Undergraduate Projects

Asymptotic analysis considers the long-term behaviour of a function. This project is particularly concerned with studying the asymptotic growth of functions through the family of Bachmann Landau notations. 𝑂 and 𝑜 seek to provide an upper bound on the asymptotic growth of a function while Ω and 𝜔 seek to provide a lower bound. Θ and 𝜃 seek to exactly characterise the asymptotic growth of a function.

The project begins by defining, justifying and exploring the properties of asymptotic domination before seeking to classify a wide range of functions in terms of asymptotic growth, using 𝑂 and Θ with visualisations used to support findings. The difference between the upper-case and lower-case forms is detailed.

Applications of asymptotic analysis of growth is discussed in brief, the traditional application being number theory in pure mathematics, and the more recent and widely used application being algorithm analysis in applied mathematics.