As I have to study Analysis(against my liking)(see my previous post) now ,I am wondering what would a good book for me to start with?
I have a basic knowledge about analysis although not so thorough
I know sequences,basic definitions(limit points,closed,open etc),continuity ,differentiability etc.
So what will be a good book for me to start i.e looking for a book just one level above being an introductory textbook
On
If you had already done calculus, I would surely recommend Zorich.
The explanations are pretty concrete (Later some things get abstract but not early on) and it has real-life examples and applications as well as some "intuitive" explanations.
Now, I have to admit that I have not found the exercises easy. Some are false (as in he states a wrong exercise), but those are rare, and some are really difficult. I also found some problem early on which solution uses multidimensional material before he even covered such material. Thus, you can easily see that the exercises need work.
I recommend you read the two volumes of Zorich WITHOUT solving exercises, then move on to Baby Rudin and solve the exercises there as well.
Good luck.
When I was a student I was exposed to mathematical analysis thru the book Principles of mathematical analysis by Walter Rudin. I must say that I loved it and I then became a working mathematician in the field of analysis also in view of that book. However I know that many students simply hate Rudin's book because it has no image at all, almost no examples, and only hard problems. Therefore I usually suggest Charles Pugh's book on Real Analysis (published by Springer-Verlag), a more gentle introduction to real analysis. I also like Tom Apostol's book on mathematical analysis (not calculus!), but it may be hard to find nowadays.