Math Notation Conventions

Superscript and Subscript

Superscript refers to the index of training examples
Subscript refers to the index of vector elements.

Sequence Notation

A sequence may be named or referred to by an upper-case letter such as "A" or "S". The terms of a sequence are usually named something like "ai" or "an", with the subscripted letter "i" or "n" being the "index" or the counter. So the second term of a sequnce might be named "a2" (pronounced "ay-sub-two"), and "a12" would designate the twelfth term.

The sequence can also be written in terms of its terms. For instance, the sequence of terms ai, with the index running from i = 1 to i = n, can be written as:
http://www.purplemath.com/modules/series.htm

Hat Operator

In statistics, the hat is used to denote an estimator or an estimated value, as opposed to its theoretical counterpart. For example, in the context of errors and residuals, the "hat" over the letter ε indicates an observable estimate (the residuals) of an unobservable quantity called ε (the statistical errors).

Prime Notation

Derivative Operator