Applied mathematics is a very general term and thus makes this question rather difficult to answer, as it can apply to almost anything where advanced mathematics is used in the study topic. For example: probability, statistics, financial analysis, mechanics, physics, discrete mathematics, graph theory, engineering, numerical analysis, and even cryptology, can all be described as applied mathematics.
The one that has the most in common with computer science however is, to my knowledge, numerical analysis. numerical analysis looks at problems in continuous mathematics that can't be solved by conventional analytical methods, and looks at developing algorithms to then solve these problems.
Computer science looks at the theory behind information and computation/programming, and applies it to every area, using programmes and software to solve all problems, instead of just the ones looked at by numerical analysis.
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At the simplest level, mathematics, sometimes called "pure mathematics" is the science of solving problems to obtain an answer. Applied mathematics is the science of solving problems in order to discover answers to problems outside of mathematics, such as within physics or economics.
The exact synonym for Applied Mathematics is impure mathematics, which does not deal with the study of the physical or biological or sociological world.
Newton "invented" "applied mathematics" and calculus.
Statistical plays a central role in almost all natural and social sciences. The methods of natural sciences are most reliable but conclusions draw from them are only probable, because they are based on incomplete evidence. Statistical helps in describing these measurements more precisely. Statistics is branch of applied mathematics. The large number of statistical methods like probability averages, dispersions, estimation etc… is used in mathematics and different techniques of pure mathematics like integration, differentiation and algebra are used in statistics.
The abstract science of number, quantity, and space. Mathematics may be studied in its own right (pure mathematics), or as it is applied to other disciplines such as physics and engineering (applied mathematics).