TEXT FLY WITHIN THE BOOK ONLY oof > m 60400 1 AN INTRODUCTION TO MATHEMATICS AN INTRODUCTION TO MATHEMATICS With Applications to Science and Agriculture BY ISATAII LESLIE MILLER Professor ofMathematics, South Dakota State College ofAgriculture and Mechanic Arts F. S. CROFTS & CO. NEW YORK MCMXXX -:- -:- COPYRIGHT, 1930,BYF.S. CROITS&Co.,INC. MANUFACTURED IN THE UNITED STATES OF AMERICA BY BRAUNWORTH & CO.,INC., BROOKLYN, NEW YORK PREFACE AFTER some fourteen years of teaching in American colleges and universities the author finds that the average high school graduate has not developed in himself a mathematical type of reasoning. lie therefore hopes that this treatment may in some measure accomplish this purpose. The first few chapters are devoted to a thorough review of high school algebra, for the author is convinced that most college freshmen need considerable drill on the fundamental processes of algebra before attempting a very extensive study of mathematics. In preparing this book theauthor haskept in mind two types of students: first, those who will never take additional work in mathematics, and second, those* who will continue the work in science or agriculture for advanced degrees and will doubtless desire to pursue additional courses in mathematics. He has therefore attempted to write a book basic in the fundamental principles of mathematics and at the same time has endeavored to make practical applications to the fields of science and agri- culture, whereverpossible. Hefeels that athorough knowledge of the material covered in this work will enable the second type of student to successfully pursue a course in analytical geometry followed by a course in the calculus. The author gratefully acknowledges his indebtedness to his colleagues, Professor Win. Asker for preparing the chapter on statistics, and Mr. H. B. MacDougal for checking much of the material, to Professor I. W. Smith of the North Dakota Agri- cultural College for using the material in mimeographed form and offering many valuable suggestions, to Dean D. A. Roth- VI PREFACE rock of Indiana University for reading most of the manuscript and to Professor Wm. Marshall of Purdue University for encouraging him in the work. The author also desires to thank Professor E. S. Crawley of the University of Pennsylvania for his generous permission to use the greater part of his Tables of Logarithms as a portion of this book. I. L. MILLER SOUTH DAKOTA STATE COLLEGE