Topology additionally includes the now solved Poincaré conjecture, and the still unsolved areas of the Hodge conjecture. Other ends in geometry and topology, together with the 4 shade theorem and Kepler conjecture, have been proven only with the help of computers. Understanding and describing change is a standard theme within the pure sciences, and calculus was developed as a tool to investigate it. Functions come up right here as a central idea describing a altering quantity. The rigorous study of real numbers and functions of an actual variable is recognized as actual analysis, with complicated evaluation the equal subject for the complex numbers.

We additionally examine a special class of p-polynomials which are generated by the longest word in the symmetric group and describe pattern...