Topology Books for Beginners - John Milnor's Differentiable Viewpoint

[LBloom]

Hey guys,

So my prof assigned John Milnor's book about topology from a differentiable viewpoint for out topology and geometry class. I was wondering if anyone had a book they could recommend as an introduction into topology because I don't think professor Milnor's book really is an introductory book although I could be wrong.

I do have some basic knowledge of topology that I've picked up from reading books on tensors (tensor geometry by dodson and part of tensors on manifolds by bishop). I was considering Munkres, but does anyone have any other recommendations? On a sidenote I'm primarily a physics major but I don't know if that matters for a topology book on that level.

Thanks.

 

[Goldbeetle]

Try also this as intro for meaning and intuition: https://www.amazon.com/dp/0486419614/?tag=pfamazon01-20
and this, rigourus:
https://www.amazon.com/dp/0486663523/?tag=pfamazon01-20

 

[MathematicalPhysicist]

Munkres is as good as it gets for UG, though I haven't tried other books of UG Topology.

 

[jbunniii]

I second Goldbeetle's recommendation of Mendelson's "Introduction to Topology." It is an absolutely crystal clear treatment of the basics of metric spaces and point-set topology. It doesn't cover as much material as Munkres, but for what it does cover I think it's superior. And you can't argue with the price: $6.65 from Amazon.

 

[mathwonk]

read milnor. that is the best book of its kind in existence. ask questions here for help. when you pay money to be taught by experts, do not resist what they are trying to do for you. take their advice.

 

[hitmeoff]

read milnor. that is the best book of its kind in existence. ask questions here for help. when you pay money to be taught by experts, do not resist what they are trying to do for you. take their advice.

Can't comment on Milnor, but Professors aren't infallible. Case in point, we are using Gamelin and Green for our undergrad Topology. Its a fine book, but even the professor admitted that its geared more towards grad level students. I have supplemented the book with the Medelson text (supplemented, not replaced). Heck, I even supplement with my Ross Analysis text. Not sure if I could handle the class if all I had to rely on was Gamelin and lectures.

 

[LBloom]

Well unfortunately my library doesn't have Mendelson now, so for the time being it is Munkres and I feel MathematicalPhysicist is probably right. I will make sure to check out Mendelson though once I can find it.

MathWonk- Believe me if a professor assigns a book I'll get it. I definitely plan on reading Milnor I'm just looking for a book over the summer to help me learn about Topology first. I feel like Milnor's book is more advanced. (he mentions some terms I don't know offhand).

Thanks for the advice!

 

[PieceOfPi]

I used Czes Kosniowski's https://www.amazon.com/dp/0521298644/?tag=pfamazon01-20 for my topology class. The first ten chapters of this book are on point-set topology that is suited for anybody who is learning topology for the first time. I thought the book was very well written, and it did a fantastic job interlacing abstract concepts and concrete examples.

But since your professor recommends a book that has more emphasis on differential topology, the later chapters in this book might not be helpful.

 

[hitmeoff]

Well unfortunately my library doesn't have Mendelson now, so for the time being it is Munkres and I feel MathematicalPhysicist is probably right. I will make sure to check out Mendelson though once I can find it.

MathWonk- Believe me if a professor assigns a book I'll get it. I definitely plan on reading Milnor I'm just looking for a book over the summer to help me learn about Topology first. I feel like Milnor's book is more advanced. (he mentions some terms I don't know offhand).

Thanks for the advice!

Yeah, I truly believe Mendelson would be be the ideal place to start self-studying over the summer. You can get it new for about $11 at Amazon or your local Barnes and Nobel, or get it used from half.com for about...half that :). The only downside is that there are no solutions to the problems. That upper div Gamelin book I mentioned that we use in an undergrad class is not bad, just to..."polished" (as grad books are) but the plus side is that nearly all answers are in the back. Book cost is about 15 bucks.

Never read Munkrese, but it does seem to be the defacto modem undergrad Topolgy book, so that its available at your library is great!

Dunno what you know about topology or why you'd want to take it, but Topology is very similar to Analysis. For what ever reason I absolutely hate anlysis, but I am really enjouyinjg topology, as hard as it may, I love topology