Introduction of Mathematics:

Mathematics research is the pursuit of knowledge and understanding in one of the most fundamental and abstract fields of human inquiry. It encompasses the exploration of patterns, structures, and relationships using logic and quantitative reasoning.

Number Theory:

Investigating the properties and relationships of numbers, including prime numbers, Diophantine equations, and the Riemann Hypothesis.

Algebra and Geometry:

Exploring abstract algebraic structures and geometric spaces, with applications in cryptography, coding theory, and computer graphics.

Differential Equations:

Studying equations involving derivatives to describe dynamic processes in physics, engineering, and biology.

Probability and Statistics:

Developing techniques for modeling uncertainty and analyzing data, with applications in finance, epidemiology, and machine learning.

Combinatorics:

Examining the arrangement and combination of objects, with applications in network theory, optimization, and cryptography.