# Reference request for CMI M.Sc entrance exam

Today I would like to ask you for any references, books, pdf's etc. that comprises of a lot problems with the level advance graduate.

The syllabus is that of teaching in most under-graduate program in the topics algebra, analysis, complex analysis, general topology. I'm specifically looking for the type of books that deals with mostly problems that cross over different topics. For example, consider the following problem whose solution requires concepts from analysis and algebra:

let $R$ be a ring of all real valued continuous functions on the closed unit interval . If M is a maximal ideal of R , prove that there exists a real number $\gamma$ , $0\leq \gamma \leq 1$ such that $M=\{f(x)\in R :f(\gamma)=0\}$ .

The books i mostly use are :

Alegbra: Herstein , dummit-foote , Artin ,Hoffman kunze , Sheldon Axlers

Real analysis- Rudin ,Pugh , Apostol ,

Complex analysis - Ahlfors, Conway , Bak-Newman .

Topology -Munkers ,JK Joshi , Willard , Simmons .

I already going through many Ph-D qualifying exams of various universities across the globe . But i feel this isn't enough . I know i'm asking a lot but cracking this exams means a lot to me . Any help will be greatly appreciated . Thank you all .

• Can you let us know what PhD qualifying exams of various universities are you going through? Otherwise this question seems to me to be a little broad. – user 170039 Jun 6 '17 at 14:18
• Which university are you in? How did the exam go? It has been over a year now. – Subhasis Biswas Aug 15 '18 at 9:04
• I did better than I expected in the written test . Got interview for both M.Sc applied math and pure math . Got rejected though . – Suman Kundu Sep 13 '18 at 13:39
• Did you not try for ISI? – Subhasis Biswas Sep 24 '18 at 1:33
• Pardon me if this is going off topic, but I am extremely curious. – Subhasis Biswas Sep 24 '18 at 1:33