/sci/ - Science & Math

Forget about visualization, focus on the $300k starting

>>3084056
depends on the "higher levels" you're talking about

visualizations REALLY help with higher applied math like partial differential equations and shit

but it doesn't help one iota in real analysis

>mfw i try to visualize higher level maths

>>3084056

I'm majoring in applied mathematics and taking differential equations at the moment. We've yet to use any graphs and from the looks of it, we won't be referring to any. The last time I plotted any sort of graph was when I was doing triple integrals to get the volume of three dimensional objects.

>>3084075
I'm a pure math major, not an applied math..

Does that mean visualization will be less useful to me?

>>3084085
Is that a result of the inherent nature of the math, or a preference in the teaching methodology of your teacher?

>>3084089
Not necessarily. This is an assumption, but if pure mathematics is more centered around the developing or proving of new mathematical theories, then I'd imagine you'd need to use graphs often. You might not need to rely on them heavily, but to do the aforementioned it would be useful.

>>3084094
Good question. I think it's a little bit of both. We're focusing mainly on classifying the types of differential equations and understanding the methods by which to "solve" the equations. But, because I attend a university with a quarter system, professors condense a lot of the material, and although they don't admit it, I feel as if they leave out very crucial elements of the material. However, there is a division of differential equations dedicated to geometry.

To visualize things like real analysis you will need to take some psychedelics like LSD or DMT.

code word for future self: build C visualize this math graphical detail interesting thing figure it out understanding etc

>>3085112
yeah, how do you represent a compact set?

Higher math is using your imagination in a highly ordered and formal way.

You can visualise things if it helps you. The main thing is keeping track of subtle delicate properties.

Well you can visualise things in the sense of drawing a blob to represent the total space of a line bundle, and another blob to represent the base space, and a sort of arrow from one to the other taking a line in the total blob to a point in the base blob, representing the projection.

Basically you're interested in relationships between things in an orderly way respecting delicate rules.

In pure math the only "visualization" is diagrams to aid the imagination. There is virtually no use of actual graphs with accurate numerical properties.

>>3084085
in PDE in particular you will deal with engineering-type problems, where you can only "invent" the equations after drawing diagrams and shit

>>3084089
Depending on field, again. What classes are you planning on taking. I will say that I never needed visualizations for my upper levels (complex analysis, real analysis, algebraic structures, discrete math, number theory, combinatorics, etc.)

However, the little topology I studied on my own was made INFINITELY easier by drawing little sketches.

I don't know about you guys, but I visualise topics mathematics all the time.
Some more vividly than others - colours, shape, texture etc
Trying to describe them is like trying to describe a dream though - far too much information and the english language is simply insufficient.