Mathematics has therefore always been divided into a pure and an applied branch. However, these have never been strictly separated. Almost all pure mathematics is related to problems which occur in applications, and almost all applied mathematics is based upon pure mathematics. Even number theory which has long been considered to be the purest area of mathematics plays nowadays an eminent role in cryptography, the study of codes, and is thus related, for example, to safe data transfer on the internet. At UAB we are particularly interested in the connections between pure mathematics, mathematical physics, and dynamical systems.
Mathematical physics is the rigorous mathematical study of structures which occur in physics.
It cannot be understood without a broad background in mathematics and at least an undergraduate level knowledge of physics. This area deals with such diverse topics as the study of atoms and molecules, the theory of relativity, the study of waves in crystals with impurities, or how to determine the internal structure of something from the way it scatters x-rays or ultrasound waves. These topics among others are studied in our department. Mathematical research areas of our department related to these topics include spectral theory, differential geometry, complex analysis and ordinary and partial differential equations. A dynamical system is a mathematical description of the time evolution of something, e.g., a system of atoms and molecules, the financial market, or the weather.