Information Technology Reference
In-Depth Information
Chapter 9
Mathematics
Mathematics is no more than a symbolism. But it is the only
symbolism invented by the human mind which steadfastly resists
the constant attempts of the mind to shift and smudge the mean-
ing …. Our confidence in any science is roughly proportional to
the amount of mathematics it employs—that is, to its ability to
formulate its concepts with enough precision to allow them to be
handled mathematically.
Jacob Bronowski and Bruce Mazlish
The Western Intellectual Tradition
If you want to learn about nature, to appreciate nature, it is nec-
essary to understand the language that she speaks in.
Richard P. Feynman
The Relation of Mathematics to Physics
Mathematics gives solidity to abstract concepts. As for writing in general, there
are well-established conventions of presentation for mathematics and mathematical
concepts. Reading mathematics is difficult work at the best of times, unpleasant work
if the mathematics is badly presented, and pointless if the mathematics does not make
sense.
Often, a statement can be made clearer by using mathematics to express the ideas.
Mathematical notation can be used to describe algorithms, data structures, automata,
or just about any of the objects that computer scientists study. The discipline of
describing work in a mathematical form can expose inconsistencies and gaps, and
provides a basis for making formal statements about the ideas being studied. While
mathematics should not be used unnecessarily—to dress up uninteresting ideas, for
example—ultimately a great deal of computer science has amathematical foundation.
Clarity
In mathematical writing it is essential to be precise. For example, an ambiguous
statement of a theorem can make its proof incomprehensible.
