# Recommendations for introductory online analysis books

Can someone please recommend me books for mathematical analysis that can be found online? I need chapters about some pretty basic stuff like sets, absolute value, supremum, infimum, functions, relations. I also need examples of problems. I've tried searching it online but all the stuff I found were too advanced for me.

• Have you looked at Thomson/Bruckner, Elementary Real Analysis? It's available as a free (legal) PDF: classicalrealanalysis.info/documents/… It's also published as a book, check the reviews at Amazon: amazon.com/Elementary-Real-Analysis-Brian-Thomson/dp/143484367X I think it's a very good introduction.
– user169852
Oct 21 '15 at 17:58
• No, I haven't seen it before. I think that it will be of great help to me. Thank you very much. Oct 21 '15 at 18:04
• The citation should be "Thomson/Bruckner/Bruckner." Don't forget Andy, or was it Judy you forgot? Oct 21 '15 at 18:49

One site that many students and instructors find useful is the American Institute of Mathematics (AIM) open source textbook collection. Here is a link.

We have put our Elementary Real Analysis textbook there. (Thanks Mr Bungo for the plug.)

I think the future will bring many more free textbooks, especially for mathematics. Our original motivation for making the text free was the familiar narrative of our dealing with a major publisher who will not be named (Pearson). They priced the text at an outrageously high level, and then dropped it from their list after a few years and solicited more mathematicians to write similar texts. William Trench, whose real analysis textbook is also free on the AIM site, had an identical experience in the same time period with the same publisher.

We got our copyright back and just posted the PDF on the web. Very soon there were tens of thousands of downloads and that prompted us to make a second edition.

Remember too that old textbooks that are now in the public domain (and may have been scanned) can still be valid and useful presentations of elementary real analysis. There is nothing much new in the subject since it was mostly developed to this level long ago. If you can find a copy of Hardy's Course of Pure Mathematics you will be learning from a master and, at the same time, not enriching the big publishing companies (who will not be named).

• Our advanced $\text{Real Analysis}$ textbook is not on the AIM site since they are currently interested only in undergraduate mathematics texts. But our ClassicalRealAnalysis.com website has that too for free download. Oct 21 '15 at 18:47
• Thanks mate, i will look it up. Oct 21 '15 at 18:52
• @B.S.Thomson: Sorry about the lazy citation above! I own and very much enjoy both this book and its sequel (Bruckner/Bruckner/Thomson), so there's no excuse for getting it wrong. I applaud you and the Bruckners for making them freely available, and also want to mention that the print editions are very reasonably priced.
– user169852
Oct 22 '15 at 5:19