The main results are functional central limit theorems for superpositions of randomly selected partial sums in which the random variables being summed are independent and have distributions in the ...

Proceedings of the American Mathematical Society, Vol. 126, No. 4 (Apr., 1998), pp. 1181-1189 (9 pages) The aim of this paper is to investigate the properties of the maximum of partial sums for a ...

Convergence theorems form the backbone of probability theory and statistical inference, ensuring that sequences of random variables behave in a predictable manner as their index grows. These theorems, ...

Fourier series have long served as a cornerstone for representing periodic functions through harmonic components. In higher dimensions, these tools become indispensable for analysing complex systems, ...

The techniques of 100-level calculus are applied and extended in the study of infinite series, vector-valued functions and functions of two or more variables. Topics include convergence of power ...

I was having dinner with a visiting colleague this week when talk turned to what we were teaching this term. He mentioned the part of calculus dealing with infinite series (the bane of many students) ...

Introductory course on using a range of finite-difference methods to solve initial-value and initial-boundary-value problems involving partial differential equations. The course covers theoretical ...