AMS Chelsea Publishing 1961; 631 pp; hardcover Volume: 354 Reprint/Revision History: reprinted 2005 ISBN10: 0821838636 ISBN13: 9780821838631 List Price: US$76 Member Price: US$68.40 Order Code: CHEL/354.H
 At the beginning of the twentieth century, college algebra was taught differently than it is nowadays. There are many topics that are now part of calculus or analysis classes. Other topics are covered only in abstract form in a modern algebra class on field theory. Fine's College Algebra offers the reader a chance to learn the origins of a variety of topics taught in today's curriculum, while also learning valuable techniques that, in some cases, are almost forgotten. In the early 1900s, methods were often emphasized, rather than abstract principles. In this book, Fine includes detailed discussions of techniques of solving quadratic and cubic equations, as well as some discussion of fourthorder equations. There are also detailed treatments of partial fractions, the method of undetermined coefficients, and synthetic division. The book is ostensibly an algebra book; however, it covers many topics that are found throughout today's curriculum:  calculus and analysis: infinite series, partial fractions, undetermined coefficients, properties of continuous functions,
 number theory: continued fractions,
 probability: basic results in probability.
Though the book is structured as a textbook, modern mathematicians will find it a delight to dip into. There are many gems that have been overlooked by today's emphasis on abstraction and generality. By revisiting familiar topics, such as continued fractions or solutions of polynomial equations, modern readers will enrich their knowledge of fundamental areas of mathematics, while gaining concrete methods for working with their modern incarnations. The book is suitable for undergraduates, graduate students, and researchers interested in algebra. Readership Undergraduates, graduate students, and research mathematicians interested in algebra. Reviews "The author has arranged a great variety of classical, elementary material in a very original manner, which every college student or grammarschool master can still considerably profit from, even so in these days."  Zentralblatt MATH From a review of the previous edition: "This book contains more than would seem possible from the title ... the author demonstrates that he is taking pains to bring scientific rigor into accord with pedagogical considerations."  translation of Jahrbuch Database review cited in Zbl. Reviews Table of Contents Numbers  The natural numberscounting, addition, and multiplication
 Subtraction and the negative
 Division and fractions
 Irrational numbers
 The imaginary and complex numbers
Algebra  Preliminary considerations
 The fundamental operations
 Simple equations in one unknown letter
 Systems of simultaneous simple equations
 The division transformation
 Factors of rational integral expressions
 Highest common factor and lowest common multiple
 Rational fractions
 Symmetric functions
 The binomial theorem
 Evolution
 Irrational functions. Radicals and fractional exponents
 Quadratic equations
 A discussion of the quadratic equation. Maxima and minima
 Equations of higher degree which can be solved by means of quadratics
 Simultaneous equations which can be solved by means of quadratics
 Inequalities
 Indeterminate equations of the first degree
 Ratio and proportion. Variation
 Arithmetical progression
 Geometrical progression
 Harmonical progression
 Method of differences. Arithmetical progressions of higher orders. Interpolation
 Logarithms
 Permutations and combinations
 The multinomial theorem
 Probability
 Mathematical induction
 Theory of equations
 The general cubic and biquadratic equations
 Determinants and elimination
 Convergence of infinite series
 Operations with infinite series
 The binomial, exponential, and logarithmic series
 Recurring series
 Infinite products
 Continued fractions
 Properties of continuous functions
 Answers
 Index
