Algorithm

Algorithms are well-defined procedures for solving problems. Computer science is sometimes defined as the study of algorithms. Algorithms are essential because they serve as the systematic procedures that computers follow.

Simulation is a popular programming application. Generation of random number is important in simulation. The following Java Applet generates ten random numbers between 1 to 6. The probability of each integer that occurs will be 1/6.

One of the application of Numerical Analysis is to find the roots of equations of the form f( x ) = 0 by iterative methods. It involves constructing a series of guesses of the root that gradually approaches the actual root. The simplest iterative method is the bisection method. To solve the equation f( x ) = 0, we start with guessing an interval [ left0 , right0 ] within which the root certainly lies.

computer algebra system (CAS) is to automate tedious and sometimes difficult algebraic manipulation tasks. The principal difference between a Computer Algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The specific uses and capabilities of these systems vary greatly from one system to another, yet the purpose remains the same: manipulation of symbolic equations. Computer Algebra systems often include facilities for graphing equations and provide a programming language for the user to define his/her own procedures.

Computational geometry is concerned with the design and analysis of algorithms for solving geometric problems. Applications can be found in such fields as VLSI design, computer graphics, robotics, computer-aided design, pattern recognition, and statistics.

Numerical Analysis is the area of Mathematics and Computer Science concerned with the solution of Mathematical problems using a Computer. Such problems include data fitting, evaluation of various types of integrals, solution of algebraic equations and systems of equations, solution of ordinary, partial, integral and integro-differential equations.