Applied mathematics is the application of mathematical methods by different fields such as science, engineering, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics.
A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming. Modern computers have the ability to follow generalized sets of operations, called programs. These programs enable computers to perform an extremely wide range of tasks.
Computer science is the study of the theory, experimentation, and engineering that form the basis for the design and use of computers. It is the scientific and practical approach to computation and its applications and the systematic study of the feasibility, structure, expression, and mechanization of the methodical procedures (or algorithms) that underlie the acquisition, representation, processing, storage, communication of, and access to, information. An alternate, more succinct definition of computer science is the study of automating algorithmic processes that scale. A computer scientist specializes in the theory of computation and the design of computational systems. See glossary of computer science.
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change. It has no generally accepted definition.
Science (from Latin scientia, meaning "knowledge") is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.
Take a look at George Gamow, who is now recognized as one of the great cosmologists of the last hundred years. I speculate that he probably didn't win the Nobel Prize because people could not take him seriously. He wrote children's books. His colleagues have publicly stated his writing children's books on science had an adverse effect on his scientific reputation, and people could not take him seriously when he and his colleagues proposed that there should be a cosmic background radiation, which we now know to be one of the greatest discoveries of 20th-century physics.
Michio Kaku, in "Borrowed Time: Interview with Michio Kaku".
Computer science is neither mathematics nor electrical engineering
Alan Perlis (1968) title of article "Computer Science is neither Mathematics nor Electrical Engineering" in: A. Finerman (Hg.), University Education in Computing Science, New York, London, pp. 69-77
Computer science is an empirical discipline. [...] Each new machine that is built is an experiment. Actually constructing the machine poses a question to nature; and we listen for the answer by observing the machine in operation and analyzing it by all analytical and measurement means available. Each new program that is built is an experiment. It poses a question to nature, and its behavior offers clues to an answer.
Allen Newell (1975) Computer Science as Empirical Inquiry: Symbols and Search. p. 114