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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.
Any real number can be written in the form m × 10 ^ n in many ways: for example, 350 can be written as 3.5 × 10 2 or 35 × 10 1 or 350 × 10 0. In normalized scientific notation (called "standard form" in the United Kingdom), the exponent n is chosen so that the absolute value of m remains at least one but less than ten ( 1 ≤ | m | < 10 ).
The cells in the human body are not outnumbered 10 to 1 by microorganisms. The 10 to 1 ratio was an estimate made in 1972; current estimates put the ratio at either 3 to 1 or 1.3 to 1. [300] The total length of capillaries in the human body is not 100,000 km.
The results of the examinations are usually declared in the first week of May to mid-June. In general, about 80% of candidates receive a passing score. [8] The Delhi High Court has directed the Central Board of Secondary Education and Delhi University to discuss the ways by which the results of the main exam, revaluation, and compartment exam can be declared earlier than usual so that ...
The average student takes about 10 of these tests per year (e.g., one or two reading comprehension tests, one or two math tests, a writing test, a science test, etc.). [58] The average amount of testing takes about 2.3% of total class time (equal to about four school days per year). [59] Standardized tests are expensive to administer.
Each homology class is an equivalence class over cycles and two cycles in the same homology class are said to be homologous. [6] A chain complex is said to be exact if the image of the (n+1)th map is always equal to the kernel of the nth map. The homology groups of X therefore measure "how far" the chain complex associated to X is from being ...
For instance, in the case of n = 2, the superpermutation 1221 contains all possible permutations (12 and 21), but the shorter string 121 also contains both permutations. It has been shown that for 1 ≤ n ≤ 5, the smallest superpermutation on n symbols has length 1! + 2! + … + n! (sequence A180632 in the OEIS). The first four smallest ...
Also, many mathematical theories, which had seemed to be totally pure mathematics, were eventually used in applied areas, mainly physics and computer science. A famous early example is Isaac Newton 's demonstration that his law of universal gravitation implied that planets move in orbits that are conic sections , geometrical curves that had ...