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Byerly's Syllabi.

By W. E. BYERLY, Professor of Mathematics in Harvard University. Each, 8 or 12 pages, 10 cents.

Syllabus of a Course in Plane Trigonometry.

Syllabus of a Course in Plane Analytical Geometry.

Syllabus of a Course in Plane Analytic Geometry. (Advanced Course.)

Syllabus of a Course in Analytical Geometry of Three Dimensions. Syllabus of a Course on Modern Methods in Analytic Geometry. Syllabus of a Course in the Theory of Equations.

Elements of the Differential and Integral Calculus.

With Examples and Applications. By J. M. TAYLOR, Professor of Mathematics in Madison University. 8vo. Cloth. 249 pages. Mailing Price, $1.95; Introduction Price, $1.80.

THE

HE aim of this treatise is to present simply and concisely the fundamental problems of the Calculus, their solution, and more common applications. Its axiomatic datum is that the change of a variable, when not uniform, may be conceived as becoming uniform at any value of the variable.

It employs the conception of rates, which affords finite differentials, and also the simplest and most natural view of the problem of the Differential Calculus. This problem of finding the relative rates of change of related variables is afterwards reduced to that of finding the limit of the ratio of their simultaneous increments; and, in a final chapter, the latter problem is solved by the principles of infinitesimals.

Many theorems are proved both by the method of rates and that of limits, and thus each is made to throw light upon the other. The chapter on differentiation is followed by one on direct integration and its more important applications. Throughout the work there are numerous practical problems in Geometry and Mechanics, which serve to exhibit the power and use of the science, and to excite and keep alive the interest of the student.

The Nation, New York: It has | pages, and at the same time leaves two marked characteristics. In the the impression that all that is necesfirst place, it is evidently a most sary has been said. In the second carefully written book. There is place, the number of carefully senothing vague or slipshod in it. lected examples, both of those worked Nearly every sentence, certainly out in full in illustration of the text, every theorem, seems to have been and of those left for the student to constructed with a strenuous effort work out for himself, is extraordito give it clearness and precision. nary. From this point of view, those This constant attention to the form teachers and pupils who are accusof expression has enabled the author tomed to or prefer a different textto be concise without becoming ob- book, would still do well to provide scure. We are acquainted with no themselves with this, regarding it text-book of the calculus which com- merely as a collection of examples presses so much matter into so few and without any reference to the text.

Elementary Co-ordinate Geometry.

By W. B. SMITH, Professor of Physics, Missouri State University. 12mo. Cloth. 312 pages. Mailing Price, $2.15; for introduction, $2.00.

WHILE in the study of Analytic Geometry either gain of

knowledge or culture of mind may be sought, the latter object alone can justify placing it in a college curriculum. Yet the subject may be so pursued as to be of no great educational value. Mere calculation, or the solution of problems by algebraic processes, is a very inferior discipline of reason. Even geometry is not the best discipline. In all thinking, the real difficulty lies in forming clear notions of things. In doing this all the higher faculties are brought into play. It is this formation of concepts, therefore, that is the essential part of mental training. And it is in line with this idea that the present treatise has been composed. Professors of mathematics speak of it as the most exhaustive work on the subject yet issued in America; and in colleges where an easier textbook is required for the regular course, this will be found of great value for post-graduate study.

Wm. G. Peck, Prof. of Mathe- | mirably arranged. It is an excellent matics and Astronomy, Columbia book, and the author is entitled to College: I have read Dr. Smith's Co- the thanks of every lover of matheordinate Geometry from beginning matical science for this valuable conto end with unflagging interest. Its tribution to its literature. I shall well compacted pages contain an im- recommend its adoption as a text mense amount of matter, most ad- book in our graduate course.

Academic Trigonometry: Plane and Spherical.

By T. M. BLAKSLEE, Ph.D. (Yale), Professor of Mathematics in the University of Des Moines. 12mo. Paper. 33 pages. Mailing Price, 20 cents; for introduction, 15 cents.

THE Plane and Spherical portions are arranged on opposite pages.

The memory is aided by analogies, and it is believed that the entire subject can be mastered in less time than is usually given to Plane Trigonometry alone, as the work contains but 29 pages of text. The Plane portion is compact, and complete in itself.

Examples of Differential Equations.

By GEORGE A. OSBORNE, Professor of Mathematics in the Massachu

setts Institute of Technology, Boston. 12mo. Cloth. vii+ 50 pages. Mailing Price, 60 cents; for introduction, 50 cents.

A

SERIES of nearly three hundred examples with answers, systematically arranged and grouped under the different cases, and accompanied by concise rules for the solution of each case.

Selden J. Coffin, lately Prof. of Its appearance is most timely, and it Mathematics, Lafayette College: supplies a manifest want.

Determinants.

The Theory of Determinants: an Elementary Treatise. By PAUL H HANUS, B.S., recently Professor of Mathematics in the University of Colorado, now Principal of West High School, Denver, Col. 8vo. Cloth. viii + 217 pages. Mailing Price, $1.90: for introduction, $1.80.

THIS

HIS book is written especially for those who have had no previous knowledge of the subject, and is therefore adapted to self-instruction as well as to the needs of the class-room. The subject is at first presented in a very simple manner. As the reader advances, less and less attention is given to details. Throughout the entire work it is the constant aim to arouse and enliven the reader's interest, by first showing how the various concepts have arisen naturally, and by giving such applications as can be presented without exceeding the limits of the treatise. The work is sufficiently comprehensive to enable the student who has mastered the volume to use the determinant notation with ease, and to pursue his further reading in the modern higher algebra with pleasure and profit.

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