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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.
On Equations involving indeterminate Questions of the 2nd Degree On Equations involving Rectangles In Bijaganita Bhāskara II refined Jayadeva 's way of generalization of Brahmagupta's approach to solving indeterminate quadratic equations, including Pell's equation which is known as chakravala method or cyclic method.
One of the basic principles of algebra is that one can multiply both sides of an equation by the same expression without changing the equation's solutions. However, strictly speaking, this is not true, in that multiplication by certain expressions may introduce new solutions that were not present before. For example, consider the following ...
The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...
The NFL playoffs are nearly in sight and the heat is on for some teams still in the fight to make the postseason.. Week 15 saw the number of teams that have qualified for the playoffs increase to ...
Larry Mullen Jr. has always found it difficult to comprehend arithmetic, and now he knows why.. After years of struggling with numeracy skills such as adding and counting, the U2 drummer, 63, has ...
Jimmy Carter’s grandson, Jason Carter, said in a new interview his grandfather is “not that active” these days, but he’s still “stubborn” after spending nearly two years in hospice ...
Solutions to polynomial systems computed using numerical algebraic geometric methods can be certified, meaning that the approximate solution is "correct".This can be achieved in several ways, either a priori using a certified tracker, [7] [8] or a posteriori by showing that the point is, say, in the basin of convergence for Newton's method.
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