Glossary
Algebra Dealing with letters instead of numbers so as to extend arithmetic,
algebra is now a general method applicable to all mathematics and its
applications. The word ‘algebra’ derives from ‘al-jabr’ used in an Arabic text of
the ninth century AD.
Algorithm A mathematical recipe; a set routine for solving a problem.
Argand diagram A visual method for displaying the two-dimensional plane
of complex numbers.
Axiom A statement, for which no justification is sought, that is used to define
a system. The term ‘postulate’ served the same purpose for the Greeks but for
them it was a self-evident truth.
Base The basis of a number system. The Babylonians based their number
system on 60, while the modern base is 10 (decimal).
Binary number system A number system based on two symbols, 0 and 1,
fundamental for computer calculation.
Cardinality The number of objects in a set. The cardinality of the set {a, b,
c, d, e} is 5, but cardinality can also be given meaning in the case of infinite sets.
Chaos theory The theory of dynamical systems that appear random but have
underlying regularity.
Commutative Multiplication in algebra is commutative if a × b = b × a, as in
ordinary arithmetic (e.g. 2 × 3 = 3 × 2). In many branches of modern algebra
this is not the case (e.g. matrix algebra).
Conic section The collective name for the classical family of curves which
includes circles, straight lines, ellipses, parabolas and hyperbolas. Each of these
curves is found as cross-sections of a cone.
Corollary A minor consequence of a theorem.
Counterexample A single example that disproves a statement. The
statement ‘All swans are white’ is shown to be false by producing a black swan as
a counterexample.
Denominator The bottom part of a fraction. In the fraction 3/7, the number
7 is the denominator.
Differentiation A basic operation in Calculus which produces the derivative
or rate of change. For an expression describing how distance depends on time,