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(1-1) An application is any program that a computer runs that enables you to get things done. This includes things like word processors for creating text, graphics packages for drawing pictures, and communication packages for moving data around the globe.
(1-2) Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing “output” and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.
(1-3) The starting-point in the late 1940s was Alan Turing’s question “Can computers think?”, and the question remains effectively unanswered although the “Turing Test” is still used to assess computer output on the scale of human intelligence. But the automation of evaluative and predictive tasks has been increasingly successful as a substitute for human monitoring and intervention in domains of computer application involving complex real-world data.
(1-4) Computing research is rife with examples of the scientific paradigm. Cognition researchers, for example, hypothesize that much intelligent behavior is the result of information processes in brains and nervous systems; they build systems that implement hypothesized information processes and compare them with the real thing.
(1-5) the focus of modern computer science research is shifting to problems concerning large data sets. Thus, a theoretical foundation and science base is required for rigorously conducting studies in many related areas. The theory of large data sets is quite different from that of smaller data sets; when dealing with smaller data sets, discrete mathematics is widely used, but for large data sets, asymptotic analysis and probabilistic methods must be applied. Additionally, this change in the theoretical foundation requires a completely different kind of mathematical intuition.