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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.
The Secondary School Admission Test (SSAT) is an admission test administered by The Enrollment Management Association in the United States to students in grades 3–11 to provide a standardized measure that will help professionals in independent or private elementary, middle, and high schools to make decisions regarding student test taking.
It is also the year in which all students in maintained schools undertake National Curriculum tests (known as SATs) in the core subjects of English and Mathematics. [5] Year 6 is usually the final year of Primary or Junior School. In some areas of England, Year 6 is a year group in Middle school, which covers the year 5–8 or 4–7-year groups.
The competition consists of 15 questions of increasing difficulty, where each answer is an integer between 0 and 999 inclusive. Thus the competition effectively removes the element of chance afforded by a multiple-choice test while preserving the ease of automated grading; answers are entered onto an OMR sheet, similar to the way grid-in math questions are answered on the SAT.
A typical sequence of secondary-school (grades 6 to 12) courses in mathematics reads: Pre-Algebra (7th or 8th grade), Algebra I, Geometry, Algebra II, Pre-calculus, and Calculus or Statistics. However, some students enroll in integrated programs [3] while many complete high school without passing Calculus or Statistics.
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 ...
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