I'm a self-learner trying to learn Math while enrolled in a wrong major (Humanities). I have gone through the many amazing questions and answers here (& elsewhere, including Prof. Tao's blogs) about learning mathematics. However, I face one problem :

When reading and learning, I make it a point not to treat math like a "spectator sport" and make sure that I am simultaneously proving the theorems, solving examples and so on. I seem to do very well in that frame of time. I understand, I am able to extend concepts and am able to predict ideas that will follow and solve the examples given at the end of the chapter. I also make it a point to see the "big picture" rather than get caught in details, especially with proofs. I keep notes and mindmaps to review the material on a later day.

However, if because of my course load (of the wrong major) I am unable to concentrate of my math for some time, when I return back a few weeks later (2-3 weeks at most), I seem to have lost it all. I only remember bits and parts of what happened and seem to have lost the big pictures and the intuition. Reviewing my mindmaps or notes doesn't help either, it again helps me temporarily to "have information" rather than knowledge. It's not my memory that's a problem, I feel I am not doing something right w.r.t. learning math on my own.

Can someone tell me what it is that I'm doing wrong?

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    $\begingroup$ I suppose this will likely be closed. But, personally I think you are taking the wrong approach with memory maps and mind maps. Most of the ideas you are learning are so low level that you just need to practice. It would be like having memory maps of the alphabet. $\endgroup$ – simplicity May 8 '12 at 8:42
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    $\begingroup$ Personally, you get to a stage where the things before you are so trivial that you don't need to remember them. Certainly, all of calculus is trivial and I can do it even without thinking. At a certain point everything becomes super hard and you might be forced to think outside the box. But, personally upto say a first course in Topology everything is trivial and you should just be practing your skills. $\endgroup$ – simplicity May 8 '12 at 8:44
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    $\begingroup$ @simplicity - "all of calculus is trivial" really ? :O $\endgroup$ – Belgi May 8 '12 at 9:12
  • $\begingroup$ Not really a mathematical question. $\endgroup$ – lhf May 8 '12 at 11:16
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    $\begingroup$ @Self_Learner: Why don't you change your major? That's what I did. I only started majoring in maths in my third year. $\endgroup$ – Tara B May 8 '12 at 11:19

In my opinion, you have answered your own question when you stated:

I also make it a point to see the "big picture" rather than get caught in details, especially with proofs.

Good mathematical intuition is the result of hands-on practice, not its substitute. Yes, you must also keep the big picture in mind, but if you really want to learn this stuff, you have to get your hands dirty. Especially with proofs.

(I also agree with @skullpatrol's answer.)

  • $\begingroup$ So, what you are suggesting is that I keep practicing? Like, till it becomes a second nature? (I believe @skullpatrol is stating something similar as well) $\endgroup$ – Self_Learner May 8 '12 at 14:41
  • $\begingroup$ Close. I'm suggesting that you let/force yourself get caught in details, instead of only trying to see the "big picture". $\endgroup$ – JeffE May 8 '12 at 14:56
  • $\begingroup$ I'll try this out. $\endgroup$ – Self_Learner May 8 '12 at 15:02

In my opinion, you have answered your own question when you stated:

" I am unable to concentrate of my math for some time, when I return back a few weeks later (2-3 weeks at most) I seem to have lost it all. "

Simply don't not concentrate on math for that long. Do some sort of review daily.

  • $\begingroup$ I wish I could but it's just not possible. Some times, there are essays I need to write which take my complete attention and time. Also, I don't have an issue remembering the history I learnt (without any interest) 8 weeks ago but I can't remember the Math I read (with interest and focus) 2 weeks ago. $\endgroup$ – Self_Learner May 8 '12 at 12:27
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    $\begingroup$ @Self_Learner You have to find a way to make it possible. Any sort of quick review must necessarily be done at least twice a day and everyday until the math "sticks." $\endgroup$ – skullpatrol May 8 '12 at 12:59
  • $\begingroup$ @skullpatrol Thanks! $\endgroup$ – Bill Dubuque Jan 17 '14 at 2:37
  • $\begingroup$ @BillDubuque thank you for returning. $\endgroup$ – skullpatrol Jan 17 '14 at 9:59

Learning math is like learning anything else. It is most effectively done with daily time set aside for the task. Promise yourself 20 minutes per day on task.

Try to give yourself a set of mental exercises that you can do while involved in mundane activities. For example, I am trying to improve my arithmetic skills. In particular, i would like to be able to effortlessly multiply 2 digit numbers mentally. To do so, I need to create a database of particular products, know all the squares from 1-100, know all the products of successors x(x+1), and be able to subtract. When I swim, as I count my laps, I compute the squares and successors. When I walk, I do some sequential subtraction problems. I also do routine calculations when washing dishes, showering, and doing my toilet. Such methods depend on a short-term memory, and develop long-term memories. To be honest, I can't do the multiplication trick yet. I anticipate it will take a few more years to develop.

But if you are trying to learn calculus, then compute derivatives as you walk. If you are trying to learn linear algebra, then imagine intersections among planes as you shower. If you are trying to learn group theory, try listing the symmetries of a polygon as you go to sleep. Avoid visual mathematical calculations while driving!


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