Advanced Course In Algebra (1904) - Couverture souple

Wells, Webster

Couverture souple

ISBN 10 : 1436761174 ISBN 13 : 9781436761178

Editeur : Kessinger Publishing, 2008

Synopsis

""Advanced Course In Algebra"" is a comprehensive textbook written by Webster Wells and published in 1904. This book is designed for students who have already completed an introductory course in algebra and are looking to further their knowledge in the subject. The book covers a wide range of topics, including equations, functions, polynomials, matrices, and determinants. It also includes advanced topics such as group theory, field theory, and Galois theory. The book is structured in a clear and concise manner, with each chapter building on the previous one. It includes numerous examples, exercises, and problems to help students understand and apply the concepts covered in the book. This textbook is an essential resource for students studying algebra at an advanced level, as well as for teachers and researchers in the field of mathematics.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

A propos du livre

Présentation de l'éditeur

In preparing the present work, the author has endeavored to meet the needs of Colleges and Scientific Schools of the highest rank. The development of the subject follows in the main the author's College Algebra; but numerous improvements have been introduced. Attention is especially invited to the following : 1. The development of the fundamental laws of Algebra for the positive and negative integer, the positive and negative fraction, and zero, in Chaps. I and II. In the above treatment, the author has followed to a certain extent The Number System of Algebra, by Professor H. B. Fine ; who has very courteously permitted this use of his treatise. 2. The development of the principles of equivalence of equations, and systems of equations, both linear and of higher degrees; see §§ 116-123, 182, 233-6, 396, 442, 470, 477, and 478. 3. The prominence given to graphical representation. In Chap. XIV, the student learns how to obtain the graphs of linear equations with two unknown numbers, and of linear expressions with one unknown number. He also learns how to represent graphically the solution of a system of two linear equations, involving two unknown numbers, and sees how inde- terminate and inconsistent systems are represented graphically. The graphical representation of quadratic expressions, with one unknown number, is taken up in § 465 ; and, in § 467, the graphical representation of equal and imaginary roots. The principles are further developed for simultaneous quad- ratics, in §§ 482 and 483; and for expressions of any degree, with one unknown number, in §§ 744 and 745. At the end of Chap. XVIII, the student is taught the graphi- cal representation of the fundamental laws of Algebra for pure imaginary and complex numbers. In Chap. XXXVII, the graphical representation is given of Derivatives (§ 751), of Multiple Boots (§ 755), of Sturm's Theorem (§ 762), and of a Discontinuous Function (§ 766). 4. In Chap. VII, there are given the Remainder and Factor Theorems, and the principles of Symmetry. 5. In Chap VIII will be found every method of factoring which can be done advantageously by inspection, including factoring of symmetrical expressions. In this chapter is also given Solution of Equations by Factoring (§ 182). 6. In the earlier portions of Chap. XI, the pupil is shown that additional solutions are introduced by multiplying a fractional equation by an expression which is not the L.C.M. of the given denominators ; and is shown how such additional solutions are discovered. 7. In §§ 264 and 265, the student is taught how to find the values of expressions taking the indeterminate forms ^j — > Ox 00, and oo — oo. 8. All work coming under the head of the Binomial Theo- rem for positive integral exponents is taken up in the chapter on Involution. 9. In developing the principles of Evolution, all roots are restricted to their principal values. 10. In the examples of § 398, the pupil is taught to reject all solutions which do not satisfy the given equation, when the roots have their principal values. 11. The development of the theory of the Irrational Num- ber, and its graphical representation (§§ 399-406). 12. The development of the fundamental laws of Algebra for Pure Imaginary and Complex Numbers (Chap. XVIII). 13. The use of the general form ax^ + 6a; + c = 0, in the theory of quadratic equations (§§ 454-6). 14. The discussion of the maxima and minima values of quadratic expressions (§ 461). 15. The chapter on Convergency and Divergency of Series (Chap. XXVI). 16. In Chap. XXVIII is given Euler's proof of the Binomial Theorem, for any Eational Exponent. 17. The solution of logarithmic equations (§ 604). 18. The proof of the formula for the number of permuta- tions of n different things, taken r at a time (§ 624).

Présentation de l'éditeur

This book was originally published prior to 1923, and represents a reproduction of an important historical work, maintaining the same format as the original work. While some publishers have opted to apply OCR (optical character recognition) technology to the process, we believe this leads to sub-optimal results (frequent typographical errors, strange characters and confusing formatting) and does not adequately preserve the historical character of the original artifact. We believe this work is culturally important in its original archival form. While we strive to adequately clean and digitally enhance the original work, there are occasionally instances where imperfections such as blurred or missing pages, poor pictures or errant marks may have been introduced due to either the quality of the original work or the scanning process itself. Despite these occasional imperfections, we have brought it back into print as part of our ongoing global book preservation commitment, providing customers with access to the best possible historical reprints. We appreciate your understanding of these occasional imperfections, and sincerely hope you enjoy seeing the book in a format as close as possible to that intended by the original publisher.

Détails de l'édition

• Éditeur: Kessinger Publishing
• Date d'édition: 2008
• Langue: anglais
• ISBN 10: 1436761174
• ISBN 13: 9781436761178
• Reliure: Broché
• Nombre de pages: 632
• Coordonnées du fabricant: non disponible
• Personne responsable: KreGa Onlinehandel GmbH; 4950000000000; info@krega-onlinehandel.de; ; Birkenweg 31; Brakel; 33034; Allemagne