جبر دانشگاهی (انتشارات آرمس چلسی)

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 fourth-order 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.

the Author States In His Preface, In This Book I Have Endeavored To Develop The Theory Of The Algebraic Processes In As Elementary And Informal A Manner As Possible, But Connectedly And Rigorously, And To Present The Processes Themselves In The Form Best Adapted To The Purposes Of Practical Reckoning. Five Early Chapters Cover Natural, Irrational, Imaginary, And Complex Numbers. The Rest Of The Book, 38 Chapters, Covers Algebra, Progressing From Preliminary Considerations Through Properties Of Continuous Functions. The Book Was Originally Published In Boston By Ginn And Company In 1905. Author Information Is Not Given. Annotation ©2005 Book News, Inc., Portland, Or

Includes discussions of techniques of solving quadratic and cubic equations, as well as some discussion of fourth-order equations. This book covers topics such as: calculus and analysis - infinite series, partial fractions, undetermined coefficients, and properties of continuous functions; number theory - continued fractions; and, probability.