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I am currently a junior at college and am considering doing an independent study (one-on-one with professor) in Real Analysis. The professor has suggested that we use Royden's Real Analysis (3rd ed) for this course. I am a little concerned because I have come across numerous postings in URCH and other websites that describe Royden as a graduate text and advise against using it for a first course in analysis. In addition, the non- independent study (regular) Real Analysis classes normally offered by the math department at my college use books that are either at the level of baby Rudin or below Rudin. However, my professor thinks that I have the ability to understand this book and do fine in the class. Has anyone heard of an undergraduate analysis course that used Royden? I am willing to take on the challenge and work my a$$ off, but I would like to know what you guys think of this idea. Does it seem like a bad idea? or are there people out there who have done well in a first undergraduate analysis course that used Royden? Also, does Royden leave out any important topics that are otherwise covered in an introductory undergraduate analysis course that uses baby Rudin or other books at the level of Rudin? As compared to Rudin, how well do you think Royden would prepare me for a second course in undergraduate analysis such as Real Analysis II. I look forward to your replies.
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