The statistical physics of graphs and partition functions represents a vibrant intersection of graph theory, statistical mechanics and computational complexity. By summing over an ensemble of ...

All quadratic functions have the same type of curved graphs with a line of symmetry. The graph of the quadratic function \(y = ax^2 + bx + c \) has a minimum turning point when \(a \textgreater 0 \) ...

All quadratic functions have the same type of curved graphs with a line of symmetry. The graph of the quadratic function \(y = ax^2 + bx + c\) is a smooth curve with one turning point. The turning ...

In this paper the generating function for the numbers of variations with repetitions and a certain type of restrictions is determined. The variations in question are connected with paths in ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

In the applet below is intended to help you understand the connection between the graph of a function and the function itself. Recall that a function can be thought of as a machine which takes an ...