A set of one-line text-book-style mathematical expressions is defined by a context free grammar. This grammar generates strings which describe the expressions in terms of mathematical symbols and some simple positional operators, such as vertical concatenation. The grammar rules are processed to abstract information used to drive the parsing scheme. This has been called syntax-controlled as opposed to syntax-directed analysis. The parsing scheme consists of two operations. First, the X-Y plane is searched in such a way that the mathematical characters are picked up in a unique order. Then, the resulting character string is parsed using a precedence algorithm with certain modifications for special cases. The search of the X-Y plane is directed by the particular characters encountered.