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I am currently a first year undergraduate majoring in mathematics. I'm taking an introductory analysis course and find it very hard compared to other math couses. I know that the topics covered in the course are really the basics of real analysis, such as properties of $\mathbb{R}$, sequences and series, limits, continuity, Riemann integral, etc. I work much harder in analysis than in other courses such as abstract algebra, and am spending a lot of time to memorize all the theorems and their proofs mentioned in class. However, when it comes to work out a problem in the book or in the assignment on my own, I'm stuck. My guess is that I never learned how to do math rigorously, and I always rely on my intuition, which proved usually accurate in the past.

The textbook we are using is "Introduction to Real Analysis" by Robert Bartle, 3rd ed., but I also downloaded and use some extra analysis notes from a few professors' webpages.

Could you please give me any advice on how to study analysis? I'm now really desperate :(

  • 2
    Try [this book](https://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwjF_e7Y1K_PAhUHro8KHZxsB_YQFggbMAA&url=http%3A%2F%2Ftalegari.wdfiles.com%2Flocal--files%2Fstatic%3Astart%2Fcalculus%2520-%2520basic%2520concepts%2520for%2520high%2520schools%2520-%2520tarasov.pdf&usg=AFQjCNFwZ3msqM5YGtmSNU4E_QL6djVC9w).2016-09-27

7 Answers 7