Expert: Scott A Wilson - 1/4/2011

Question
Hi there!

So I've completed my high school mathematics. I've done equation after equation, most pertaining to nothing and mindlessly fed to me in an attempt to add a subject and grade to my report. I had to learn for myself what the practicalities of each concept behind the equations were.

And I'm a practical kind of guy. Recently my interest in math has been inexplicably been sparked, and I like to grab a hold of these inspirations and milk them until I get my fill. The problem is this: I've never been taught or taught about higher level math, and I can't seem to find what you can actually do with the extra knowledge that comes from pursuing higher maths.

So in essence, this is less of a math question than a question about math. The question is this: "What extra practical skills would I gain from teaching myself math beyond the 12th grade level?"

I'm tired of algebraic word problems and nested theories relating to nothing resembling everyday life. On the other hand, I can't find any resource that actually informs me about what you can do with higher maths. I hear of experts compiling such complex things as human behavior and deriving quantum particle interactions , not to mention predict subtle patterns everywhere and in every field known to man. It just doesn't 'add up' and doesn't seem possible with the flimsy 'math' I've been taught so far.

Thank you for your time, and sorry for throwing you such a curve ball.

Answer
After the basics of algebra, geometry, and trig, there is a whole lot more math.

For example, given a line, find the slope, and that is the derivive.
If f(x) = x², then the derivative { or slope } is written as f'(x) = 2x.
To clarify things, "f'(x)" is "f prime of x".

The second derivative is f"(x), and is "f double prime of x".

There is also the area underneath curves, and that is known as the integral.

These are both used in engineering to calculate the stress on sidewalks, streets, wheels, floors, multi-level builds, foundations, etc.

Almost every profession there is uses mathematics.

For example, at the store, the revenue for an item is the number sold times the price.

For cars, the mph is the expected number of miles divided by the number of gallons, and this is mpg.  This value can be used when a long trip is taken to determine if gas is needed.  Nowadays, however, gas stations aren't too far apart.  In Eastern Oregon, I did see a sign that said, "Warning: next gas station over 100 miles away".


For music, there are usually 3 or 4 beats per measure.  The number of beats is whole notes, half notes, quarter notes, sixteenth notes, and sometimes triplets, which are used to divide any of these into three notes.  Usually half notes and quarter notes are divided into triplets, so we get 6 or 12 beats to the measure if the time is 4 4.  The first 4 is for how many beats and the second 4 is for quarter notes.  If the times was 3 2, that would mean there were 3 half notes per measure.

For planes, the amount of lift from an airplane wing needs to be calculated to determine how big of a wing to use and the weight restrictions placed on the airplane.  For elevators, the size of the motor determines the maximum occupancy of the elevator, though for most elevators it is greater than the number of people that can fit.

For planes approaching the speed of sound, there are shock waves and rarefaction fans developed from the airplane wings.  A rarefaction fan is the opposite of a shock wave.  A shock wave occurs when, mathematically, there should be more air in on space that is possible.  A rarefaction fan occurs when the air should be a vaccuum.  Due to air pressure, this is quickly filled in.

For noisy engines, the sound needs to be below a certain level.  The distance from the object is inversely proportional to the amount of sound it generates.

In constructing the Golden Gate Bridge in San Francisco, the shape of the wires was calculated and then the tension required was done.

For doctors, the cc's in shot depend on a person's weight and what area is to be affected.
Doctors also need to know how many liters of blood to hook up to someone depending on a few factors, and I think the main one is the person's weight.

For bankers, the interest has mathematical formulas.

For investors, the value of a product will decrease (in most cases) over time.
This equation needs to be known.

Most people don't even realize they're using math and do it by trial and error.
However, for big jobs, the amount of force, speed, friction, weight, gas, or other data is very important and relies on the equations to be known.

For electrical people, they need to determine how much to charge on electricity to meet the expenses.


Now most jobs don't seem like they use much math, but for really great jobs,
a lot of math is needed on occasion.  Nowadays, most people can use a calculator.