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entropy1
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Do you visualize equations abstracly when doing math?
Would you care to elaborate?BvU said:Yes and no
to the questionBvU said:Yes and no
is actually way better than it appears at first glance. What sounds ironic is indeed what takes place.entropy1 said:Do you visualize equations abstracly when doing math?
I visualize ##c^2=a^2+b^2-2ab\,\cos(\gamma)## but do not visualize ##\Gamma^°(\mathfrak{sl}(2,\mathbb{R})) \cong \operatorname{PSL}(2,\mathbb{R})\,.##entropy1 said:Would you care to elaborate?
Thanks ! You made my day ! (seriously)fresh_42 said:is actually way better than it appears at first glance
Well, I have some difficulty understanding formulas and equations because I can't imagine what they mean: I need a 'mental picture' and have some difficulty contructing it. Math costs me energy for that reason. So I was wondering if I am just doing something wrong or that mathematics is not the game for me... Also, I'm very curious how other people and mathematicians process mathBvU said:What did you have in mind when you posted your question ?
I visualise that you forgot a parenthesis in therefresh_42 said:but do not visualize ##\Gamma^°(\mathfrak{sl}(2,\mathbb{R}) \cong \operatorname{PSL}(2,\mathbb{R})\,.##
Wouldn't worry too much. It doesn't look as if you intend to be the one to solve grand unification or quantum gravity.entropy1 said:Well, I have some difficulty understanding formulas and equations because I can't imagine what they mean: I need a 'mental picture' and have some difficulty contructing it. Math costs me energy for that reason. So I was wondering if I am just doing something wrong or that mathematics is not the game for me... Also, I'm very curious how other people and mathematicians process math
BvU said:Wouldn't worry too much. It doesn't look as if you intend to be the one to solve grand unification or quantum gravity.
Try to find out what your ...
BvU said:Funny, I'm allergic and hypersensitive wrt printing errors, yet I missed that one ! Must have the same angle as @fresh_42
This is another good advice. Math doesn't equal math. The way of thinking and visualizing can be very different depending on the specific field. Here's a list of which I think does have different points of view and therewith different ways of anticipation:... strenghts [strengths ] and weaknesses are in the learning process: exploit the first as much as you can and challenge the latter now and then, just to see how it feels -- you don't have to master everything.
Lol. Karma is a ... (But to be honest, the spell checker underlined it, for otherwise I wouldn't had recognized it.)BvU said:strenghts [strengths ] -- put that one down to excitement: my 2 fingers (!) can't keep up
I should refine that: I can "see" the "workings" of variables in the equation like the ones in the nominator contributing to increasing growth and the ones in de denominator contributing to decreasing it, except if the values of the variables shrink under 1, in which case we have the reverse. I have difficulty imagining the effect in an equation of a square root because most of the time it contains a whole equation in itself. And I know the deravative of ex is itself so it grows proportionally to its own value, which is relatively easy to imagine. And so with a derivative, we have the speed of growth also.entropy1 said:Well, I have some difficulty understanding formulas and equations because I can't imagine what they mean: I need a 'mental picture' and have some difficulty contructing it. Math costs me energy for that reason. So I was wondering if I am just doing something wrong or that mathematics is not the game for me... Also, I'm very curious how other people and mathematicians process math
yes, and I do math daily. What helps me (visually oriented) enormously is grabbing a pencil and sketching partial dependencies. Nowadays taking excel and plotting a function is a piece of cake, so that's the next (emphasis: not the first) step.entropy1 said:some of you recognize this sort of thing
And I love chalk and a blackboard! Way better than a computer.BvU said:What helps me (visually oriented) enormously is grabbing a pencil and sketching partial dependencies.
Visualizing equations abstractly involves mentally breaking down the equation into its individual components and understanding how they relate to each other. This can involve creating mental images or using other visual aids to better understand the equation.
While it may not be necessary for everyone, visualizing equations abstractly can be a helpful tool for understanding and solving math problems. It can provide a deeper understanding of the concepts and relationships within the equation.
Yes, anyone can learn to visualize equations abstractly with practice and by using different techniques. Some people may naturally have a stronger ability to visualize, but it is a skill that can be developed and improved upon.
Yes, there are several benefits to visualizing equations abstractly. It can improve problem-solving skills, enhance understanding of mathematical concepts, and make complex equations easier to comprehend.
One way to improve your ability to visualize equations abstractly is to practice regularly. You can also try using different techniques, such as drawing diagrams or creating mental images, to see which works best for you. Additionally, seeking help from a tutor or teacher can also be beneficial in improving your visualization skills.