Reddit reviews Basic Topology (Undergraduate Texts in Mathematics)
We found 6 Reddit comments about Basic Topology (Undergraduate Texts in Mathematics). Here are the top ones, ranked by their Reddit score.
I was in the same position as you in high school (and am finishing my math major this semester). Calculus is not "math" in the sense you're referring to it, which is pure mathematics, without application, just theory and logic. Calculus, as it is taught in high school, is taught as a tool, not as a theory. It is boring, tedious, and has no aesthetic appeal because it is largely taught as rote memorization.
Don't let this bad experience kill your enthusiasm. I'm not sure what specifically to recommend to you to perk your enthusiasm, but what I did in high school was just click around Wikipedia entries. A lot of them are written in layman enough terms to give you a glimpse and you inspire your interest. For example, I remember being intrigued by the Fibonacci series and how, regardless of the starting terms, the ratio between the (n-1)th and nth terms approaches the golden ratio; maybe look at the proof of that to get an idea of what math is beyond high school calculus. I remember the Riemann hypothesis was something that intrigued me, as well as Fermat's Last Theorem, which was finally proved in the 90s by Andrew Wiles (~350 years after Fermat suggested the theorem). (Note: you won't be able to understand the math behind either, but, again, you can get a glimpse of what math is and find a direction you'd like to work in).
Another thing that I wish someone had told me when I was in your position is that there is a lot of legwork to do before you start reaching the level of mathematics that is truly aesthetically appealing. Mathematics, being purely based on logic, requires very stringent fundamental definitions and techniques to be developed first, and early. Take a look at axiomatic set theory as an example of this. Axiomatic set theory may bore you, or it may become one of your interests. The concept and definition of a set is the foundation for mathematics, but even something that seems as simple as this (at first glance) is difficult to do. Take a look at Russell's paradox. Incidentally, that is another subject that captured my interest before college. (Another is Godel's incompleteness theorem, again, beyond your or my understanding at the moment, but so interesting!)
In brief, accept that math is taught terribly in high school, grunt through the semester, and try to read farther ahead, on your own time, to kindle further interest.
As an undergrad, I don't believe I yet have the hindsight to recommend good books for an aspiring math major (there are plenty of more knowledgeable and experienced Redditors who could do that for you), but here is a list of topics that are required for my undergrad math degree, with links to the books that my school uses:
And a couple electives:
And a couple books I invested in that are more advanced than the undergrad level, which I am working through and enjoy:
Lastly, if you don't want to spend hundreds of dollars on books that you might not end up using in college, take a look at Dover publications (just search "Dover" on Amazon). They tend to publish good books in paperback for very cheap ($5-$20, sometimes up to $40 but not often) that I read on my own time while trying to bear high school calculus. They are still on my shelf and still get use.
In addition to the ones mentioned already, another excellent book is Topology by James Dugundji. I know a lot of older mathematicians who prefer that book over both Munkres' and Kelley's, because it covers more material and has very clear and concise explanations, plus some more challenging exercises (including some esoteric material not normally found at a book at this level).
For a simpler introduction, I think that Basic Topology by M.A. Armstrong is pretty good. It starts out with point-set topology then goes into algebraic topology. It takes an intuitive and geometric approach, and has a good conversational style that's well-suited for an elementary course at the undergrad level.
We're using Armstrong, which has gotten mixed reviews but I think that it's alright, its informal style suits me. But I have a copy of Munkres just in case. Which book are you using?
Ghrist's book makes a great overview of not only a bunch of topics in algebraic and differential topology, but also has a bunch of applications. I don't think it would be very good as a first introduction to topology, but it's certainly good for browsing and getting a general idea of things.
For a textbook, you might be best getting Munkres and working through that. Another book I really like that is shorter than Munkres is Armstrong's topology book.
Armstrong and Lee are both worth checking out.
I prefer terse books for some reason, so Armstrong is my personal favorite, but other people may prefer Lee, which includes lots and lots of explanations and examples.
Try Basic Topology by M.A. Armstrong. It presents the material in a much more intuitive and geometric way than Munkres.