Exmple: Mathematics as Language
The following section is an excerpt from the example laboratory report,
titled Proper Inflation of a Basketball. (The entire example report
is available in either Microsoft
Word Format for printing, or HTML
format for online viewing.)
It is important to realize that the number of strokes needed to properly
inflate the basketball is valid only for the particular pump that we have
used. The important quantity is the pressure of the air that is in the
ball. Fortunately, we can use the ideal gas law to determine the pressure
in the ball from our measurements. The ideal gas law states that (Serway,
1997, p. 542)
|
 |
(2) |
where P is the pressure of an amount of gas, V is the volume
the gas occupies, n is the number of molecules in this amount of
gas, T is the temperature of the gas, and k is Boltzmann's
constant. In SI units, k = 1.38 ´
10- 23 J/K (Serway, 1997,
p. 542). In this equation, the temperature is measured on the absolute
scale of degrees Kelvin or K.
When we use a pump to inflate a basketball, we take a fixed number of
air molecules, n, initially at room temperature and pressure, and
squeeze them into a smaller volume. Although the process of compressing
the gas heats it, it quickly looses this heat and returns to room temperature.
Since n and T in Equation (2) are constants, we can rewrite
this equation as
|
 |
(3) |
where the subscripts "1" and "2" refer to the initial and final conditions
of the gas. Here, the initial pressure of the gas is atmospheric pressure
at room temperature, Patm. The initial volume of the
gas is the volume of the basketball, Vball, and N
times the volume of the pump, Vpump. Recall that N
is the number of strokes of the pump we used to inflate the ball.
Note what's here:
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Every equation is part of a sentence. No equation appears without an extensive
explanation. A sentence such as "The equation we used was..." is not sufficient--explain
what the equation means!
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Each variable is identified the first time it is used.
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Equations broken out from the text are numbered. Thereafter, they are referred
to by number. In-line equations are not numbered.
Note what's missing:
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Equations on a separate page. Every equation must appear as part of the
text. They are not figures, tables, appendices, or any other part of the
document.
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One equation after another. There are words--lots of words--to explain
every equation and every step.
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Non-standard notation. Do not use "*" for multiplication, SQRT(...) for
the square root, etc. in equations in your reports.