A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections. “It’s a bit of a surprise, at least for me, that such a combination ...

In this paper, we study the symmetric and the generating functions for odd and even terms of the second-order linear recurrence sequences. we introduce a operator in order to derive a new family of ...

A function is a rule that is applied to one set of values to give another set of values. A function can be illustrated on a graph – points are plotted as coordinates and joined by either a straight ...

A translation is a shift of the graph either horizontally parallel to the \(x\)-axis or vertically parallel to the \(y\)-axis. If \(f(x) = x^2\), then \(f(x) + a = x^2 + a\). The value of \(a\) ...