(1) Elementary Calculus (2) Calculus for Beginners: A Text-book for Schools and Evening Classes (3) A First Course in the Calculus (4) Exponentials Made Easy, or The Story of “Epsilon” (5) Mathematics for Technical Students: Junior Course (6) Elementary Algebra (7) A Concise Geometry (8) Co-ordinate Geometry (Plane and Solid) for Beginners (9) Elements of Practical Geometry: A Two Years' Course for Day and Evening Technical Students

Abstract

(1) PROF. OSGOOD'S “Elementary Calculus” supplies a need—the need of the young mathematician for a sound introduction to the differential calculus. The treatment is almost without blemish and is so simple and clear that the beginner should have no serious difficulty. Chaps. 1–4 introduce only algebraic functions; chaps. 5–8 are concerned with trigonometric and exponential functions and the corresponding inverse functions. The treatment of infinitesimals and differentials in chap. 5 is specially to be commended. The author has one or two hobby-horses. One that he ought not to have ridden here is the denial of the existence of “infinity.” He says (p. 27): “We should not read ' Z approaches infinity,'... but ‘ Z becomes infinite ’;... the statement sometimes made that ‘ Z becomes greater than any assignable quantity ’ is absurd. There is no quantity greater than any assignable quantity.” This last remark contains a certain misunderstanding, and, in any case, such subtleties are not suited to beginners. Among minor points it is curious to note that there is no definition of a limit in the book. Some proof, or at least a reference, should be given for the proposition quoted on p. 113: “A convex curved line is less than a convex broken line which envelops it and has the same extremities.”

(1) Elementary Calculus.

By Prof. William F. Osgood. Pp. ix + 224. (New York: The Macmillan Company; London: Macmillan and Co., Ltd., 1921.) 12s. 6d. net.

(2) Calculus for Beginners: A Text-book for Schools and Evening Classes.

By H. Sydney Jones. Pp. ix + 300. (London: Macmillan and Co., Ltd., 1921.) 6s.

(3) A First Course in the Calculus.

Part 2, Trigonometric and Logarithmic Functions of x, etc. By Prof. William P. Milne G. J. B. Westcott. (Bell's Mathematical Series for Schools and Colleges.) Pp. xv + 181–402 + xv–xxxix. (With answers.) (London: G. Bell and Sons, Ltd., 1920.) 5s.

(4) Exponentials Made Easy, or The Story of "Epsilon."

By M. E. J. Gheury de Bray. Pp. x + 253.(London: Macmillan and Co., Ltd., 1921.) 4s. 6d. net.

(5) Mathematics for Technical Students: Junior Course.

By S. N. Forrest. Pp. viii + 260. (With answers.) (London: Edward Arnold, 1920.) 7s. 6d. net.

(6) Elementary Algebra.

Part 2. By C. V. Durell R. M. Wright. (With answers.) (Cambridge Mathematical Series.) Pp. xxiii + 253–551 + xlvii–lxxxv. (London: G. Bell and Sons, Ltd., 1921.) 5s. 6d. net.

(7) A Concise Geometry.

By Clement V. Durell. (Cambridge Mathematical Series.) Pp. viii + 319. (London: G. Bell and Sons, Ltd., 1920.) 5s. net.

(8) Co-ordinate Geometry (Plane and Solid) for Beginners.

By R. C. Fawdry. (Bell's Mathematical Series for Schools and Colleges.) Pp. viii + 215.(London: G. Bell and Sons, Ltd., 1921.) 5s.

(9) Elements of Practical Geometry: A Two Years' Course for Day and Evening Technical Students.

By P. W. Scott. Pp. v + 185. (London: Sir Isaac Pitman and Sons, Ltd., 1921.) 5s. net.