Mast Kalandar

bandar's colander of random jamun aur aam

Wed, 06 Mar 2013

The Scale of Problems


education, research [link] [comments ()] [raw]

The following is based on my experience with Mathematics. It may be applicable in other disciplines --- or it may not.

My aim in the note below is to try to understand how the assignments one does during the early stages link up to summer projects and research.

If you wish to figure out why it is not reasonable for students to propose a research problem and then ask faculty members to guide them, (especially students who do not solve assignment problems!) then read on!

There is a whole scale of problems which starts at routine computations and goes all the way to research proposals. Access to later stages is premised on competence in the earlier stages!

As Gauss said, "There is no royal road to Mathematics!"

It is always easiest (and best) to start with routine computations. These are the typical assignments that are given in your early (mathematics) courses. The teacher gives you a sequence of steps which, if carried out systematically, will result in the solution.

In later assignments, you may be required to think out your own strategy. There is no recipe for discovering such a strategy --- you are now required to do something which a computer cannot easily be instructed to do! A model answer is often provided as a way to discover solutions to similar problems.

Electives and summer projects give the chance to have one's own choice influence the topic of study and/or a instructor/guide. The problem proposed is one where extended study is required. The solution cannot be explained in one or two lines and needs to be written down in detail to be convincing.

The final-year project is about learning something in depth and doing something significant with it. The student needs to read research papers to get the background and also needs to make a calculation (or give a proof) which is not already available in the literature.

PhD research takes this a step further, with the student and the guide working together for a while to come up with a reasonable problem statement.

Post-doctoral research is when one works without a guide --- to pick a problem and to work at its solution.

Finally, as a faculty member one writes research proposals which lead to the creation of research programmes.


Archives

< March 2013 >
SuMoTuWeThFrSa
      1 2
3 4 5 6 7 8 9
10111213141516
17181920212223
24252627282930
31      

2016, 2015, 2014, 2013, 2012, 2011, 2010, 2009, 2008, 2007, 2006, 2005, 2004, 2003, 2002, 2001, 2000, 1999, 1997, 1995,