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Practical Foundations of Mathematics (Cambridge Studies in Advanced Mathematics)
Practical Foundations collects the methods of construction of the objects of twentieth-century mathematics. Although it is mainly concerned with a framework essentially equivalent to intuitionistic Zermelo-Fraenkel logic, the book looks forward to more subtle bases in categorical type theory and the machine representation of mathematics. Each idea
is illustrated by wide-ranging examples, and followed critically along its natural path, transcending disciplinary boundaries between universal algebra, type theory, category theory, set theory, sheaf theory, topology and programming. Students and teachers of computing, mathematics and philosophy will find this book both readable and of lasting value as a reference work.
Contents:
1
First order reasoning
- 2
Types and induction
- 3
Posets and lattices
- 4
Cartesian closed categories
- 5
Limits and colimits
- 6
Structural recursion
- 7
Adjunctions
- 8
Algebra with dependent types
- 9
The quantifiers.
Brief Description:
This book is about the basis of mathematical reasoning both in pure mathematics itself and in computing.
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