Through this booklet I get anopportunity to share my viewswith young and energeticmathematicians, seeking their careerin mathematics. I feel pride whenrealize that very few teachers &professors of maths get a chance to talkto such a large number of students ofvarious universities. Though ithappens through pen but I’m luckyenough. Thanks to my readers!!It is seen that amateurmathematicians—in fact, Lawyers,Philosophers, and priests by professionbut mathematicians by chance hadgreat contribution to the developmentof mathematics as a subject we studytoday. Have you ever given a thoughtthat why is it so? How they are able tothink on the typical mathematicalpattern?It seems that they areconditioned to think upon thePROBLEM in totality. They might haveunderstood the word “PROBLEM”perfectly and therefore whileattacking the problem, they attackedevery part of the ‘PROBLEM’. For them,the word ‘PROBLEM’ is first to findanswer or at least something from it.It is only after that the subject of theproblem is concerned. This might bethe reason that they had used theideology, concept & thoughts ofdifferent subjects while providing thesolutions for “the then existingproblems”—whether correct orincorrect. And therefore, theirinnovative approach in the quest ofsolutions had given them a visionwhich often came out as a ‘theorem’though they themselves might nothave been able to proved it at that timeor the proof given by them is incorrecttoday. But their theorem is beyonddoubt remarkable. Fermat’s lasttheorem is a remarkable example.This brings us to the point thatwhile learning something, the understanding of the word PROBLEMshould be in priority, because whilelearning, delivering something orexamining ourselves, we come acrossthis word invariably. So let’s startthinking about the word“PROBLEM”—Before I define the wordPROBLEM, Let me clear that this wordis not stick to one subject—Mathematics. We are concerned withthe word PROBLEM in totality—wherever it may appear, let it be. e.g.financial matters, family matters,national or international affairs or itcan even be ‘Love affair’ or any thingyou may think of. Here I try to defineof the word PROBLEM. —“A problem is set ofinformation (implicit or explicit orboth) with one or more questions”Seems interesting!!Now, if we adopt thisdefinition of the word ‘PROBLEM’ it isnot difficult to define the wordSOLUTION; Here it comes as a naturalconsequence:“The ‘SOLUTION’ is to find the ‘rightsequence’ of the informations given inthe PROBLEM, which leads us to theanswer of the questions raised in theproblem”.Let us start analysis of thedefinition of ‘solution’. This definitioninvolves two important parametersone is “information” and the other is“the right sequence”. It varies fromperson-to-person that how he or sheextracts information from the givenproblem because it's not always thatall the useful information in anyproblem are in explicit form. Whereasthe implicit information comes out onlyafter a reasonable investment of timein the problem. As for the 'rightsequence' is concerned it is not thenumber of information but theperspective from which a person sees the information which decides that how& when it (the right sequence) will beobtained. Obviously a good commandover the technicality of subjects relatedto the problem may help the studenthandle the information and getting theright sequence.Here is an observation whichwill give a strong support to my logicsclaiming importance of right sequenceof information for solutions—Have you ever noticed, thatwhy in most of the examinations likebanks, railway recruitments, SSC, evencivil services (IAS) or any other exam,mathematical and verbal/non-verbalreasoning based questions are asked.Even in these questions, you are askedto find the missing numbers in the seriesor sequence (the right sequencerequired!). Sometimes, you are givencertain figures and then asked to findthe unknown figure? Here also you areasked to catch a pattern (rightsequence!!).Now, you might have realizedwhy the pattern of most of theexaminations, right from Macaulay tothe present time, still persists.So dear students, you mighthave got some ideas regardingproblems and their related aspects.Hope you will start thinking over theword PROBLEM and try to attack andfind solutions in your own innovativeways. Now you might have chain ofthoughts in your mind regardingproblems and solutions. Feel free towrite to me at rajendra@dipsindia.com.Or you can send me through letters atthe address of DIPS Academy. I’ll bereally happy and thankful to you if youshare your views regarding this articleor the points I have raised here.Rajendra Dubey
(The author is a mentor of Higher
Mathematics and CEO of DIPS Pvt. Ltd.)
(Freedom starts in the mind, not by cutting ropes)
0 comments:
Post a Comment