Re: I am slow in math... how do I improve my speed?
- From: quasi <quasi@xxxxxxxx>
- Date: Mon, 25 Jul 2005 20:47:49 -0700
On Mon, 25 Jul 2005 16:38:04 -0700, "Jane" <lunaliu3@xxxxxxxxx> wrote:
>I am not satisfied at my speed in computing and thinking math.
>
>My current status is above average.
>
>But in order to succeed in some exams and in future career, I want to be
>faster.
My recommendation:
Go for depth (true understanding) and breadth (a wide range of
applicable math areas) over speed.
>For instance, we really need to practice and solve problems in order to
>learn math well. I have seen some students worked out all the problems from
>the textbook and still have energy and time to search for other
>resources/problems from Internet or other books to work out. (graduate class
>levels)... No need to mention that they are always star students and very
>genious in research and career also.
No need to compare yourself based on speed. Agreed in the real world
there are always time constraints, so you can't be too slow, but
assuming reasonable speed, what counts more is quality.
In your studies you will gain certain insights, and the complete
collection of these insights you can view as uniquely yours.
Have pride in your uniqueness -- uniqueness can trump speed.
>I think "doing math fast" and "thinking math" fast are of the fundamental
>importance to success.
I disagree -- not if such speed is just rote memorization followed by
mechanical implementation.
>My slowness rooted in from the Calculus I, II, III. So I plan to review from
>Calculus I, II, III and do as many as possible advanced engineering problems
>at the level of math undergraduate and first year graduate level . This
>needs huge amount of time, but once this is accomplished, and once the tools
>are sharpened, there won't be any obstacle in my future research and career.
>I think I need focus myself for about 100 problems daily, but currently my
>time commitment can only allow me do 30 problems daily. That's bad. Again
>this is because slowness in speed. My mind really needs sharpened. Sometimes
>if I go fast, the correct ratio will go down.
Don't burn yourself out. Instead, try to categorize the different
strategies, and put the effort into recognizing which is likely to
apply to a given problem and why.
Then go through the problems testing yourself on recognizing the type
of problem and the appropriate method of solution, but don't actually
do the problem. That saves lots of time! Of course, you do have to do
a few of each type just to convince yourself that you could do it if
you really had to.
>I am wondering if this is the most efficient and productive approach.... Can
>anybody suggest a systematical/scientific approach of improving math speed?
>Can anybody suggest good problems that can help?
Look ahead at the courses you plan to take to see what math is
actually used, and let that guide your review. Then carefully select
textbooks in each of those areas and review / self study the parts you
feel are key.
> Working on non-meaningful problems will be simply wasting time...
yep
>My final goal is to review all the undergraduate math and first a few years
>of graduate maths and finally have a unified knowledge of all these maths in
>my mind, since I am currently at the initial stage of my graduate school.
>
>Thanks a lot!
>
Your strong desire to really learn and your willingness to work hard
to achieve your goals are admirable, but it's important to work smart,
not just hard (which I guess is the point of your query).
quasi
.
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