Is baby rudin a good first exposure to analysis?

[battousai]

hello. i am a freshman, and i will be taking an analysis (honors) course next quarter, and the textbook used will most likely be baby rudin. That will be my first exposure to the subject, although i did take an honors multivar calculus sequence last quarter that attempted to be more rigorous and formal than your typical calculus class. right now I'm taking an honors linear algebra (lower div) class which so far is below the level we treated calculus.

i've heard that rudin's book is hard and i feel like i might be unprepared for it. can i read something in advance so that i won't be struggling to keep up when the time comes?

 

[mathwonk]

why don't you go to the library and search around in the analysis section? almost any book will be more readable than rudin. are you familiar with one variable calculus at the level of spivak? or apostol? try books by berberian, or george simmons, to name just two authors who try to be clear and not just as brief as possible like rudin.

 

[Fredrik]

Most people don't think Rudin is easy enough to read, so I think it's a good idea to look for options. There are other threads about this, so you should start by doing a search.

 

[battousai]

well, the non honors analysis classes at my school uses ross. would that be a good book for starters?

the book we worked with for honors calculus is williamson/trotter multivariable mathematics

 

[battousai]

also, i took ap calculus in high school, so i did not have a "spivak level" single variable

 

[JG89]

^ Then it'll be a good idea to get exposed to rigorous calculus proofs. Get a hold of Spivak's, Apostol's, or Courant's book and work through it. It'll pay off when you start baby Rudin, GUARANTEED.

Also, as an alternative to Rudin you might want to take a look at Pugh's "Real Mathematical Analysis"

 

[Jorriss]

Also, as an alternative to Rudin you might want to take a look at Pugh's "Real Mathematical Analysis"

This. Pugh's analysis book is incredible. He starts off fairly informal so it may feel like he lacks rigor, but it's all there.

 

[battousai]

other people have recommended abbott understanding analysis, what about that?

 

[Sankaku]

Ross is a very gentle introduction - well written, standard progression.

Abbott is about the same level but a bit more interesting (in my opinion). Still a gentle introduction (compared to Rudin), but more motivation than Ross for the central ideas of analysis. Either would give you a good intro, if you can find one at the library.

Rudin is more of a reference book than a textbook. The difficulty of your class will really depend on how good a professor you get and how fast the material is covered.