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The Foundations of Mathematics [Paperback]

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Item specifics

Condition
Brand New: A new, unread, unused book in perfect condition with no missing or damaged pages. See all condition definitionsopens in a new window or tab
EAN
9780198706434
UPC
9780198706434
ISBN
9780198706434
MPN
N/A
Item Length
21.1 cm

About this product

Product Information

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 Identifiers

Publisher
Oxford University Press
ISBN-13
9780198706434
eBay Product ID (ePID)
209461089

Product Key Features

Number of Pages
416 Pages
Publication Name
The Foundations of Mathematics
Language
English
Subject
Mathematics
Publication Year
2015
Type
Textbook
Author
David Tall, Ian Stewart
Format
Paperback

Dimensions

Item Height
214 mm
Item Weight
508 g
Item Width
141 mm

Additional Product Features

Country/Region of Manufacture
United Kingdom
Title_Author
Ian Stewart, David Tall

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VAT number: GB 118119922
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