AMS Chelsea Publishing 1967; 441 pp; hardcover Volume: 209 ISBN10: 0821875671 ISBN13: 9780821875674 List Price: US$55 Member Price: US$49.50 Order Code: CHEL/209.H
 Four volumes in one: On the Congruence of Sets and Their Equivalence by Finite Decomposition, by W. Sierpinski; The Mathematical Theory of the Top, by F. Kleinwellknown lectures on the analytical formulas relating to the motion of the top; Graphical Methods, by C. Runge; Introduction to the Theory of Algebraic Equations, by L. E. DicksonDickson's earliest account of the subject, presented with a historical, elementary perspective. Table of Contents On the Congruence of Sets and Their Equivalence by Finite Decomposition by Waclaw Sierpinski  Congruence of sets; Translation of sets; Equivalence of sets by finite decomposition; Some theorems on the equivalence of sets by decomposition into two parts; Equivalence of a rectangular isosceles triangle to a square by finite decomposition; Equivalence of a segment of the straight line to one of its proper subsets by finite decomposition; Paradoxical decompositions; Decomposition of the interval \([0\leq x < 1]\) into an enumberable infinity of disjoint sets each two of which are equivalent by decomposition into two parts; Some theorems on the equivalence of sets by finite decomposition; The Hausdorff paradox; The paradox of Banach and Tarski; Banach measure. The generalized problem of measure; The absolute measure; The paradox of J. von Neumann; Appendix
The Mathematical Theory of the Top by Felix Klein  Lecture I; Lecture II; Lecture III; Lecture IV
Graphical Methods by C. Runge  Graphical Calculation: Graphical arithmetic; Integral functions; Linear functions of any number of variables; The graphical handling of complex numbers
 The Graphical Representation of Functions of One or More Independent Variables: Functions of one independent variable; The principle of the slide rule; Rectangular coördinates with intervals of varying size; Functions of two independent variables; Depiction of one plane on another plane; Other methods of representing relations between three variables; Relations between four variables
 The Graphical Methods of the Differential and Integral Calculus: Graphical integration; Graphical differentiation; Differential equations of the first order; Differential equations of the second and higher orders
Introduction to the Theory of Algebraic Equations by Leonard Eugene Dickson  Solution of the general quadratic, cubic, and quartic equations. Lagrange's theorem on the irrationalities entering the roots; Exercises
 Substitutions; Rational functions; Exercises
 Substitution groups; Rational functions; Exercises
 The general equation from the group standpoint; Exercises
 Algebraic introduction to Galois' theory
 The group of an equation; Exercises
 Solution by means of resolvent equations
 Regular cyclic equations; Abelian equations
 Criterion for algebraic solvability
 Metacyclic equations; Galoisian equations
 An account of more technical results
 Appendix; Symmetric functions; On the general equation; Index
