Solutions of the Examples in Higher Algebra (Latex Enlarged Edition)

This work forms a Key or Companion to the Higher Algebra, and contains full solutions of nearly all the Examples. In many cases more than one solution is given, while throughout the book frequent reference is made to the text and illustrative Examples in the Algebra. The work has been undertaken at the request of many teachers who have introduced the Algebra into their classes, and for such readers it is mainly intended; but it is hoped that, if judiciously used, the solutions may also be found serviceable by that large and increasing class of students who read Mathematics without the assistance of a teacher. In this edition, the entire manuscript was typeset in a bigger size font 10 pt: DejaVu Serif'] (honoring readers' suggestions) using the LaTeX document processing system originally developed by Leslie Lamport, based on TeX typesetting system created by Donald Knuth. The typesetting software used the XeLaTeX distribution. We are grateful for this opportunity to put the materials into a consistent format, and to correct errors in the original publication that have come to our attention. Most of the hard work of preparing this edition was accomplished by Neeru Singh, who expertly keyboarded and edited the text of the original manuscript. She helped us put hundreds of pages of typographically difficult material into a consistent digital format. The process of compiling this book has given us an incentive to improve the layout, to doublecheck almost all of the mathematical rendering, to correct all known errors, to improve the original illustrations by redrawing them with Till Tantau's marvelous TikZ. Thus the book now appears in a form that we hope will remain useful for at least another generation. Table of Contents EXAMPLES I: Ratio

EXAMPLES II: Proportion

EXAMPLES III: Variation

EXAMPLES IV: Arithmetical Progression

EXAMPLES V: Geometrical Progression

EXAMPLES VI: Harmonical Progression

EXAMPLES VII: Scales of Notation

EXAMPLES VIII: Surds and Imaginary Quantities

EXAMPLES IX: The Theory of Quadratic

EXAMPLES X: Miscellaneous Equations

EXAMPLES XI: Permutations and Combinations

EXAMPLES XIII: Binomial Theorem Positive Integral Index

EXAMPLES XIV: Binomial Theorem. Any Index

EXAMPLES XV: Multinomial Theorem

EXAMPLES XVI: Logarithms

EXAMPLES XVII: Exponential and Logarithmic Series

EXAMPLES XVIII: Interest and Annuities

EXAMPLES XIX: Inequalities

EXAMPLES XX: Limiting Values and Vanishing Fractions

EXAMPLES XXI: Convergency and Divergency of Series

EXAMPLES XXII: Undetermined Coefficients

EXAMPLES XXIII: Partial Fractions

EXAMPLES XXIV: Recurring Series

EXAMPLES XXV: Continued Fractions

EXAMPLES XXVI: Indeterminate Equations of the First Degree

EXAMPLES XXVII: Recurring Continued Fractions

EXAMPLES XXVIII: Indeterminate Equations of the Second Degree

EXAMPLES XXIX: Summation of Series

EXAMPLES XXX: Theory of Numbers

EXAMPLES XXXI: The General Theory of Continued Fractions

EXAMPLES XXXII: Probability

EXAMPLES XXXIII: Determinants

EXAMPLES XXXIV: Miscellaneous Theorems and Examples

EXAMPLES XXXV: Theory of Equations

MISCELLANEOUS EXAMPLES