 g
Height:
136 cm
Width:
213 cm
Thickness:
30 cm
Condition
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Very good
Almost no signs of wear. Book pages have no markings, accessories are intact and all other media are in good condition.
€18,89