Approximation theory is a field of study that deals with finding the best approximation to a function or set of data using various mathematical techniques. There are several synonyms for this field, such as approximation algorithms, numerical analysis, and computational mathematics. Other terms used in the field include computational science, numerical optimization, and scientific computing. All of these terms are related to the process of finding the best approximation of a function or data set using mathematical techniques. Approximation theory applies in many fields of science and engineering, including physics, economics, and computer science, making it an essential area of study for researchers and practitioners alike.