some programmers think breaking the process into smaller parts allows them to better understand what the procedure being programmed does
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When the low-level implementation details are not immediately obvious to the programmer, the top-down approach can help reveal them.
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Logical errors are grammatical errors or mistakes made by a programmer in java, it may not affect the program design but it can change the context of the statements.
Textual programming is normally referred to as syntax programming. It is a low-level format for drawing the design of the program.
Yes. A computer programmer will at least use simple arithmetic. Most computer science degrees require a year of calculus, though I must admit that the most useful math classes I've taken were discrete mathematics. Math that deals with sequences, series, and sets tends to be the most common and useful (in my experience). Of course it all depends on what specific field of programming you will be in. If you will be doing a lot of network programming, then graph theory will probably be part of your everyday programming. Graphics programmers will need to know a good bit of geometry and trigonometry.
The difference between a program and programming is programming is the actual activity of writing computer code in any of the various computer languages available, the end result of which is a program. The program can then be ran by the computer and perform the task the programmer told it to do.