Congruence of Sets and Other Monographs

Inbunden, Engelska, 2013

AvW. Sierpinski,F. Klein,C. Runge,L.E. Dickson

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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. Klein--well-known 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. Dickson--Dickson's earliest account of the subject, presented with a historical, elementary perspective.

Produktinformation

Utgivningsdatum2013-03-30
Vikt455 g
FormatInbunden
SpråkEngelska
SerieAMS Chelsea Publishing
Antal sidor441
FörlagAmerican Mathematical Society
ISBN9780821875674

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Algebra inom Naturvetenskap och teknik

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 coordinates 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