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 ...
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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.
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Add this copy of The Foundations of Mathematics to cart. $5.95, good condition, Sold by ThriftBooks-Reno rated 5.0 out of 5 stars, ships from Reno, NV, UNITED STATES, published 1977 by Oxford University Press, USA.
Add this copy of The Foundations of Mathematics to cart. $7.63, good condition, Sold by BooksRun rated 4.0 out of 5 stars, ships from Philadelphia, PA, UNITED STATES, published 1977 by Oxford University Press.
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Good. Ships in a BOX from Central Missouri! May not include working access code. Will not include dust jacket. Has used sticker(s) and some writing or highlighting. UPS shipping for most packages, (Priority Mail for AK/HI/APO/PO Boxes).
Add this copy of The Foundations of Mathematics to cart. $19.00, very good condition, Sold by HPB-Ruby rated 5.0 out of 5 stars, ships from Dallas, TX, UNITED STATES, published 2015 by Oxford University Press.
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Very good. Connecting readers with great books since 1972! Used books may not include companion materials, and may have some shelf wear or limited writing. We ship orders daily and Customer Service is our top priority!
Add this copy of The Foundations of Mathematics Format: Paperback to cart. $28.94, new condition, Sold by indoo rated 4.0 out of 5 stars, ships from Avenel, NJ, UNITED STATES, published 2015 by Oxford University Press.
