The Art of Problem Solving texts have been used by tens of thousands of outstanding students, including many winners of major national contests such as MATHCOUNTS and the American Mathematics Competitions.
This lecture covers the use of iteration to build programs whose execution time depends upon the size of inputs. It also introduces search problems and brute force and bisection for solving them.
Topics covered: Termination, decrementing functions, exhaustive enumeration, brute force, while loop, for loop, approximation, specifications, bisection search.
Problem solving consists of using generic or ad hoc methods, in an orderly manner, for finding solutions to problems. Some of the problem-solving techniques developed and used in artificial intelligence , computer science , engineering , mathematics , or medicine are related to mental problem-solving techniques studied in psychology.
In computer science and in the part of artificial intelligence that deals with algorithms ("algorithmics"), problem solving encompasses a number of techniques known as algorithms , heuristics , root cause analysis , etc. In these disciplines, problem solving is part of a larger process that encompasses problem determination, de-duplication , analysis, diagnosis, repair, etc.
Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery. Such experiences at a susceptible age may create a taste for mental work and leave their imprint on mind and character for a lifetime. (26, p. v.)
A ladder 5 meters long leans against a wall, reaching over the top of a box that is 1 meter on each side. The box is against the wall. What is the maximum height on the wall that the ladder can reach? The side view is:
Assume the wall is perpendicular to the floor. Use your calculator to find the maximum height to the nearest.01 meter.
Early interest in the creative process examined the natural approaches taken by highly creative people in applying their personal creativity when solving problems (e.g., Crawford, 1937; Dewey, 1910; Ghiselin, 1950; Poincaré, 1924; Spearman, 1931; Wallas, 1926). The effort to make these creative processes more visible, explicit, and deliberate has been one of the most formidable challenges for researchers for many years.
Basadur, M. S., Graen, G. B. & Green, S. G. (1982). Training in creative problem solving: Effects on ideation and problem finding in an industrial research organization. Organizational Behavior and Human Performance, 30 , 41-70.
Any job will also bring problems to be faced. It is important to show to a recruiter that you have the right skills to resolve these problems, and the personal resilience to handle the challenges and pressure they may bring.
Solving these problems involves both analytical and creative skills. Which particular skills are needed will vary, depending on the problem and your role in the organisation, but the following skills are key to problem-solving: