This book developed from lecture notes for a class that I have taught for several years at the IBM Systems Research Institute. This is an eight-week class on mathematical methods used in function evaluation routines for digital computers. So far as I know, this is the frst textbook to contain all the main topics relevant to this subject . Indeed, much of the material was not available in books at all and could be found only in original papers and in the documentation of existing computer programs. As the reader can see, the topics included in the book make a varied and interesting assortment and would probably not be grouped together under any other heading.

A short course or seminar based on this book should ft nicely into almost any computer science curriculum. Besides being of special interest in comput*ing, the material provides opportunities for students to employ techniques learned in other courses. Thus, in some exercises a numerical analysis student can exploit his knowledge of numerical methods for solving nonlinear equa*tions. Similarly there are exercises in which a student can make use of his ability to program a language for algebraic manipulation (such as Formac). To be able to do some of the exercises properly, a student should be able to program in a language l ike Algol, Fortran, or PL/I, and should have access to a computer