Discrete Mathematics for New Technology

In the nine years since the publication of the first edition, we have received
feedback on the text from a number of users, both teachers and students. Most
have been complimentary about the clarity of our exposition, some have pointed
out errors of detail or historical accuracy and others have suggested ways in which
the text could be improved. In this edition we have attempted to retain the style
of exposition, correct the (known) errors and implement various improvements
suggested by users.
When writing the first edition, we took a conscious decision not to root the
mathematical development in a particular method or language that was current
within the formal methods community. Our priority was to give a thorough
treatment of the mathematics as we felt this was likely to be more stable over
time than particular methodologies. In a discipline like computing which evolves
rapidly and where the future direction is uncertain, a secure grounding in theory
is important. We have continued with this philosophy in the second edition.
Thus, for example, Z made no appearance in the first edition, and the object
constraint language (OCL) or the B method make no appearance in this edition.
Although the discipline of computing has indeed changed considerably since
the publication of the first edition, the core mathematical requirements of the
undergraduate curricula have remained surprisingly constant. For example, in
the UK, the computing benchmark for undergraduate courses, published by the
Quality Assurance Agency for Higher Education (QAA) in April 2000, requires
undergraduate programmes to present ‘coherent underpinning theory’. In the
USA, the joint ACM/IEEE Computer Society Curriculum 2001 project lists
‘Discrete Structures’ (sets, functions, relations, logic, proof, counting, graphs
and trees) as one of the 14 knowledge areas in the computing curriculum ‘to
emphasize the dependency of computing on discrete mathematics’.