Mathematics books to master limits. This question is intended to ask for recommendations of books, maybe calculus books, that pay special attention on acquiring proficiency in the topic of limits. I'm currently "reading" CET from J. Stewart -8th Ed. to be specific- and I do OK with almost everything. However, I still have difficulties with limits, specially with the epsilon-delta proofs. Again, I want a book specifically for limits, or one that includes this topic broadly.
Also, I'd appreciate any recommendations on other Math books that might help improve my level. One that focuses on Proofs would be nice.
Finally, is there any simple way to input formulas in the questions, or must I get used to MathJax?
Thanks in advance.
E.
 A: In the late 1990s I wrote several handouts on limits for my students. Not all of these have been posted somewhere on the internet, but I did manage to find this one and this other one. Here’s another such handout that I refurbished for use in 2003.
Below are three books I know about that deal in large part with limits at the (possibly honors) elementary calculus level.
Sequences, Combinations, Limits by S. I. Gelfand, et al. (1969/2002)
A Concept of Limits by Donald W. Hight (1966/2010)
Limits and Continuity by P. P. Korovkin (1969)
The first two books are fairly well known and easily available. Since Korovkin’s book does not seem to be either (I’m rather surprised, as it’s in The Pocket Mathematical Library series to which several well known books belong), I’ll give its table of contents. Incidentally, each of the 21 sections of Korovkin's book ends with a short list of problems to work.
Table of Contents (Korovkin’s book)
Chapter 1. Functions (pp. 1-23).

  
*
  
*Variables and Functions. Intervals and Sequences (pp. 1-9). 2. Absolute Values. Neighborhoods (pp. 9-11). 3. Graphs and Tables (pp. 12-14). 4. Some Simple Function Classes (pp. 14-20). 5. Real Numbers and Decimal Expansions (pp. 21-23).
  

Chapter 2. Limits (pp. 24-72).


  
*Basic Concepts (pp. 24-32). 7. Algebraic Properties of Limits (pp. 32-37). 8. Limits Relative to a Set. One-Sided Limits (pp. 37-43). 9. Infinite Limits. Indeterminate Forms (pp. 43-48). 10. Limits at Infinity (pp. 49-53). 11. Limits of Sequences. The Greatest Lower Bound Property (pp. 53-57). 12. The Bolzano-Weierstrass Theorem. The Cauchy Convergence Criterion (pp. 58-62). 13. Limits of Monotonic Functions. The Function $a^x$ and the Number $e$ (pp. 62-72).
  

Chapter 3. Continuity (pp. 73-115).


  
*Continuous Functions (pp. 73-79). 15. One-Sided Continuity. Classification of Discontinuities (pp. 79-83). 16. The Intermediate Value Theorem. Absolute Extrema (pp. 83-89). 17. Inverse Functions (pp. 89-92). 18. Elementary Functions (pp. 92-101). 19. Evaluation of Limits (pp. 101-105). 20. Asymptotes (pp. 105-111). 21. The Modulus of Continuity. Uniform Continuity (pp. 111-115).
  

Answers to Even-Numbered Problems (pp. 116-122).
Index (pp. 123-125).
A: Check out some upper level texts. "Advanced Calculus" by Patrick Fitzpatrick, "Calculus" by Michael Spivak, and "Understanding Analysis" by Stephen Abbott are all great texts to learn the more rigorous theory of limits, including $\epsilon\text{-}\delta$ proofs. If you're interested in learning more about the proof-based and more rigorous side of calculus, then you may want to continue reading these texts after the limits sections!
