Physicists often apply mathematics research to their experiments and tests to prove the legitimacy of their theories. Sometimes, however, they create their own mathematical models to explain their concepts. For example, Isaac Newton invented calculus to describe the force of gravity. String theory -- the hypothesis that all elementary particles are manifestations of the vibrations of one-dimensional strings -- is another example of physicists conducting experimental observations to substantiate their mathematical constructs.
Mathematics is extensively used by computer science. Theoretical computer science is a branch of both computer science and mathematics. Computer coders use mathematical algorithms to create software programs, and to learn these you will need a solid background in combinatorics and graph theory.
Combinatorics, or the science of counting, is a branch of mathematics dealing with the selection, arrangement and combination of elements within sets. A simple example would be the number of possible bridge hands. Graph theory is the study of mathematics concerned with the study of graphs -- two-dimensional drawings showing a relationship between two sets of numbers by means of a line, curve, a series of bars or other symbols.
Harvard University mathematician and biologist Martin Nowak uses mathematics to explain complex phenomena such as tracing back evolution to the time life began on earth. For example, he explains the origin of life by assigning zeroes and ones to the simplest possible chemical blocks of life he calls monomers. His mathematical model describes how two types of monomers self-assemble and then self-replicate, generating life. According to Nowak, “mathematics is the proper language of evolution.”
The probability branch of mathematics has many applications in social sciences, particularly population sciences. Probability is used to measure a population’s fertility, mortality and mobility. The Egyptians carried out population counts as early as 3000 B.C., and Blaise Pascal worked on probability theory in 1654. Since the 17th century, population sciences have depended on probability. Researcher Daniel Courgeau mentioned that Pierre-Simon Laplace accurately estimated the French population in 1782.