Math is a unique subject, based on logic, axiom and definitions.there are few tips to do better in it.
1..at research one should be clear in its research topic and future research plan.if you some research papers, try to mention journel rating.
2..geometry , figures and graph are the tool to describe math,soyou have commend on it.one should well prepared for graph of simple curve trignometrical ratio, mod fuction, greatest and least integer fuction, logarithem and exponential fuctions.
3..you should have at least famaliar with mathmatica and matlab software.if your are opting N.A or O.R , then it is nesseary.
4..if you trying for faculty position,then do some practice on lcd screen also.
5..for ph.d selection interview, one should make a good mix of pure and applied subjects for broad spectrum.
6..try to mention, with example , if converse of theorem is not true.converse of theroms are important concept in maths, because they test the limit of generilisation.
7.stess on definations, b/c there are pillars of mathematical structure.never discuss the proof of defination.also clear the concept of axiom.
8.. LINEAR ALGEBRA is safe bet for ph.d interview.it bridges pure and applied maths.students are well aware of matrix notation, so it is easy for them to comprehand linear algebra.every matrix represents a linear transformations.
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