4 ms·

I strongly second the recommendation of Munkres' Topology. It's basically the gold standard. However, I think don't think it's accessible to junior/senior under

I strongly second the recommendation of Munkres' Topology. It's basically the gold standard. However, I think don't think it's accessible to junior/senior undergraduates unless they've taken a prior course in analysis. Technically Munkres' Topology has no formal prerequisites, but it's a rough go of it if you haven't had a rigorous exposure to continuity and metric spaces already. The second part of the book also assumes knowledge of elementary abstract algebra. If the person you're replying to is a junior or senior undergrad in a math major they might be alright (presumably they'll have taken analysis by then). If not, Topology is not what I'd recommend as the first place to learn about metrics and continuous functions (Calculus doesn't cut it for that).

bigmit37 8y ago
Thank you. I am actually a self- learner and have only take calculus, linear algebra, probability, statistics. Currently learning bayesian statistics and reading “first course in abstract algebra” by John B Fraleigh. I am guessing I should do Real Analysis and then the Munkres book to get an idea of topology ?
- magoghm 8y ago
  Right now, I'm self-studying analysis with Stephen Abbott's "Understanding Analysis". I strongly recommend it. It has clear explanations that help to develop the intuition about each concept and what I think are well chosen exercises.
  - nikofeyn 8y ago
    there is a book by jay cummings called real analysis: a long-form mathematics textbook that i highly recommend checking out. used with a more "advanced" book, it could be a nice complement. Real Analysis: A Long-Form Mathematics Textbook https://www.amazon.com/dp/1724510126/ https://www.amazon.com/dp/1724510126/
drilldrive 8y ago
I personally really enjoy Gamelin and Green's Topology, and (if you need it) the first chapter goes through topology of metric spaces. The rest of the book is well written; I couldn't quite find myself to like Munkres.
nikofeyn 8y ago
agreed. i had it in mind the person was a math major. although i think topology is approachable without analysis with some dedication, it certainly helps provide context for the abstraction. i listed another nice book in another comment, but metric spaces: iteration and application by victor bryant is a pretty fun introduction to metric spaces and analysis at a very approachable level.

bigmit37 8y ago

Thank you. I am actually a self- learner and have only take calculus, linear algebra, probability, statistics. Currently learning bayesian statistics and reading “first course in abstract algebra” by John B Fraleigh. I am guessing I should do Real Analysis and then the Munkres book to get an idea of topology ?

magoghm 8y ago
Right now, I'm self-studying analysis with Stephen Abbott's "Understanding Analysis". I strongly recommend it. It has clear explanations that help to develop the intuition about each concept and what I think are well chosen exercises.
- nikofeyn 8y ago
  there is a book by jay cummings called real analysis: a long-form mathematics textbook that i highly recommend checking out. used with a more "advanced" book, it could be a nice complement. Real Analysis: A Long-Form Mathematics Textbook https://www.amazon.com/dp/1724510126/ https://www.amazon.com/dp/1724510126/

drilldrive 8y ago

I personally really enjoy Gamelin and Green's Topology, and (if you need it) the first chapter goes through topology of metric spaces. The rest of the book is well written; I couldn't quite find myself to like Munkres.

nikofeyn 8y ago

agreed. i had it in mind the person was a math major. although i think topology is approachable without analysis with some dedication, it certainly helps provide context for the abstraction. i listed another nice book in another comment, but metric spaces: iteration and application by victor bryant is a pretty fun introduction to metric spaces and analysis at a very approachable level.