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Descripción Hardcover. Condición: new. Hardcover. 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 undergraduatesand 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, andexplicitly 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 countingto 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. Theapproach 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. The transition from school 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. This book bridges the divide. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Nº de ref. del artículo: 9780198706441
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Descripción HRD. Condición: New. New Book. Delivered from our UK warehouse in 4 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. del artículo: L1-9780198706441
Descripción Hardcover. Condición: Brand New. 2nd edition. 391 pages. 8.50x5.50x0.75 inches. This item is printed on demand. Nº de ref. del artículo: zk0198706448