According to Vault, mathematics and physics research can be divided into the following areas:
Applied Mathematics
Applied mathematicians “use mathematical theories and principles to address real-world problems. They might create mathematical models to calculate the characteristics of new products, systems, or population trends.�
Theoretical Mathematics
Theoretical mathematicians work with pure and abstract mathematical concepts to expand and define the scope of mathematical knowledge.�
Experimental Physics
Experimental physics uses experiments to gather information.
Theoretical Physics
Theoretical physics constructs theories to explain experimental results.