1. Analytic Geometry (1924), by Raymond W Brink.
Amer. Math. Monthly 33 (6) (1926), 332.
This is intended to be a text book for the usual course in the subject. It aims to be a book on the general subject of analytic geometry rather than one on the conic sections, as so many have been. The author opens with a short chapter devoted to things involving coordinates of isolated points, such as the distance between two points and the point dividing a line segment in a given ratio. One wonders why it did not include the slope of the line joining two points and the area of a triangle, derived by the trapezoid method, a method which seems to most beginners less cumbersome than the one involving the base and the altitude. ...
Amer. Math. Monthly 42 (8) (1935), 505.
This text is a very thorough revision and expansion of an earlier edition ... New figures, better paper and typography, and a large increase in the number of problems constitute the most noticeable changes. There has been added a well written chapter on Curve Filling ...
2.2. Review by: Anon.
The Mathematics Teacher 29 (2) (1936), 99-100.
This book is a complete revision of the author's earlier text. The chapter on Conic Sections has been simplified and clarified. A short chapter on Curve Fitting has been added with an introduction to the method of least squares, to meet the needs of students in engineering, statistics, or laboratory sciences. ... Throughout the book the emphasis is placed upon logic and method rather than on information. This is as it should be in all mathematics courses. It does not mean that the book is not adequate in its content of information.
Amer. Math. Monthly 36 (2) (1929), 92-94.
Professor Brink sets forth his own plan and purpose very definitely at the beginning of the preface of his text, "to keep clearly before the student the values which he may expect to receive in return for his efforts." The book begins consistently with a discussion of practical situations and gives a good variety of applied problems throughout. When the student has seen something of the usefulness of the trigonometric functions, has grown somewhat accustomed to the idea of the general angle, with its unrestricted size and double quality value, a more detailed analytical study is made of the functional relations. The final lists of exercises on completing the chapters furnish excellent problem material. ... As has been said, the text aims, in true American fashion, to gain the interest of the students through its practical values, believing this interest will carry over into a more analytical and critical study of the background of the subject.
Amer. Math. Monthly 48 (2) (1941), 141.
The present [edition] has been so extensively revised that it is really a new book. The treatment is rather full. It is felt that the approach to a new concept can best be made by an ample explanation of the idea involved. The progress is very gradual, and amply illustrated by long lists of examples.
4.2. Review by: James McQueen Dobbie.
National Mathematics Magazine 15 (5) (1941), 263-264.
As the author states in the preface, "This book is a complete revision of the author's 'Plane Trigonometry'." The numerous illustrative examples are mostly new and well chosen. The exercises are adequate and well graded. In general, the topics are treated in detail and with some repetitions, so that the book is quite long. However, by the omission of certain indicated topics and some contractions, the text could be adapted for use in the usual two hour semester course.
Amer. Math. Monthly 38 (8) (1931), 451.
The need for carefully selected and well-arranged exercises in trigonometry has been realised in the publication of this book. In each set of exercises not only is the student led by definite, graded steps to the more difficult problems, but enough exercises are given to effect a drill on each principle.
Mathematics News Letter 8 (2) (1933), 46-47.
This book is an excellent text for the student who has had either two or three semesters of algebra in high school whether he intends to pursue the study of mathematics beyond the more elementary courses or not, The first portion of the book reviews the material of high school advanced algebra but being written from a more mature point of view also serves as an introduction to college algebra. The terminology is useful to the student who proposes to continue the study of mathematics. He becomes familiar with terms so often discovered for the first time in advanced courses. Care has been used to present complete proofs or, where the complete discussion is beyond the scope of the book, to state explicitly the assumptions made and the consequent limitations of the theorem. In the few instances where the proof is too advanced for the course, attention has been directed to the omission and a reference made to where the proof can be found.
6.2. Review by: Malcolm Foster.
Amer. Math. Monthly 41 (3) (1934), 184.
This text contains a generous supply of material for the review of elementary algebra. It is designed for students who have had either two or three semesters of high school algebra and contains almost as many examples on this review material as one would find in an elementary text. ... On the whole the treatment of the various topics is conservative and excellent.
6.3. Review by: Anon.
The Mathematics Teacher 26 (7) (1933), 444-445.
This textbook for colleges and for nor mal and technical schools is noteworthy because of its completeness, its logic, its devices for the development of a high degree of technical skill, and its adapt ability to courses of various lengths and purposes. An especial effort has been made in this book to present proofs in logically complete and accurate form.
The Mathematics Teacher 45 (6) (1952), 480.
This text supplies the material for a thorough and complete course in college algebra. Students who have had three semesters of high school algebra should be able to handle the content readily. The book is well organized and is adaptable to courses of different lengths and purposes. An admirable feature of the book is the clarity of explanation of content. Examples to illustrate new content are used frequently and should prove to be very valuable to the learner. ... Definite steps are taken in the text to help the learner organize his knowledge. This emphasis should result in a greater appreciation and understanding of logical thought by the student.
The Mathematics Teacher 29 (2) (1936), 96.
This book is designed for use in college classes in which the students have previously had only two semesters of high school algebra and in secondary school classes for students who are preparing themselves for college. In the case of college and preparatory students who have had only two semesters of algebra the book is intended to supply such students not only with the necessary preparation in algebra but also for courses in physics, statistics, biology, business, medical science, and other sciences for which strictly college algebra is not required. The idea of the function is stressed as it should be and its early introduction is a feature. The book is adaptable to courses of varying lengths and purposes and should be of interest to all teachers of algebra.
National Mathematics Magazine 19 (1) (1944), 52.
This book is written for students who have had one year of high school algebra. It would also serve well as a "refresher" for various types of students, including those whose morale would be improved by proceeding with the expressed hypothesis that they have merely forgotten what they thoroughly accomplished several years ago. ... Presented with uniform clearness and with a sufficiency of well chosen illustrative examples, this book should please a teacher who wishes to give a drill course on the material in question.
The Mathematics Teacher 45 (6) (1952), 478.
This is a rather extensive text, easily adapt able to courses of varying lengths, for students with a background of one year of elementary algebra. Elementary topics are reviewed in a mature manner suitable for college students. The new beginning chapter on real numbers is well done for this level of instruction. Determinants are presented briefly in connection with the work on linear equations; determinants of the third order are expanded by the diagonal method only. The explanation of and exercises on principal roots and fractional exponents have been carefully written. Beyond the work on quadratics there are chapters on ratio, proportion and variation; progressions; logarithms; and the binomial theorem. The binomial theorem is stated for positive integral exponents; no proof is given of it.
National Mathematics Magazine 12 (2) (1937), 103-104.
This text presents a new organization of college algebra, analytic geometry, and trigonometry combined. The book is not divided into these separate units, though it would be easy to pick sequences of chapters in such a way as to give a thorough course in each. Coordinates and graphs, and function concept unify the course as presented. Since some analytic geometry is ordinarily included in each of the other subjects, this text eliminates useless duplications. ... Almost every paragraph and problem from Professor Brink's 1933 'College Algebra' and his 1928 'Plane Trigonometry' are incorporated in the new text with only minor revisions aside from order of presentation; several of the earlier chapters of 'College Algebra' are placed in the appendix. On the other hand, there is considerable revision of the 'Analytic Geometry' as compared with the author's 1924 text. Practically every problem is new, and the presentation of theory is better adapted to the unified course.
Amer. Math. Monthly 46 (7) (1939), 444-445.
This book is an abridged edition of his earlier text entitled 'Analytic Geometry, Revised Edition'. The shorter book is better suited to the needs of a usual course in analytic geometry of four or five hours a week for one quarter, although the reviewer feels that it is well for even freshman college students to have books containing more material than is actually needed for the course. Such would serve as a source for reference for topics which can be-used for extra work by the brilliant students in the class, or as sources for information on analytic geometry needed later in following courses in mathematics. For the ordinary student, however, a compact text covering only the material needed in the course is a delight, and to this end this new book will serve a definite purpose.
Amer. Math. Monthly 50 (5) (1943), 324-325.
This little book begins with a review of the geometry of the sphere, featuring spherical distances, spherical angles and triangles, and polar triangles. Then comes the trigonometry of a right spherical triangle, including Napier's Rules and the discussion of species. This is followed by a similar discussion of oblique triangles. The law of sines, law of cosines, both for sides and for angles, and the half-angle and half side formulas are fully treated. The discussion of Napier's analogies is followed by a rather full treatment of the ambiguous cases. A short final chapter is devoted to the celestial sphere. ... The rather brief treatment is not essentially different from that in other texts, hardly justifying the claims of originality in the preface.