Never studied higher math. Can I start with Munkres?

>>8786864
Starting with topology is odd.
You certainly _could_ if you were comfortable enough with abstract, proof-based mathematics but you probably aren't.

>>8786883
i should give myself more credit than i did. i am familiarish with very basic set theory proofs.

>>8786883
it's just i dont know analysis, but dont know if that is a pre-req for this book. i badly want to learn and want to know if it is feasible. believe ill start very soon and ask on here if i run into any questions after great effort.

You should study analysis first, particularly shit like the intermediate value theorem, extreme value theorem, and metric spaces. Topology generalizes ideas from analysis. IMO, starting with lots of axioms like metrizable and Hausdorff (i.e. metric spaces) then pealing them away is more logical and motivated then starting with the bare minimum before adding on T0, T1, etc.

>>8786864
Since you know the basics of proofs, then Munkres' topology is a great start. Are you interested in analysis, or algebraic topology, or (differential) geometry? You can study topology while learning these as well.

>>8786892
i just want to jump into analysis, can i learn whatever i need in anaysis along the way with munkres? I plan to do the exercises and not skip anything.

>>8786893
im mostly interested in group theory. been reading 'visual group theory' and plan to move to pinter afterwords.

>>8786893
my idea is to do algebra + topology in parallel. the visual group theory book is pretty easy to go through, so once i finish it i'll supplement it with pinter like my initial post stated, but i want something more rigorous (now) to supplement my basic group theory learning and think topology (munkres) would be a great first exposure to that

>>8786892
Oh, also stuff in analysis dealing with compactness and convergence of sequences. For example, in metric spaces, we have sequentially compact \iff limit point compact \iff compact. These aren't true in the general topological setting, and topology will dig into which directions necessitate which axioms.

>>8786897
Then you'll like algebraic topology, but like other posters have said, you should probably learn analysis first. i'd suggest reading
- basic group theory
- analysis a la baby rudin
then when you're done, do munkres. without a good grounding in analysis, you won't have enough motivation to enjoy the results in topology.

>>8786904
thanks for the suggestion

>>8786894
Sure, Munkres will teach you everything. It just goes in a direction that I don't like. I prefer approaching a study of topology by starting with analysis, which is the study of a special category of topological space with tons of structure, and from there peeling this structure away.

Munkres will start with no structure and build it up. It will feel unmotivated, IMO. But ultimately it does cover everything. Just not in the order I prefer.

>>8786908
ok makes sense. i sort of like the 'ground up' approach, but i understand your point

>>8786904
Really you don't even need all of Rudin. The first two chapters are probably sufficient to have a reasonable springboard for topology.

>>8786864
No. Nothing will be motivated nor useful.

Start with linear algebra out of Hoffman and Kunze or Axler. The material is useful but also obvious and gives good practice on proving things.

Now learn analysis. I highly recommed Rosenlicht for a first book. After that read Rudin's principles.

Now you can read Munkres. At least for the general topology. Algebraic topology requires some algebra. I recommend Herstein's topics in algebra for this. I hated both Artin and Dummit and Foote but they're well liked so take a look at them if you don't like Herstein.

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Bit off topic, but what kind of knowledge prerequisite would one need, to begin to learn topology?

>>8786913
op here, found a pdf of rudin. i will go thru the first 2 chapters then switch to munkres. rudin will be my first exposure to analysis

>>8786945
Pugh covers more or less the same material as Rudin but goes into a lot more detail and is generally a lot more user-friendly. IMO it's a much better choice for self-study, especially if this is your first math book.

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>>8786908
What are some books that explain it the way you prefer?

>>8786923
proofs
modern/abstract algebra
analysis

after these you can take any subject in mathematics

>>8786945
Op here, ok thanks!

>>8786864
popular textbooks for 200

>>8786864
It is doable, but some definitions will seem a little weird without motivation from analysis.

You should learn basic real analysis (even just a short into like Rosenlicht). Point set topology is the point at which you might start to miss the motivation. Just FYI, point set topology (and especially digging through all of Munkres) is dry as fuck. Actual geometry and topologists don't really do things in this style. Prepare to be bored to tears.

>>8788009
not him but Foundations of Topology by Patty gives a good treatment of the subject with roughly that presentation and motivation

great book; far superior to Munkres in my opinion