Reddit reviews Elementary Analysis: The Theory of Calculus
We found 7 Reddit comments about Elementary Analysis: The Theory of Calculus. Here are the top ones, ranked by their Reddit score.
You are missing Abstract Algebra that usually comes before or after Real Analysis. As for that 4chan post, Rudin's book will hand anyone their ass if they havent seen proofs and dont have a proper foundation (Logic/Proofs/Sets/Functions). Transition to Higher Math courses usually cover such matters. Covering Rudin in 4 months is a stretch. It has to be the toughest intro to Real Analysis. There are tons of easier going alternatives:
Real Mathematical Analysis by Charles Pugh
Understanding Analysis by Stephen Abbot
A Primer of Real Functions by Ralph Boas
Yet Another Introduction to Analysis
Elementary Analysis: The Theory of Calculus
Real Analysis: A Constructive Approach
Introduction to Topology and Modern Analysis by George F. Simmons
...and tons more.
The 1st Course In Math Analysis by Brannan
Analysis I by Terrence Tao
Yet Another Intro To Real Analysis by Bryant
Understanding Analysis Stephen Abbott
Elementary Analysis: The Theory of Calculus Kenneth A. Ross
Metric Spaces by Robert Reisel
A Problem Text in Advanced Calculus by John Erdman. PDF
Advanced Calculus by Shlomo Sternberg and Lynn Loomis.PDF
If Rudin is too demanding for you, don't despair. A fairly good book that is not as challenging is Ross. Once you get through that, Rudin may be a bit more amenable.
Many of the graduate level macro textbooks (e.g. SLP) are best read after getting some experience in mathematical analysis (at least one class at even a low level like that of Ross would probably make a huge difference in your comfort level with the material).
Romer's text is the first thing that comes to mind as something that is at a higher level than undergrad texts, but simple enough that someone well-versed in econ and differential equations can jump into without having a background in analysis.
If you're interested in autoreggresions, maybe a text on time series econometrics would be best.
I've always liked Ross' Elementary Analysis
This was true for me as well. A great introductory book is this one:
http://www.amazon.com/Elementary-Analysis-The-Theory-Calculus/dp/038790459X
Full of good pictures and lots of exposition.
I hear that Rudin's book is pretty dense, so initially, I won't be using it, though I'm not entirely familiar with Spivak/Rudin beyond the comments on Amazon/Reddit.
Instead, I'm reading from Ross and [Bartle] (https://www.amazon.ca/Introduction-Real-Analysis-Robert-Bartle/dp/0471433314) right now, which I hear are good books for people starting out in Analysis. As I progress through the series, I might start teaching from Rudin and a variety of other sources.