EDIT: Alright, I'm convinced that this isn't such a good idea. You guys have some very good points, thanks for discussing!
From my experience, much of basic analysis is greatly simplified [and also made more intuitive] if you have a good understanding of basic topology. Being familiar with metric spaces is so essential to basic analysis that often the beginning of advanced calculus / intro analysis classes is solely devoted to discussing metric spaces and continuous functions between them.
Why, then, do we generally teach analysis before a course in general topology? Analysis relies so heavily on topology that I would think it would be easier to get all of the necessary topological background and intuition out of the way in a separate course rather than spend a third of an intro analysis class just building up the topological prerequisites. It would save time for covering more advanced material from analysis.
One argument against this that I could think of is that topology is more abstract than advanced calculus usually is, so this might be too much for students who haven’t developed enough mathematical maturity yet. I’d be curious to hear what others think, though.
Hey all! I'm a junior math undergrad and I recently have been watching too many videos and reading too many articles on topology to not be super excited about it. I'm curious what background is recommended to start studying topology?
I currently have experience in multivariable calc, intro complex analysis, and linear algebra. I'm sure I need some real analysis or some graph or set theory, but if anyone has some good advice and/or some book recommendations I would be forever grateful!
Thanks!
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19 comments
I'm a CS graduate student. This semester I signed up for a undergrad/grad introduction to algebraic topology course. I /may/ have started to read ahead and I felt a little behind since it seems to be kind of heavy on abstract algebra which I've never really had formally.
I completed a Math/CS major for my undergrad career, but I was pretty heavy on probability and statistics.
I'm just trying to double-check that I'm not in over my head. I suspect I'm OK since it is, after all, an introduction course.
Thanks for your thoughts!
EDIT:
In case you're in the same boat, there's also a general topology course at my university which is supposed to be a prerequisite. Oh well!
I'm physics student interested in GR and I'll be a junior next fall [in two months]. I'm gonna be taking a Geometry and Topology in Physics course then.
I've been in contact with the professor asking what to study before so that I can do well in the class. He told me to study intro to Real Analysis and me said that I should be comfortable with Advanced calculus. [I'm not entirely sure what he means by that].
For Real Analysis I'm reading Kolmogorov's book. But I'm not sure what to study from for Advanced calculus.
Are these really necessary for a course like that, or is their introduction in the class sufficient? The reason I'm asking is because I don't have a lot of time these days, so I wanna spend the time that I have most effectively.
So given that I don't much time, what topics are considered most crucial to prepare me for this class?
Thank you all in advance
Point set, algebraic, differential... I'm a bit confused as to which comes first, and what the prerequisites are for each one. From what I understand, real analysis is a prerequisite for point set... I don't know anything other than that.
I bought it a few months ago to help understand some relations I noticed in logic design, but I can't even get through the first chapter! Intuition points me towards analytic geometry or maybe general logic, but I'm a bit lost as a hobbyist. Ten years ago I took calculus, linear algebra, vector calc, and logic design, as well as a hodgepodge of random 'casual math' stuff on YouTube; e.g. 3blue1brown, blackpedredpen, etc.
Specific book recommendations as well as general advice would be well appreciated!
My goal is to eventually learn the "big 3" core math subjects, Topology, Real Analysis and Abstract Algebra.
I've heard that Topology tends to be people's favorite and the subject that people claim was most useful. I even watched the video about turning a sphere inside out and so topology is the subject that I'm most motivated to learn at the moment.
Is calculus I, calculus II [differential & integral] and discrete mathematics [learned a bit about set theory] good enough before I attempt to learn from the Munkres textbook? Or should I go through the long route and study multivariable calculus, differential equations, linear algebra, and abstract algebra before I attempt to learn Topology?
I currently only have a formal education up to high-school calculus and an informal knowledge about logic, sets, and functions. How would I go from where I am to being able to really understand it?
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Posted byu/[deleted]9 years ago
13 comments
Hi guys,
I am trying to teach myself some basic topology and I was wandering what is the prior knowledge required to be able to learn that subject on your own. I don't want to grab a book on the subject and then have no clue what I am reading. I know calculus [single and multi var], DE, Linear Algebra, and I took a class in Abstract Algebra [group theory mostly]. I also just began one of those MIT open courseware in Real Analysis [I thought it would be helpful].
So what is something that you guys would recommend learning before topology?
Thanks in advance.
ps: Additionally, if you know any good books or resources on topology please share.
pss: In case someone replys "depends on the type of topology you want to learn" I would say that for now I just want to learn some General Topology. Hopefully, once I have a good grasp on the basics I could work my way into differentiable manifolds and the kind.
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Posted by8 years ago
11 comments