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During the past fifteen years the author has taught classes in practical mathematics in the evening school at the Armour Institute of Technology, Chicago. These classes have been composed of men engaged in practical pursuits of various kinds. The needs of these men have been carefully studied; and, so far as possible, those mathematical subjects of interest to them have been taken up. The matter presented to the classes has necessarily been of an intensely practical nature.

This has been worked over and arranged in a form that was thought most suitable for class use; and was printed in Palmer's Practical Mathematics, four volumes, in 1912 and appeared in a revised edition in 1918. The four volume edition has been used by thousands of men for home study. It is to ' meet the needs especially of such men that this one volume edition has been made.

The subject matter includes all that is in the four volumes; and to this has been added a few new topics together with many solutions of exercises, and suggestions that make the text more suitable for home study. It is hoped that it will find a place in the library of the man who applies elementary mathematics, and who wishes occasionally to brush up his mathematics.

Usually when the practical man appreciates the fact for himself that mathematics is a powerful tool that he must be able to use in performing his work, he finds that even the arithmetic that he learned at school has left him. A student of this kind is discouraged if required to pursue the study of mathematics in the ordinary text-books.

This work has been written for the adult. The endeavor has been to make the student feel that he is in actual touch with real things. The intention has been to lay as broad a foundation as is consistent with the scope of the work. The nearly 3000 drill exercises and problems are, in most cases, new. Many of them are adapted from engineering and trade journals, from handbooks of various kinds, and from treatises on the steel square and other mechanical devices; other problems are from the author's experience; and a large number of the specially practical problems were proposed by members of the classes pursuing the course during its growth.

Much information on various matters to which mathematics is applied, is incidentally given in the problems. Many devices and methods used by the practical man are given. Care has been taken to make these true to practice; but, in so wide a range of matter, there are undoubtedly errors. It is thought that the answers to the exercises are given to a reasonable degree of accuracy. It is hoped that the volume, as a whole, will not be found unmathematical.

The main features of Part I are the concise treatment of various subjects in arithmetic and their applications, checks of processes, degree of accuracy possible in solutions, and contracted processes.

In Part II, the endeavor has been to state definitions so as to give a clear idea of the term or object defined, and yet not to be too technical. Wherever possible, the attempt is made to discuss a fact or principle of geometry in such a way that its reasonableness will be apparent. While the subjects are treated in the mathematical order, many applications are given under separate headings. Such are brickwork, lumber, the steel square, screw threads, circular mils, belt pulleys, and gear wheels.

In Part III, the intention is to give sufficient drill in algebra for one who wishes to make direct applications to practical problems. Much attention is given to formulas and theirtransformations. The equation is applied to many practical problems. Graphical methods are considered, and many articles on special subjects are given.

In Part IV, the intention is to give sufficient work in logarithms to secure a fair degree of skill in computations. In trigonometry, those parts are emphasized that may be applied directly to practical problems; while the portions chiefly necessary as an aid in the study of more advanced mathematical subjects, are either treated very slightly or omitted. Many applications are given. The tables are given to four decimal places.

The author wishes to acknowledge his great indebtedness to the more than 1000 men who made up his classes during the growth of this work, and to the hundreds of men from various parts of the country who have offered kindly criticisms and suggestions; for, without their help and sympathy, the present results would have been impossible.

Because of the remarkable success of the previous editions, it is with the greatest pleasure that this special edition is submitted to our practical men.

June, 1919.

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