# Numerical Methods: Approximation Numerical methods serve to approximate solutions to mathematical equations and solve mathematical problems using computational power after algorithms have been developed. Methods exist for finding roots of polynomial equations for example or factoring matrices. Generally a convergence process if stable leads to the right result much like Taylor polynomials approximating the values of various functions where the Taylor polynomials act as a series progressing towards infinite.

Relevant concepts from calculus are the mean value theorem and the intermediate value theorem as well as Rolle’s theorem which all serve to answer how a bounded well-behaved function reflects its various properties in terms of itself. This is all analysis.

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Pure Mathematics and Literature
Pure mathematics starts as a great model for the mind. There is the concept of axiom of choice, which is dependent on the future, and being able to select subsets out of sets extending into the future. There is the axiom of determinism which states that one can win a game with start parameters if you use the best moves. These two axioms are incompatible. Taken together, these axioms guide... 