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The Foundations of Mathematics by Ian Stewart, David Tall, David Orme Tall is a mathematics available to read on EtoBox.

What is The Foundations of Mathematics about?

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

Who reads The Foundations of Mathematics?

Author

Ian Stewart, David Tall, David Orme Tall

Publisher

IRL Press at Oxford University Press

Published

2015

Language

EN

ISBN

9780191016486

Category

mathematics

Subjects

Mathematics, Stem

Rating

4.5 / 5 (90 ratings)

Updated

2026-03-14