How do you know if one is good at abstract thinking?

[thrill3rnit3]

How do you know if one is good at abstract thinking? I'm self evaluating myself if I can do pure maths in college, so any advice would be appreciated.

 

[symbolipoint]

Letting yourself act in a trail of interests can influence how abstractly you learn to think. Can you foresee a sequence of interests which if you study and perform them might move your activities and thoughts into Mathematics? What do you currently like to do or think about?

 

[symbolipoint]

Maybe I misunderstood your question. What I tried to help you accept is that you CAN DEVELOP ABSTRACT THINKING based on your interests and activities.

 

[TMFKAN64]

I was thinking about asking for an example of how to do this, but I decided that it would be counter-productive.

 

[symbolipoint]

I was thinking about asking for an example of how to do this, but I decided that it would be counter-productive.

Find topics that you want to learn about and find skills which you want to learn to do; then READ and THINK. If some things to practice are presented, then PRACTICE them. That is just very general. If you want more specific suggestions, this is difficult, since we do not know what your interests and your favorite instruction-related activities are. Since you placed an emphasis on Mathematics, you should involve yourself with something or things which can lead you to Mathematics. Try learning music, enroll in science courses (specific ones, not just unspecified "Science"), learn a computer programming language, study Algebra and some important forms of Geometry (like "College Preparatory Geometry", and Trigonometry), learn photography. Some of this you can start before entering college; and all of it you can start or continue when you are enrolled in college.

Most of what I listed relies on abstract thinking. You may need to put in a great effort for many of them, but becoming a more abstract thinker relies on your putting in this effort. Mathematics is probably one of the more abstract subjects mentioned there. I'd say many people stop their efforts at their mathematical development because they do not put in the patient effort to deal with the abstractness of the topics; not because they cannot think abstractly.

 

[TMFKAN64]

OK, I guess I was just being too abstract there... :-)

 

[Choppy]

If you enjoy 'abstract' thinking and the courses in mathematics that you've taken up until now, those are positive indicators. Another one is that you specifically seek out new ideas in the field - you read outside of assigned work and work on problems that you take a personal interest in.

Ultimately the only way to really know is to jump in and see what the water's like.

 

[qspeechc]

Just keep working as hard as you can and you will develop the skills at abstract thiking. These skills are acquired and you are not born with them.

 

[thrill3rnit3]

I guess my question should be "what exactly is abstract thinking"? I mean in mathematical terms.

All I've been reading about is that mathematicians mainly deal with abstractions, and so therefore should be good in abstraction.

On the side note, are those IQ tests good indicators if one can think abstractly or not?

 

[union68]

Do you like math? Do you have initiative? Do you have good self-discipline?

If yes, yes, and yes...then that's all you need. Quit trying to over-analyze it.

 

[Sankaku]

How do you know if one is good at abstract thinking? I'm self evaluating myself if I can do pure maths in college, so any advice would be appreciated.

Motivation.

If you are reasonably intelligent, anything can be achieved with enough willpower. Brains do not get you through university, motivation does.

 

[thrill3rnit3]

OK, let's get back to topic. What is abstract thinking in math? I've never really bothered to look up that question, I'm just doing my math sequences without worrying if I can abstractly think or not (until now, that is).

 

[union68]

I was on topic.

I'm just doing my math sequences without worrying if I can abstractly think or not.

Keep doing this. Worry about the subject matter.

Don't believe the pure math elitists when they gush over all that other pretentious stuff...they'll make you think that you have to be the next Euler to succeed in math.

 

[Bourbaki1123]

Go with what interests you and see how far you can go. If you want to do pure math and you are passing your math classes with decent grades or think that you could if you put in more effort, you will probably do fine. If you enjoy the subject and like to learn outside of class you will do at least as well as the average math major ( there are a few exceptions; I know a guy who has a very slim aptitude for math but has been pursuing a computer science degree for 6 years grinding through the prerequisite math and constantly repeating classes, but that seems to be pretty rare).

If you find that you have to keep repeating math classes in order to pass them in college, math might not be right for you, otherwise just persevere.

 

[Gasparri]

How do you know if one is good at abstract thinking? I'm self evaluating myself if I can do pure maths in college, so any advice would be appreciated.

Well, I would not advise you to do what I did, or rather get did to me.
There was a unfortunate accident with a tractor at 6. I got clobbered
in the head and all the thoughts in my brain fell off the shelves
and broke. Gluing all the pieces back together has not been easy
or fully successful. Perhaps the rewiring cause my abstraction abilities.
And precluded others.

I think if you enjoy sunrises, beauty of the land, and what makes things
work you will do just fine because all of those things are abstract and
if you find a way to communicate them you will become a master
of the art of abstractions.