the mathematics of information, data, and signals is a multifaceted field that includes data analysis, interpretation, and manipulation. data can emerge from a variety of sources, such as imagery, acoustics, structured or random networks, and spatial or temporal sensors. to suitably process the data, a range of mathematical tools from various areas are needed. these include probability and statistics, random matrix theory,  graph theory, harmonic analysis, signal processing theory, geometry, linear algebra, and optimization. beyond its theoretical importance, this discipline also has significant practical applications.