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2. List of unsolved problems in mathematics - Wikipedia

   en.wikipedia.org/wiki/List_of_unsolved_problems...

   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.

3. Classification of discontinuities - Wikipedia

   en.wikipedia.org/wiki/Classification_of...

   The term removable discontinuity is sometimes broadened to include a removable singularity, in which the limits in both directions exist and are equal, while the function is undefined at the point . [a] This use is an abuse of terminology because continuity and discontinuity of a function are concepts defined only for points in the function's ...

4. List of undecidable problems - Wikipedia

   en.wikipedia.org/wiki/List_of_undecidable_problems

   The halting problem for a register machine: a finite-state automaton with no inputs and two counters that can be incremented, decremented, and tested for zero. Universality of a nondeterministic pushdown automaton: determining whether all words are accepted. The problem whether a tag system halts.

5. Singularity (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Singularity_(mathematics)

   Branch points are generally the result of a multi-valued function, such as or ⁡ (), which are defined within a certain limited domain so that the function can be made single-valued within the domain. The cut is a line or curve excluded from the domain to introduce a technical separation between discontinuous values of the function.

6. Domain (mathematical analysis) - Wikipedia

   en.wikipedia.org/wiki/Domain_(mathematical_analysis)

   In complex analysis, a complex domain (or simply domain) is any connected open subset of the complex plane C. For example, the entire complex plane is a domain, as is the open unit disk, the open upper half-plane, and so forth. Often, a complex domain serves as the domain of definition for a holomorphic function.

7. Critical point (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Critical_point_(mathematics)

   Similarly, when dealing with complex variables, a critical point is a point in the function's domain where its derivative is equal to zero (or the function is not holomorphic). [3] [4] Likewise, for a function of several real variables, a critical point is a value in its domain where the gradient norm is equal to zero (or undefined). [5]