420 Further ReadingSee also DH, Ch. 3, for a general discussion of solvability. An historical
survey of the theory of equations and group theory appears in Cajori
(Hist), p. 349-363.
Ruler and compasses constructions: Bo, Ch. 9; Moise, Ch. 19.
For a more comprehensive, but elementary, introduction to Galois the-
ory, see the book by Hadlock. An elementary approach to the topological
ideas behind the fundamental theorem is found in the book by Chinn &
Steenrod. Those who would like to see the Fundamental Theorem in the
hands of its discoverers should consult Struik.
Chapter 5. General: Di (1914), Ch. X; Cajori (Hist), 363-366.
Descartes rule: Bu, Ch. II; Di (1939)) Ch. VII; DH, Sect. 5.3.
Bounds: Bu, Ch. VIII; Us, Ch. IV.
Fourier-Budan: Bo, Ch. 6; Bu, Ch. IX.
Approximation of roots: Bo, Ch. 7; Us, Ch. VIII; Bu, Ch. X; Di (1939),
Ch. VIII; Vilenkin.
Separation of roots: Rolle’s Theorem: Us, Ch. VI.
Sturm’s Theorem: Bo, Ch. 6; Bu, Ch. IX; Us, Ch. VII; MacD, Ch. 4; Di
(1939), Ch. VII; DH, Sect. 5.4.
Continued fractions: Us, App. 2; Olds
Location of zeros: Polya-Szegii, Part III, Ch. 1, Sect. 2.
A discussion of criteria for stability of polynomials appears in Chapter 7
of Kaplan.
Chapter 6. Symmetric functions of roots: Bo, Ch. 11; Us, Ch. XI; MacD,
Ch. 6; DH, Sect. 2.4, 2.5.
Newton’s formula for power sums: Us, Ch. XI.
Chapter 7. Finite differences and interpolation: Milne-Thomson, Ch.
I-IV; Scarborough; Ralston, Ch. 3.
Lagrange interpolation: DH, Sect. 2.2.
A succinct, but advanced, introduction to approximation theory is given
in Lorentz. This includes a treatment of Bernstein and Tchebychev poly-
nomials. The alternation property is discussed in Section 7.3.