Deep water said:
I actually can't understand whether I should post this under Academic guidance and am confused about the title I've used too. anyway, I am just curious to know what a CS professor would do if he gets interested in some branch of Pure Math, let's say, Group theory or Analytic Number theory or Algebraic Topology? if he self teach himself (well, he may collaborate with some mathematician expert in the field he's interested in) and publish few papers on this, will he be eligible to be a faculty of a Math department? Of course I here have assumed that, the professor's PhD topic was about Automata theory or Complexity theory and was from CS department, even he never have taken courses like Abstract algebra or Topology in his academic life just focused on CS and some courses of EE
Hey Deep water and welcome to the forums.
This is a good question and I think that you get different answers depending on the person involved, the field they work in, their work/research environment and the relationships between their field and the field they are pursuing.
For the environment issue, you should be aware that in universities you have access to dozens, maybe even hundreds of specialists in their own particular area. This kind of environment (can) make(s) it very easy if someone else wants to learn something new or get an idea of what to pursue, what to read, and if a particular direction looks fruitful or not so fruitful. A quick conversation with someone who knows something inside out can yield these kinds of questions and more.
Also you need to understand the environment from the term of expectations on the employees. If you are doing research for a private firm, then chances are you won't be afforded the kind of freedom that you may get as an academic (I'm not saying academics can just do what they want, but in some instances they get more freedom in how they work and what they do in their work). It depends on your role of course, but you need to be aware of the context of the environment.
If you are a lone researcher or one that has a lot of freedom but no "go-to" guy/girl like the above scenario, then you probably go out and get books, search the internet and do all those kinds of things to get started.
Now with the connection between existing area and new area.
Some areas although different and distinct have many common threads between them. Many interdisciplinary areas already exist and if your proposed synthesis of areas has no real point of reference, then it will definitely be a lot muddier for you than if you are working in an interdisciplinary area that has existed for a while.
This is where things get interesting. If you are dealing with some areas then you may find some really solid information in not only things like journals, but also textbooks as well. If the field is really new and doesn't have much of a history, then the only resource might be the notes of some professor or manuscripts that have not been edited for public disclosure. There may not even be any notes that exist if you pick the right field!
In terms of the existing field they work in, this again is an important factor. Although we are becoming more prone to creating interdisciplinary fields in ways that we not considered 'orthodox' before, there still is a measure of 'orthodox' in todays world.
To put the above into context, think about the idea of doing mathematical modelling with the brain in terms of modelling neurosystems with differential equations. A long time ago, this kind of thing would be 'unorthodox' due the nature of the subject in terms of perspective of thought, ideas, trends and so on. As time moves on, and as interest moves on, and the number of people doing science grow, these barriers are slowly coming down (think of bioinformatics as a good example of this), but they are still there and it might be a fruitful exercise to examine why this is still the case.
Now to put this into the context of your question, in conjunction with the above discourse, one should also realize that one does not need a 'class' on something, nor does one need to do 'every exercise in the textbook' to gain a deep understanding of something. If you actively work on a project that forces you to gain an understanding, then that is how you have become acquainted with something and how you learn and comprehend it.
It might be helpful to view things in this way, because in reality this is how things get done: you have a project of some sort, and things need to be figured out. One advantage that something like university offers is that the material is presented in a form that is extremely concise and refinely polished so that you don't have to go to all the trouble that you would otherwise do if you had to figure everything out for yourself. Sometimes this is good, and sometimes it can be detrimental but that is for another conversation.
