Expert: Scott A Wilson - 5/13/2009

Question
A bit of background (with apologies for the length) - When I was younger I
was lucky (unlucky?) enough to have been tested for a very high IQ and was
placed in a school for "gifted" children. This was, in many ways, a wonderful
experience as we went on several class trips a month, were exposed to all
sorts of wonderful things, and our creativity was given free reign.
Unfortunately, the downside to this education was that there was very little to
no structure or discipline at all. So, for example, if math was being taught, if
you didn't feel like doing it, you were allowed to go off and do personal
projects (usually concerning the softer arts of language and history, etc.)
because it was assumed you understood it and were just "bored."

As you can imagine, this produced a very uneven education. Math was not
presented as the key to science or the language of the universe, it was simply
something tedious to be avoided. Now I am in my early 30s and have been
successful in the 'soft arts', but have always regretted my atrocious math
skills and have begun to seriously consider a radical career change into some
field of science or another that will, undoubtedly, have a deep understanding
of advanced mathematics as a pre-requisite.

So, my question is this: Assuming I know close to zero about even the most
basic math, and am willing to put in the time and energy to begin the long
process of getting myself to a point, hopefully, of advanced math
comprehension, if you were to look back and plot a sequential course
through the math disciplines, what general order might you suggest for
maximum understanding?

I ask because I understand that at advanced levels Math is much like a
language. I want to really be able to hopefully understand it hopefully, to be
comfortable with its underlying concepts and how values interact so I can
actually use them rather than slavishly regurgitating formulas that I don't
truly understand.

I hope this made sense, and any help or advice you can give would be very
much appreciated.

Answer
I forgot to attach that note with the math tables on it, so I guess I'll paste them in here, though it might be hard to read them.
Just remember each row and then count through the row questions.
Like is you get 4 * 7, look at multiply.  One the 4 row, you can count 7 numbers.  That is 4, 8, 12, 16, 20, 24, 28 as 1, 2, 3, 4, 5, 6, 7.  On the 7 row, you can count 4 numbers.  7, 14, 21, 28.
As can be seen, 4*7 = 28.  Note that the first number in each row is which row it is.  In the multiplication table, you then get *1, *2, *3, *4, *5, *6, *7, *8, *9, and *19.  The * is for 'times'.

addition   1   2   3   4   5   6   7   8   9   10
1   2   3   4   5   6   7   8   9   10   11
2   3   4   5   6   7   8   9   10   11   12
3   4   5   6   7   8   9   10   11   12   13
4   5   6   7   8   9   10   11   12   13   14
5   6   7   8   9   10   11   12   13   14   15
6   7   8   9   10   11   12   13   14   15   16
7   8   9   10   11   12   13   14   15   16   17
8   9   10   11   12   13   14   15   16   17   18
9   10   11   12   13   14   15   16   17   18   19
10   11   12   13   14   15   16   17   18   19   20
                             
subtraction   1   2   3   4   5   6   7   8   9   10
1   0   1   2   3   4   5   6   7   8   9
2   -1   0   1   2   3   4   5   6   7   8
3   -2   -1   0   1   2   3   4   5   6   7
4   -3   -2   -1   0   1   2   3   4   5   6
5   -4   -3   -2   -1   0   1   2   3   4   5
6   -5   -4   -3   -2   -1   0   1   2   3   4
7   -6   -5   -4   -3   -2   -1   0   1   2   3
8   -7   -6   -5   -4   -3   -2   -1   0   1   2
9   -8   -7   -6   -5   -4   -3   -2   -1   0   1
10   -9   -8   -7   -6   -5   -4   -3   -2   -1   0
                             
multiply   1   2   3   4   5   6   7   8   9   10
1   1   2   3   4   5   6   7   8   9   10
2   2   4   6   8   10   12   14   16   18   20
3   3   6   9   12   15   18   21   24   27   30
4   4   8   12   16   20   24   28   32   36   40
5   5   10   15   20   25   30   35   40   45   50
6   6   12   18   24   30   36   42   48   54   60
7   7   14   21   28   35   42   49   56   63   70
8   8   16   24   32   40   48   56   64   72   80
9   9   18   27   36   45   54   63   72   81   90
10   10   20   30   40   50   60   70   80   90   100

Next time you right, remind me you need them and I'll attach them as a special file.