Interview preparation for Ph.D admission

I have recently gave a written exam for admission to Ph.D program to an institute in India. I have done that exam well and hoping for an interview call. I would like to know what could be type of questions the panel would ask for a student to confirm that i am fit for them..

I am interested in Algebra so they would start with Algebra and then my choice would be topology

Usually the syllabus for algebra which almost all Indian universities would cover is :

Algebra :

• Group theory : Group actions, Automorphisms, Sylow theorems, Direct Products,finitely generated abelian groups. More or less we are expected to know first five chapters of Dummit Foote Abstract Algebra Book.
• Ring Theory : euclidean Domains, P.I.D., U.F.D., Polynomial rings, Irreducibility criterion.More or less we are expected to know all three chapters of Ring Theory part of Dummit Foote Abstract Algebra Book.
• Field and Galois theory : Algebraic extensions, splitting fields, seperable extensions, cyclotomic polynomials, fundemental theorem of galois theory cyclotomic extensions, Insolvability of quintic and more or less Chapter $13$ and chapter $14$ (except transcendental extensions, Inseperable extensions, infinite galois groups)of dummit foote Abstract Algebra Book.

Topology : We are expected to know connectedness, compactness, countability and seperation axioms, Compactness/Completeness of metric spaces and more or less first four chapters and seventh chapter of Topology book by Munkres.

I have tried to solve most of the problems in what all i mentioned for algebra part but then as i have only one month time i am not able to decide how should to start the preparation. should i just go on solving all those questions again or do something else?

I tried to see http://web.math.princeton.edu/generals/ to get some idea but then it is much more advanced.. So, I would request you to suggest me to some way to prepare for the interview... May be by posting some interesting questions which are answerable in less than ten minutes...

For example :

• give an example of an extension whose galois group is $S_3$ or $S_4$
• Computing galois group of some polynomials over $\mathbb{Q}$

Please help me to collect such problems.

Thank you.

Solution 1:

Try googling on "Algebra Qualifying Exams". This yields a slew of problems/solutions on-line, see for example http://www.math.wisc.edu/~passman/algquals.html

Solution 2:

you can check this link to know some general questions, may be asked during interview http://phdscholar.in/phd-admission-interview-questions.php