50 Mathematical Ideas You Really Need to Know

(Marcin) #1

the square root of 2).
Iteration Starting off with a value a and repeating an operation is called
iteration. For example, starting with 3 and repeatedly adding 5 we have the
iterated sequence 3, 8, 13, 18, 23,...
Lemma A statement proved as a bridge towards proving a major theorem.
Matrix An array of numbers or symbols arranged in a square or rectangle.
The arrays can be added together and multiplied and they form an algebraic
system.
Numerator The top part of a fraction. In the fraction 3/7, the number 3 is
the numerator.
One-to-one correspondence The nature of the relationship when each
object in one set corresponds to exactly one object in another set, and vice versa.
Optimum solution Many problems require the best or optimum solution.
This may be a solution that minimizes cost or maximizes profit, as occurs in
linear programming.
Place-value system The magnitude of a number depends on the position of
its digits. In 73, the place value of 7 means ‘7 tens’ and of 3 means ‘3 units’.
Polyhedron A solid shape with many faces. For example, a tetrahedron has
four triangular faces and a cube has six square faces.
Prime number A whole number that has only itself and 1 as divisors. For
example, 7 is a prime number but 6 is not (because 6 ÷ 2 = 3). It is customary
to begin the prime number sequence with 2.
Pythagoras’s theorem If the sides of a right-angled triangle have lengths x,
y and z then x^2 + y^2 = z^2 where z is the length of the longest side (the
hypotenuse) opposite the right angle.
Quaternions Four-dimensional imaginary numbers discovered by W.R.
Hamilton.
Rational numbers Numbers that are either whole numbers or fractions.
Remainder If one whole number is divided by another whole number, the
number left over is the remainder. The number 17 divided by 3 gives 5 with
remainder 2.
Sequence A row (possibly infinite) of numbers or symbols.
Series A row (possibly infinite) of numbers or symbols added together.
Set A collection of objects: for example, the set of some items of furniture
could be F = {chair, table, sofa, stool, cupboard}.

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