2024 Faculty - Madhavan Mukund

Abstract for GIS :

Mathematics

Mathematics plays a fundamental role in understanding physical phenomena in the world around us. It differs somewhat from other areas of study and the objects one has to work with are ideal and abstract. This allows us to establish absolute truths, or theorems, and uncover beautiful interconnections. However, all these abstractions have arisen from questions concerning real world applications.

Historically, areas of mathematics such as trigonometry and calculus arose from very practical needs to measure quantities. Today, we seek to explain phenomena that we create — social networks where people interact with each other, economic markets where supply, demand and personal preferences determine prices of commodities, . . . What communities do we form? How do we identify influencers? What factors determine the price of onions? Which teams are likely to well in IPL? Is there a similar formula or secret to K-pop’s success?

During this month, we will explore some of the mathematics that underlies such phenomena. Graph theory is a branch of discrete mathematics that describes objects and how they are connected together — for instance, people and who they are friends with. Probability and statistics allow us to reason about uncertainty. Inevitably, much of this analysis involves dealing with large volumes of data. This requires the use of computational tools. In addition to teaching theoretical aspects of graphs and probability, we will introduce programming in the language R, which is specifically designed for mathematical modelling in these areas.

The programme will combine lectures on mathematics with some hands-on experience with programming, followed by projects on real-world data.