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I: The Intuitive Background
1: Mathematical Thinking
2: Number Systems
II: The Beginnings of Formalisation
3: Sets
4: Relations
5: Functions
III: The Development of Axiomatic Systems
8: Natural Numbers and Proof by Induction
9: Real Numbers
10: Real Numbers as a Complete Ordered Field
11: Complex Numbers and Beyond
IV: Using Axiomatic Systems
12: Axiomatic Structures and Structure Theorems
13: Permutations and Groups
14: Infinite Cardinal Numbers
15: Infinitesimals
V: Strengthening the Foundations
16: Axioms for Set Theory
Ian Stewart is Emeritus Professor of Mathematics at the University
of Warwick. He remains an active research mathematician and is a
Fellow of the Royal Society. Famed for his popular science writing
and broadcasting, for which he is the recipient of numerous awards,
his bestselling books include: Does God Play Dice?, Nature's
Numbers, and Professor Stewart's Cabinet of Mathematical
Curiosities. He also co-authored The Science of Discworld series
with Terry
Pratchett and Jack Cohen David Tall is Emeritus Professor of
Mathematical Thinking at the University of Warwick. Internationally
known for his contributions to mathematics education, his most
recent book is
How Humans Learn to Think Mathematically (2013).
`give[s] a very comprehensive overview of the mathematics involved
in part of a first year mathematics degree. It would be of most
value to tutors and lecturers in encouraging them to think about
teaching methodologies and how they might modify them to help
students in their thinking of mathematical ideas and their
development of a coherent structure of mathematical concepts.'
John Sykes, Maths in School
`Review from previous edition There are many textbooks available
for a so-called transition course from calculus to abstract
mathematics. I have taught this course several times and always
find it problematic. The Foundations of Mathematics (Stewart and
Tall) is a horse of a different color. The writing is excellent and
there is actually some useful mathematics. I definitely like this
book.
'
The Bulletin of Mathematics Books
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