Solving problems the hard way

Date: Mon, 21 Nov 1994 09:18:13 -0800 (PST) 
From: Winnie Fan

Hello,

     My name is Winnie Fan.  I have been writing various questions to 
Dr. Math.  It is very nice for you guys to answer me back right on the 
next day.  I was just wondering what other math classes are there after 
calculus because I have a great interest in Math, maybe I'll major in 
Math in my college.  

     In my math class the biggest problem for me right now is that when my 
teacher gives me a problem, I will end up using the harder way to solve it
instead of the easy way.  Some people can quickly tell what method to 
use will make the problem a lot easier.  Sometimes the problem may be 
so simple that because of my method of using the hard way, I end up not 
able to solve it.  I need help Dr. Math!!  

                                                        Winnie Fan

Date: Mon, 21 Nov 1994 13:44:29 -0500
From: Dr. Math

Hi Winnie!

        I'm Vanessa, one of the math doctors here. That's great that you're
so interested in taking more math in college. There are endless
possiblilities for math after calculus. You can basically take a class in
any area of math that interested you in high school, just on a much more
comprehensive level. For example, there are a lot of theory classes that
spend a lot of time proving properties of the real numbers that you had
previously taken for granted. There are also a lot of computer applications
of math, and programs designed to solve different systems, which might
interest you if you like computers. 

     This brings me to another point, which is that the great thing about math 
is that so much of all of the natural and social sciences is mathematically 
based. A LOT of economics is based on derivatives, and slopes of functions. 
You also might find that you are interested in statistics. I am taking a class 
in it right now and find it really interesting because of all the different 
experiments that are done and the ability to predict an outcome based on a 
mathematical model. 

     Or maybe you're interested in biology, physics, chemistry, computer 
science, statistics, economics, accounting, or many other subjects that are
mathematically based on some level. A strong mathematical background will
help you in any of these areas.

     Now to answer your other question about always taking the hard way
on problems. That's another great thing about math. There usually is never
just one right way to attack a problem. There are usually several methods
that will bring you to the correct solution. So I guess the best advice
that I have for you is to do a lot of practice problems. After you do a
bunch of the same type of problem, you will begin to recognize which
problems can be done "the easy way" and which will require a little more
intuition or maybe even "the hard way"!

     I hope this helps and please feel free to write back with any more
questions that you may have.

-Vanessa, M.D.