She wrote a book on determinants and systems of linear equations, published as the textbook " Introduction to the Theory of Equations " by John Wiley and Sons in 1945.
12.
If x ( t ) and y ( t ) are rational functions then the techniques of the Theory of Equations such as resultants can be used to eliminate " t ".
13.
In the context where algebra is identified with the theory of equations, the exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study ".
14.
In algebra, the "'theory of equations "'is the analysis of the nature and algebraic solutions of algebraic equations ( also called " polynomial equations " ), which are equations defined by a polynomial.
15.
His main work was on the theory of equations, where he was reluctant to accept the validity of the work of Niels Henrik Abel on the insolubility of the quintic equation by Erland Bring ( 1736 1798 ), and is now called Bring Jerrard normal form.
16.
Her thesis was " Multiple Integrals and Their Geometrical Interpretation of Cartesian Geometry, in Trilinears and Triplanars, in Tangentials, in Quaternions, and in Modern Geometry; Their Analytical Interpretations in the Theory of Equations, Using Determinants, Invariants and Covariants as Instruments in the Investigation ".
17.
:* Klein proposed that group theory, a branch of mathematics that uses algebraic methods to abstract the idea of symmetry, was the most useful way of organizing geometrical knowledge; at the time it had already been introduced into the theory of equations in the form of Galois theory.
18.
Even though Vincent's theorem is the basis of the fastest method for the isolation of the real roots of polynomials, it was almost totally forgotten, having been overshadowed by Sturm's theorem; consequently, it does not appear in any of the classical books on the theory of equations ( of the 20th century ), except for Uspensky's book.
19.
These developments of the last quarter of the 19th century and the first quarter of 20th century were systematically exposed in Bartel van der Waerden's " Moderne algebra ", the two-volume monograph published in 1930 1931 that forever changed for the mathematical world the meaning of the word " algebra " from " the theory of equations " to the " theory of algebraic structures ".
20.
According to Nathan Jacobson, The proofs of Ruffini and of Abel [ & hellip; ] were soon superseded by the crowning achievement of this line of research : Galois'discoveries in the theory of equations . Galois then died in 1832 and his paper " M�moire sur les conditions de resolubilit?des �quations par radicaux " remained unpublished until 1846, when it was published by Joseph Liouville accompanied by some of his own explanations.
