Special attention has been paid to the requirements of the College Entrance Board. The book contains more material than is required for some first courses in Trigonometry, but the matter has been so arranged that the teacher can make such omissions as will suit his particular needs.

The trigonometric functions are defined as ratios; first for acute angles in right triangles, and then these definitions are extended to angles in general by means of coordinates.

The student is first taught to...

In preparing this book, the author had especially in mind classes in the upper grades of grammar schools, though the work will be found equally well adapted to the needs of any classes of beginners.

The ideas which have guided in the treatment of the subject are the following:

The study of algebra is a continuation of what the pupil has been doing for years, but it is expected that this new work will result in a knowledge of general truths about numbers, and an increased power of clear thinking.

All the differences between this work and that pursued in arithmetic may be traced to the introduction of two new elements, namely, negative numbers and the representation of numbers by letters. The solution of problems is one of the most valuable portions of the work, in that it serves to develop the thought-power of the pupil at the same time that it broadens his knowledge of numbers and their relations. Powers are developed and habits formed only by persistent, long-continued practi...

From ancient times, mathematics has developed side-by-side with physics; only in the last two hundred years they came apart as different branches of science. Extensive use of mathematics in other sciences, such as biology, chemistry, economics, pharmacology, environmental and social sciences is even more recent. Nowadays, knowledge of mathematical techniques is indispensable also for students and researchers in these fields.

The series of textbooks “Mathematics that Works” presents mathem...

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Why did the stock market crash more than 500 points on a single Monday in 1987? Why do ancient species often remain stable in the fossil record for millions of years and then suddenly disappear? In a world where nice guys often finish last, why do humans value trust and cooperation? At first glance these questions don't appear to have anything in common, but in fact every one of these statements refers to a complex system. The science of complexity studies how single elements, such as a speci...

Offers a unified discussion of generalized linear models and correlated data methods. Provides information suitable for graduate non-statistics majors or advanced undergraduate statistics majors. Includes case studies with real data. Offers material on R at the end of each chapter. Provides a solutions manual.

The three fixed lights, or windows, subsequently exchanged for our lesser luminaries, were explained one hundred and fifty years ago to signify "the three Persons, Father, Son, Holy Ghost; " and were used to find out the meridian, "when the sun leaves the south, and breaks in at the west window of the Lodge." While the "mossy bed," the ancient signs of disgust and recognition, as well as the primitive name of a Master Mason, are equally obscure at the present day; having been swept away, alon...

The present work is constructed on the same plan as my treatise on Plane Trigonometry, to which it is intended as a sequel; it contains all the propositions usually included under the head of Spherical Trigonometry, together with a large collection of examples for exercise. In the course of the work reference is made to preceding writers from whom assistance has been obtained; besides these writers I have consulted the treatises on Trigonometry by Lardner, Lefebure de Fourcy, and Snowball, an...

In the Chapter on ‘Propositions of Existence’ I have adopted a new ‘normal form,’ in which the Class, whose existence is affirmed or denied, is regarded as the Predicate, instead of the Subject, of the Proposition, thus evading a very subtle difficulty which besets the other form.

These subtle difficulties seem to lie at the root of every Tree of Knowledge, and they are far more hopeless to grapple with than any that occur in its higher branches. For example, the difficulties of the F...