Before reading this guide, you may find it helpful to read the guide on graphs from Module 7 (M7) and the guide on indices from Module 8 (M8). In Module 7 (M7) Graphs, you learned that simultaneous ...

Exponential graphs are graphs in the form \(y = k^x\). These graphs increase rapidly in the \(y\) direction and will never fall below the \(x\)-axis.

We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates for the mean and variance of the ...

This paper extends uniqueness results due to Boas and Trembinska, on entire functions with exponential growth whose real part vanishes on lattice points. Here the case is studied where the real part ...

A PHASE relation familiar to students of applied mathematics exists between a simple harmonic oscillation and its derivative. Similar relations exist between exponential functions and their ...