Mathematics for agricultural students
The present book was designed as the text for a working course in elementary Mathematics given in the College of Agriculture of the University of Wisconsin. It is not a textbook of Advanced Algebra, Trigonometry, Analytic Geometry, or "Practical Mathematics." Students pursuing a scientific course, in which but a year of college Mathematics is offered, receive little profit from a formal course in Advanced Algebra, Trigonometry, or Analytic Geometry.
On the other hand, such students benefit little from a so-called "practical" course of a type that does little more than train them to substitute in given formulas or to use formulas merely as a means to an end. Such a course does little to develop the habit or power of clear and logical thinking. This book is the outgrowth of mimeograph notes used for the past three or four years with undergraduate students of agriculture.
With the exception of the illustrations and exercises, the book contains, nevertheless, nothing which is of exclusive interest to agricultural students. It may be used equally well with any class of scientific students who desire only a short course in mathematics beyond elementary Algebra and Geometry. The plan of the book is: First, to select material primarily on the basis of its usefulness to scientific students. Second, to illustrate the principles with problems of interest to the agricultural student, or with problems having direct application to his work.
Third, to give minute and detailed explanations of all. new work, and to assume the minimum attainments in mathematical preparation on the part of the student. On the other hand, details are often omitted from work that is not new to the student, in order that they may be supplied by the student himself.
Fourth, to give detailed directions for doing work "at home" so that the student of moderate mathematical attainments may, nevertheless, "learn by doing."
Fifth, to include certain material not elsewhere readily accessible to the student of science, for the purpose of rendering the book useful for reference throughout the four years of the college course. Sixth, select the topics and the amount of material under each topic so that either a half year or a full year may be devoted to the work. In writing this book the author had in mind the preparation of a text which would:
First, train the student to do neat and careful work. Second, encourage the student to make further use of Elementary Algebra and Geometry. Third, develop in the student the habit of careful and logical thinking. Fourth, train the student to study a problem with a view of discovering the shortest and easiest method of handling it, rather than attacking it by the "first thought-of " method. Fifth, show the student, by illustrations and exercises, how mathematics may be helpful in pursuing other subjects of study and use in a "practical" way.
While this book includes enough material for a year's course of study, it is believed that it does not contain too much material for a shorter course. The inclusion of additional material in the text will at least let the student knowledge of the existence of subjects in mathematics not covered by him in the classroom. Even this superficial knowledge may be very helpful to him later in connection with other scientific work, especially if he knows he can find brief discussions in a familiar book.
The author takes this opportunity to thank Professor C. S. Slichter for assistance in the preparation of the entire manuscript; to acknowledge his indebtedness to Professor E. V. Hunting- ton for valuable suggestions and criticisms. Acknowledgements are due to Mr E. Taylor and Mr T. C. Fry for suggestions based upon their use of the preliminary notes in the classroom.
A very brief review of elementary Algebra is given in the introduction, besides a list of materials and instruments. In the appendix is given, for reference, a list of common mathematical symbols and a few formulas of mensuration. The material in the book which may be omitted when less than a full year is devoted to the course is indicated by enclosing exercise and section numbers, and chapter headings within brackets.
Contents:
Introduction 1
I Graphic Representation 23
II Logarithms. 60
III The Circular Functions: The Triangle 80
IV The Ellipse 128
V The Slide Rule 143
V The Slide Rule 143
VI Statics. 155
VII Permutations, Combinations, and the Binomial Expansion. 189
VIII Progression 200
IX Probability . . 207
X Small Errors 231
XI Point, Plane, and Line in Space 239
XII Maxima and Minima 252
XIII Empirical Equations 264
Appendix 286
Index. 303
VII Permutations, Combinations, and the Binomial Expansion. 189
VIII Progression 200
IX Probability . . 207
X Small Errors 231
XI Point, Plane, and Line in Space 239
XII Maxima and Minima 252
XIII Empirical Equations 264
Appendix 286
Index. 303
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