College Algebra by Rosenbach

Twenty-six years after the appearance of their tour de force in Fine's College Algebra, the editors at Ginn and Company wanted to follow up with a new, alternative course in classical algebra that would not be quite as detailed or exhaustive as Fine's book. The combination of the two books would thereby satisfy the needs of a larger and more varied audience for Ginn and Company's exceptional series of titles in mathematics. To accomplish this mission, Ginn & Company engaged Professor Joseph Rosenbach (1897-1951) chairman of the mathematics department at the Carnegie Institute of Technology and his colleague in the same department, Professor Edwin Whitman (1887-1978). The result of their collaboration was a superbly organized and eminently appealing text book and the next great classic in algebra to be published by Ginn and Company, in 1931 - “College Algebra” by Joseph Rosenbach and Edwin Whitman. With its wealth of cogent utilitarian explanations and thoroughly motivated illustrative examples while achieving pristine clarity and insightful depth in its theoretical discussions, the book is an ideal general course that is widely accessible to a broad range of students and readers with diverse backgrounds and interests in technological, pragmatic and applied fields and, as well, in the most rigorous programs of pure science and mathematics. Aside from masterfully fulfilling their expository objectives, the authors arrange the material developed in the separate chapters in a manner that allows maximum independence of the different chapters and optimal flexibility in selecting them for a wide choice and variety of instructional programs. They also argument the basic course with attractive and valuable auxiliary features such as the intriguing and informative excursions into the history of the subject and the important figures who created it. Intermittently and judiciously placed throughout the book, these concise articles serve as a refreshing cultural compliment to the utilitarian and theoretical emphasis of the main text. The many splendid pedagogical attributes that are displayed with admirable consistence throughout the book coalesce in particularly commanding fashion in the central chapters on the theory of equations and complex numbers. In the chapter on the theory of equations upwards of twenty theorems are rigorously proved. These include the remainders theorem, the unique factorization theorem, the theorem of the total number of roots, the process of synthetic division, the formulas relative to the coefficients with the roots of higher degree equations, the transformation theorems for modifying original equations into forms that are more accessible to solution; various theorems for evaluating integral, rational, real and complex roots; the identical polynomial theorem, Descartes' Rule of Signs, the conjunctive roots theorem, Horner's method for extracting irrational roots, etc.; the complex derivations of the methods and formulas for solving cubic and quartic equations; a clear explanation of the meaning of the fundamental theorem of algebra and its use as the basis for proving other theorems. Read more