Physical Science projects would include experiments, studies, or innovations primarily concerned with the properties of matter and energy, and the principles of their interactions. It includes, but is not limited to, projects that focus on one or more of the following:
inorganic and organic chemistry
analytical and physical chemistry
space science
astronomy
general physics
condensed matter physics
subatomic/particle physics
Mathematical Science projects would involve the abstract study of mathematical theories and structures and the theorems that can be proven to hold in these systems. It can also involve the use of mathematical models to simulate physical and biological systems.
Most areas of science require a careful use of statistics, and the study of the validity of the application of particular statistical techniques to particular areas of science would be a valid project in this category.
The more hardware aspects of computational science will normally be more appropriate for Engineering and Computing Science.