I am in a fix. I have done a graduate course in Pure Mathematics.I love to study abstract algebra.I want to do postgraduate in Mathematics especially in Abstract Algebra .
In order to enter a postgraduate program I have to qualify a screening test which comprises of three sections:
- Metric Spaces and Topology
I appeared in the test the earlier year .Though I scored a perfect 10 in Algebra,my marks in the other two topics were $3$ and $4$ out of $10$ as a result of which I failed to qualify.
Is it possible to learn Analysis now or its too late.Can I speed up the process of learning Analysis?Can someone please give some tips on how should I read this topic?I don't know why I fail in this topic very badly.Though I have studied topics like Continuity,Differentiablity,Riemann-Integral,Sequence and series of functions etc.,I fail in these topics miserably.Do I need to start from scratch now?
Also I more question I find that people ask for recommendation of books in Analysis.How important is the choice of books in a particular topic.We followed Rudin-Principles of Mathematical Analysis in our course.
In short please give some tips on how to study Analysis .I know there are many on this site who are very good at analysis.Any recommendations will be helpful