In this article, as an introduction to Part IX, we will summarize the overall approach of "finding expected values using recurrence relations." Recurrence relations are a powerful weapon for problems ...

In October 2024 I attended a workshop at Harvard University where mathematicians talked through the uses of artificial intelligence in their field. Most were less worried about the future of math than ...

Particle swarm optimization (PSO) algorithm is an optimization technique with remarkable performance for problem solving. The convergence analysis of the method is still in research. This article ...

As we know that the power series method is a very effective method for solving the Ordinary differential equations (ODEs) which have variable coefficient, so in this paper we have studied how to solve ...

Time-delay stability (TDS) analysis is a method for quantifying interactions in multivariate systems by identifying stable temporal relationships in time series data [1]. This method has been used to ...

Our July Insights column was inspired by the mathematics of the phenomenal 20th-century number theorist Srinivasa Ramanujan, whose romantic and tragic life story was the subject of the recent film The ...