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Pseudomathematics, or mathematical crankery, is a mathematics-like activity that does not adhere to the framework of rigor of formal mathematical practice. Common areas of pseudomathematics are solutions of problems proved to be unsolvable or recognized as extremely hard by experts, as well as attempts to apply mathematics to non-quantifiable ...
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Suppose that k is a non-perfect field of characteristic 2, and a is an element of k that is not a square. Let G be the group of nonzero elements x + y √ a in k[√ a].There is a morphism from G to the multiplicative group G m taking x + y √ a to its norm x 2 – ay 2, and the kernel is the subgroup of elements of norm 1.
In mathematics, a pseudogroup is a set of homeomorphisms between open sets of a space, satisfying group-like and sheaf-like properties. It is a generalisation [dubious – discuss] of the concept of a group, originating however from the geometric approach of Sophus Lie [1] to investigate symmetries of differential equations, rather than out of abstract algebra (such as quasigroup, for example).
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In physics and mathematics, a pseudotensor is usually a quantity that transforms like a tensor under an orientation-preserving coordinate transformation (e.g. a proper rotation) but additionally changes sign under an orientation-reversing coordinate transformation (e.g., an improper rotation), which is a transformation that can be expressed as a proper rotation followed by reflection.
Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent of any scientific experimentation.