Solutions of the Examples in Higher Algebra (Latex Edition)

In this edition, the entire manuscript was typeset 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. We are highly indebted to Pratham Kumar Singh for the fruitful discussions which led to the idea of masterminding this entire project.
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