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.
Science falsely so called.
I Timothy, VI. 20. Quotes reported in Hoyt's New Cyclopedia Of Practical Quotations (1922), p. 691-92
I was particularly interested in that, in working on Jurassic Park that aspect of what are the negative parts. Because in talking with the people who were doing this kind of research what I was hearing was that the most responsible of them were deciding not to proceed down certain lines of inquiry which is really a new phase in science. Traditionally in science what the scientists themselves have said is: "I might as well do it, because if I don't, someone else will. It is going to happen inevitably." I think there's recognition now, that it's no so inevitable and it's quite conceivable that if I don't do this research neither will anyone else. It's simply too dangerous.
Michael Crichton, interview Lost World section of Beyond Jurassic Park DVD.
Think of it: of the infinity of real numbers, those that are most important to mathematics—0, 1, √2, e and π—are located within less than four units on the number line. A remarkable coincidence? A mere detail in the Creator's grand design? I let the reader decide.
Eli Maor, e: The Story of a Number (1994)