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1.1 Mathematics. 1.2 Physics. 1.3 Chemistry. 1.4 Biology. ... Download as PDF; Printable version; ... This is a list of equations, by Wikipedia page under ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
The conjecture is that there is a simple way to tell whether such equations have a finite or infinite number of rational solutions. More specifically, the Millennium Prize version of the conjecture is that, if the elliptic curve E has rank r , then the L -function L ( E , s ) associated with it vanishes to order r at s = 1 .
10. Determination of the solvability of a Diophantine equation. 11. Quadratic forms with any algebraic numerical coefficients 12. Extensions of Kronecker's theorem on Abelian fields to any algebraic realm of rationality 13. Impossibility of the solution of the general equation of 7th degree by means of functions of only two arguments. 14.
A solution where all three are nonzero will be called a non-trivial solution. For comparison's sake we start with the original formulation. Original statement. With n, x, y, z ∈ N (meaning that n, x, y, z are all positive whole numbers) and n > 2, the equation x n + y n = z n has no solutions. Most popular treatments of the subject state it ...
Solving an equation symbolically means that expressions can be used for representing the solutions. For example, the equation x + y = 2x – 1 is solved for the unknown x by the expression x = y + 1, because substituting y + 1 for x in the equation results in (y + 1) + y = 2(y + 1) – 1, a true statement. It is also possible to take the ...
Equation Field Person(s) named after Adams–Williamson equation: Seismology: L. H. Adams and E. D. Williamson Allen–Cahn equation [2] [3]: Phase separation
Arithmetica (Ancient Greek: Ἀριθμητικά) is an Ancient Greek text on mathematics written by the mathematician Diophantus (c. 200/214 AD – c. 284/298 AD) in the 3rd century AD. [1] It is a collection of 130 algebraic problems giving numerical solutions of determinate equations (those with a unique solution) and indeterminate equations.