I am a high school rising senior with an interest in mathematics, and I will be taking AP calculus AB next year. I have been doing research online, and recently came across hyperreal numbers, which I believe (correct me if I'm wrong) to be an idea featuring in non-standard analysis. My question is this: What are the best introductory books for learning non-standard analysis (furthermore, does the Dover books on Mathematics series have any such books). I do have a basic understanding of proofs, but know no more computational math than simple limits, if that helps.
Thanks
To answer one of your specific questions, there is indeed a Dover Books on Mathematics on the topic of Nonstandard Analysis: Nonstandard Analysis by Alain M. Robert.
However, this book is written for somebody who has already taken a basic intro to real analysis course and I imagine it would be more difficult than necessary for somebody who has not otherwise been introduced to calculus. Further, there are other books, like Keisler's, that are written on a more introductory level. Additionally, I would note the book by Robert takes the less common Internal Set Theory approach to nonstandard analysis which differs from the approach taken using hyperreals. You may wish to research which approach you are interested in before starting.