Analysis is the branch of mathematics studying continuity, differentiation, and integration, which can be seen as continuation of calculus. The main objects of interest in research are real-valued functions, complex-valued functions, spaces of functions, and measures. Understanding analysis of functions and differential equations are important in numerical methods and mathematical modeling used frequently in the Applied Mathematics track.

Geometry and topology is the branch of mathematics studying measurement and shape of objects. Research in geometry goes beyond Euclidean geometry by looking at more general metric spaces or studying manifolds, which are higher dimensional analogue of curves and surfaces. Topology is a study of shapes or properties that are not changed under deformation. Shape of our universe and knots in our cells are examples of geometric objects appearing in other disciplines. Techniques from geometry and topology are sometimes used in visualizing big data studied in the Industrial Mathematics and Data Science program.

Discrete mathematics is the branch of mathematics studying objects which are not continuous and often involves counting (Combinatorics). Graph theory is the area that focuses on graphs which usually come from studying networks. Graph theory has application to various fields such as physics, chemistry, biology, and social sciences. In particular, research in graph theory can be used to understand data structures, network communications and related algorithms appearing in the Computer Science track.