This handbook answers some of the needs of the many people who have to deal with spoken mathematics, yet have insufficient background to know the correct verbal expression for the written symbolic one.

Mathematical material is primarily presented visually, and when this material is presented orally, it can be ambiguous. While the parsing of a written expression is clear and well-defined, when it is spoken this clarity may disappear.

For example, “One plus two over three plus OW” can represent the following four numbers, depending on the parsing of the expression: 3/7, 1 2/7, 5, 5 2j3. However, when the corresponding written expression is seen, there is little doubt which of the four numbers it represents.

When reading mathematics orally, such problems are frequently encountered. Of course, the written expression may always be read symbol by symbol, but if the expression is long or there are a cluster of expressions, it can be very tedious and hard to understand. Thus, whenever possible, one wishes to have the written expression spoken in a way that is interest retaining and easy to understand.

In an attempt to alleviate problems such as these, this handbook has been compiled to establish some consistent and well-defined ways of uttering mathematical expressions so that listeners will receive clear, unambiguous, and well-pronounced representations of the subject.

Some of the people who will benefit from this handbook are:

1) those who read mathernatics orally and have insufficient background in the subject, and their listeners;

2) those interested in voice synthesis for the computer, particularly those who deal with spoken symbolic expressions;

and 3) those technical writers and transcribers who may need to verbalize mathematics.

This edition of the handbook is a working one, and it is hoped that the people who use it will add to and refine it. The choice of material and its ordering are my own preferences, and, as such, they reflect my biases. A goal of the handbook is to establish a standard where no standard has existed, so far as I know. However, this standard represents only one of many possibilities. As a blind person, I have learned mathematics by means of others reading the material to me; so my preferences are a result of direct experience. This handbook is organized as follows: In Section I1 the various types of alphabets used in mathematics are listed. Section III lists the basic symbols used in mathematics, along with their verbalizations. Sections IV-Xi list the expressions used in some of the more common branches of mathematics, along with their verbalizations. Section XI1 contains some suggestions on how to and how not to describe diagrams.

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