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Qualitatively, a deep theorem is a theorem whose proof is long, complicated, difficult, or appears to involve branches of mathematics which are not obviously related to the ...

A line bundle is a special case of a vector bundle in which the fiber is either R, in the case of a real line bundle, or C, in the case of a complex line bundle.

The subset {0} of a ring. It trivially fulfils the definition of ideal since it is a group (specifically, the zero group), and it is closed under multiplication by any ...

Many authors (e.g., Mendelson 1963; Pervin 1964) use the term arcwise-connected as a synonym for pathwise-connected. Other authors (e.g., Armstrong 1983; Cullen 1968; and ...

A chain complex is a sequence of maps ...-->^(partial_(i+1))C_i-->^(partial_i)C_(i-1)-->^(partial_(i-1))..., (1) where the spaces C_i may be Abelian groups or modules. The ...

Just as many interesting integer sequences can be defined and their properties studied, it is often of interest to additionally determine which of their elements are prime. ...

The term "bundle" is an abbreviated form of the full term fiber bundle. Depending on context, it may mean one of the special cases of fiber bundles, such as a vector bundle ...

Caesar's method is an encryption scheme involving shifting an alphabet (so a->c, b->d, c->e, d->f, etc., x->z,y->a,z->b). It is one of the most basic encryption methods, and ...

The symbol intersection , used for the intersection of sets, and sometimes also for the logical connective AND instead of the symbol ^ (wedge). In fact, for any two sets A ...

Let j_k(alpha) denote the number of cycles of length k for a permutation alpha expressed as a product of disjoint cycles. The cycle index Z(X) of a permutation group X of ...