Dummit & Foote’s Abstract Algebra is a good algebra book and Munkres’ Topology is a good topology book. They’re pretty advanced, though. In university one normally one tackles them in late undergrad or early grad years after taking some proof-based analysis and linear algebra courses. There are gentler introductions to algebra and topology, but I haven’t read them.
A couple more topology books to consider: “Basic Topology” by Armstrong, one of the Springer UTM series; “Topology” by Hocking and Young, available quite cheap from Dover. I think I read Armstrong as a (slightly but not extravagantly precocious) first-year undergraduate at Cambridge. Hocking and Young is less fun and probably more of a shock if you’ve been away from “real” mathematics for a while, but goes further and is, as I say, cheap.
Given how much effort it takes to study a textbook, cost shouldn’t be a significant consideration (compare a typical cost per page with the amount of time per page spent studying, if you study seriously and not just cram for exams; the impression from the total price is misleading). In any case, most texts can be found online.
There’s some absurd recency effects in textbook publishing. In well-trodden fields it’s often possible to find a last-edition textbook for single-digit pennies on the dollar, and the edition change will have close to zero impact if you’re doing self-study rather than working a highly exact problem set every week.
(Even if you are in a formal class, buying an edition back is often worth the trouble if you can find the diffs easily, for example by making friends with someone who does have the current edition. I did that for a couple semesters in college, and pocketed close to $500 before I started getting into textbooks obscure enough not to have frequent edition changes.)
Dummit & Foote’s Abstract Algebra is a good algebra book and Munkres’ Topology is a good topology book. They’re pretty advanced, though. In university one normally one tackles them in late undergrad or early grad years after taking some proof-based analysis and linear algebra courses. There are gentler introductions to algebra and topology, but I haven’t read them.
Great, I’ll look into the Topology book.
A couple more topology books to consider: “Basic Topology” by Armstrong, one of the Springer UTM series; “Topology” by Hocking and Young, available quite cheap from Dover. I think I read Armstrong as a (slightly but not extravagantly precocious) first-year undergraduate at Cambridge. Hocking and Young is less fun and probably more of a shock if you’ve been away from “real” mathematics for a while, but goes further and is, as I say, cheap.
Given how much effort it takes to study a textbook, cost shouldn’t be a significant consideration (compare a typical cost per page with the amount of time per page spent studying, if you study seriously and not just cram for exams; the impression from the total price is misleading). In any case, most texts can be found online.
And yet, sometimes, it is. (Especially for impecunious students, though that doesn’t seem to be quite cursed’s situation.)
Some people may prefer to avoid breaking the law.
There’s some absurd recency effects in textbook publishing. In well-trodden fields it’s often possible to find a last-edition textbook for single-digit pennies on the dollar, and the edition change will have close to zero impact if you’re doing self-study rather than working a highly exact problem set every week.
(Even if you are in a formal class, buying an edition back is often worth the trouble if you can find the diffs easily, for example by making friends with someone who does have the current edition. I did that for a couple semesters in college, and pocketed close to $500 before I started getting into textbooks obscure enough not to have frequent edition changes.)