I need to appear for an interview for the post of Assistant Professor in Mathematics in an undergraduate college.
My Backgorund : I have studied topics like Algebra comprising of Group Theory,Ring Theory and Field Theory. I have also studied Linear Algebra and Matrices,Complex Analysis,Functional Analysis. The above topics are of interest to me and I study these topics in my PhD.
Background of College:The college also teaches undergraduate students in the courses mentioned above and also teaches some applied mathematics as a part of Bachelors in Science Course.The syllabus of the college in the website at least says this .
I received a call letter from the college that I need to give a demonstration about some topic of interest of mine for 15 minutes.
The problem is I have never given such a demonstration before and I really dont know how to handle this.In fact I have only given talks about my PhD topics for my PhD and I am pretty sure that I cant say those things for a 15 minute demonstration.
I understand that there are numerous topics on which such a demonstration can be made but I am not sure what will fit into a 15 minutes demonstration.
Can someone please help me on how to select some topics and how to manage them in 15 minutes?
NOTE:There is no powerpoint presentation involved.It should be done in Blackboard.