The Art of Problem Solving

The Art of Problem Solving

               Branch of mathematics in which we learn about types and method of problem-solving.

(1)    Inductive Reasoning :

             While there are people who study mathematics for the sheer enjoyment of the subject, the majority of the student of mathematics have at a point asked themselves, “When will I even need this?” The development of mathematics can be traced to the Egyptian and Babylonian cultures (3000 B.C.-A.D. 260) as a necessity for the problem. Their approach was an example of the “do thus and so” method: in order to solve a problem or perform an operation, a cookbook-like recipe was given, and it was performed over and over to solve similar problems.

             By observing that a specific method worked for a certain type of problem, the Babylonians and Egyptians conclude that the same method will be worked for any similar type of problem. Such a conclusion is called conjecture. A conjecture is an educated guess based upon repeated observation of a particular process or pattern. The method of reasoning we just described is called inductive reasoning.     

Definition:   

              Inductive reasoning is characterized by drawing a general conclusion (making a conjecture) from repeated observations of specific examples. The conjecture may not be true.

(2)    Deductive Reasoning:

                Deductive reasoning is characterized by applying general principles to specific examples.