Math Major: Is There a Way Around Difficult Visualization?

[sumrandomdude]

Math has pretty much always come easy to me, but I find Calc III very hard. I just can't visualize things. It has me really worried that perhaps a math major might be too difficult for me. I just want to know if there is any part of math where I wouldn't have to deal so much with visualizing things in three dimensions.

 

[Klockan3]

Many math majors sucks at visualizing things which is sad imo. You should be just fine.

 

[sumrandomdude]

Many math majors sucks at visualizing things which is sad imo. You should be just fine.

Wow. That actually made me feel better lol.

 

[VeeEight]

Pretty much everything you do in first and second year calculus you will rigorously go over later on in real & complex analysis and other courses, so your understanding of the material will get deeper as you develop more tools.

 

[arunma]

When I was doing a math major, multivariable calc was actually my easiest class. But most of the upper level math classes were more difficult for me. Maybe that means that if you're good at one, you're bad at the other (or something like that).

Seriously though, I don't remember anything in math requiring this level of spatial reasoning after calc 3. It's basically just proofs and stuff. In fact I never touched multivariable calc again, except in my upper level physics classes.

 

[Anonymous217]

I feel like being forced to visualize everything is actually harmful to me because whenever we start doing Calculus in n>3 dimensions, you have to do it without a visual (excluding level sets for n=4 and etc. obviously). I'm very similar to you because I did absolutely horrible on my first planes/lines/points in 3d with dot/cross product-quiz, but I did much better on my partial derivative midterm.

 

[Tedjn]

Many math majors sucks at visualizing things which is sad imo. You should be just fine.

I'm a math major who sucks at visualizing things. Forge onwards!

 

[ronaldoshaky]

man why do i feel like this when I study quantum physics. like what the hell is the square of the orbital angular momentum anyway...how do you visualise it.

 

[Mathnomalous]

Hey, OP, if it helps, I completed remedial Math classes (haven't even taken Calculus yet) and I intend to major in Math, probably because it will be difficult. I have no idea what people mean by "visualizing"; is it similar to imagining 3³ forms a perfect cube?

 

[VeeEight]

I have no idea what people mean by "visualizing"; is it similar to imagining 3³ forms a perfect cube?

I believe what he meant by 'visualizing' are things like surface integrals, the Laplace operator, eigenspaces, smooth manifolds, and things like that, which are studied analytically and have interesting geometric properties (and applications to things like quantum mechanics, as was mentioned before)

 

[Mathnomalous]

I believe what he meant by 'visualizing' are things like surface integrals, the Laplace operator, eigenspaces, smooth manifolds, and things like that, which are studied analytically and have interesting geometric properties (and applications to things like quantum mechanics, as was mentioned before)

Ah thanks! These sound like things I will learn later on. No need to worry about it now.

 

[VeeEight]

No problem. And it's not just complicated things that require a lot of development that have interesting geometric properties. Take a look at something like the sum of the first consecutive odd integers. Fun things like that are accessible to anyone and can give you a taste of some subtle visual aspects.

 

[sumrandomdude]

When I was doing a math major, multivariable calc was actually my easiest class. But most of the upper level math classes were more difficult for me. Maybe that means that if you're good at one, you're bad at the other (or something like that).

Seriously though, I don't remember anything in math requiring this level of spatial reasoning after calc 3. It's basically just proofs and stuff. In fact I never touched multivariable calc again, except in my upper level physics classes.

So just to make it clear, Calc 3 is the only math class that requires a ton of visualization?

By the way, I'm planning to go into a field that's called "Discrete and Algorithmic Methods."

 

[VeeEight]

So just to make it clear, Calc 3 is the only math class that requires a ton of visualization?

Not at all. Most fields of math require some visualization, whether it be algebraic geometry, topology, complex analysis, or functional analysis. The point is that you will have more tools to use to develop the theory, and the visual aspects become more clear as you get a rigorous understanding of the material.