/sci/ - Science & Math » Thread #12916640

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Is topology an interesting field to learn about?

Anonymous Fri 02 Apr 17:52:46 2021 No.12916640 View Reply Original Report

Quoted By: >>12917166

I'm an engineer and as such have little room in my schedule for pure math classes. However, for the past few years, since watching
https://www.youtube.com/watch?v=Fyl_kGgHxAQ
I've been fascinated with topology. Idk but something about working with 3d geometries and modifying them in abstract ways just appeals to me. I'm just wondering what other people think about topology as I don't want to get immersed in a field that's boring.

Also, do I have enough math knowledge for this subject? I've taken calc 2 and 3, diff eq. and I'm currently in lin alg.

Anonymous

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Anonymous Fri 02 Apr 2021 18:03:04 No.12916685 Report

Quoted By: >>12916725

You are clearly seeking an "atta boy" encouragement for your pursuit of knowledge, so here it is: Go for it, bro.

You obviously have an interest in a subject innately, you don't need us to tell you if it's an interesting field or not, because that is entirely subjective. You find yourself drawn to it.

That said, I also find it to be a wonderfully fascinating field, but I can generally get into a lot of topics with an intellectually stimulating component to them.

Start delving into it and if and when you notice your interest waning, or your other priorities in life taking over, then back away from topology for awhile, or forever.

Enjoy the journey of cultivating wisdom.

Anonymous

Anonymous Fri 02 Apr 2021 18:13:58 No.12916725 Report

Quoted By: >>12916749

>>12916685
Ok thanks for the advice. I just don't want to begin studying it and get tired of it because the parts that drew me into the field in the first place are minorly present.

Anonymous

Anonymous Fri 02 Apr 2021 18:21:34 No.12916749 Report

Quoted By: >>12916790

>>12916725
That is something you would have to discover for yourself. Without actual experience and understanding of the material, how is another person supposed to articulate to you a complex subject that you may or may not enjoy? They would have to teach it to you, and at that point you are already there learning it.

I understand your apprehension. I was the same way at one point. I'm 34 now, but when I was a teen that was my struggle. Do I learn things, or not?

If you have a genuine interest, drive, and the free time and capacity to do so, then pursue any avenue of intellectual growth. Mind, body, and spirit are all important. Cultivate each one as delicately and diligently as you would a flower.

Anonymous

Anonymous Fri 02 Apr 2021 18:29:29 No.12916790 Report

Quoted By: >>12916837 >>12918044

>>12916749
I understand. Thank you for the motivation. I just downloaded a topology book. I'll start studying it this weekend.

Anonymous

Anonymous Fri 02 Apr 2021 18:42:36 No.12916837 Report

Quoted By: >>12918044

>>12916790
Now you got me wanting to delve into this field, because if you take the world we live in and begin to look at it in the way of turning a sphere inside out you begin to connect the dots and see reality for what it truly is.

Anonymous

Anonymous Fri 02 Apr 2021 19:19:16 No.12916937 Report

Quoted By:

Yes, topology is based.

Anonymous

Anonymous Fri 02 Apr 2021 20:09:25 No.12917166 Report

Quoted By:

>>12916640
I love topology, but it's a huge field. You'll probably have to start by studying lots of point set topology before you can dive into the more 'geometrical' stuff you're thinking about. Still, I think that point set topology is really interesting as well and is great for opening up your mind to properties abstract spaces can have (which will be useful once you get into more advanced stuff). Anyway, go for it, hope you'll enjoy it. Just be prepared for the material to probably be a bit different than what you expect right now.
If you haven't chosen a book yet, I really like Munkres, and it's a classic in the field.

Anonymous

Anonymous Fri 02 Apr 2021 23:41:18 No.12918044 Report

Quoted By:

>>12916790
Run don't walk somewhere if you're reading a "general" or point-set topology book. Milnor's topology from the differentiable viewpoint is good as a second book.

>>12916837
gay

Anonymous

Anonymous Sat 03 Apr 2021 01:03:55 No.12918394 Report

Quoted By:

You just need some basic set theory. A rigorous first course in Real Analysis is recommended though, but there's not many prerequisites for elemmentary topology other than mathematical maturity. If you're interested in algebraic topology you'll need some group theory and abstract algebra, and if you're interested in differential topology you should probably know some differential geometry and differentiable manifolds, but I don't know too much about this as it's usually a graduate course.

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