**MATH CALCULATIONS IN MASTERINGASTRONOMY**

Generally, every weekly homework assignment
will have one or two problems, each of which involves a calculation or a series
of calculations. Since there are 20 questions per assignment and each question
is weighted the same, problems involving calculations may represent as much as
10% of the maximum points possible for a given assignment. Obviously, one could
skip the math-based problems and still pass the course. However, every semester
we have a significant number of students who finish the course just short of a
higher grade by a few points. The difference could be those skipped math
problems! So if you would like to increase your chances for receiving a higher
grade or simply like solving problems that involve math, here are some tips for
finding those correct answers.

** You
Can Do Math** – When it
comes to problems involving math, many students will state “I am no good at
math” or something of a similar tone. For this astronomy course, we very rarely
find this statement to be true. The reason is simple. The math in this course
involves no more than basic skills in arithmetic and elementary algebra –
skills that the vast majority of people use in their everyday lives without
realizing it. So the first thing you need to do (if you have not done so
already) is to stop saying, “I can’t do math”.

** Formulas** – The real issue with doing assignment
questions involving calculations (where student frustration is at its highest)
is with determining which formula to use (if it is not given in the actual
question). There is no magic cure for deciding which formula to use for a given
situation. It basically takes listening to your instructor during lecture, reading
your text, and comprehending the situation at hand. However, we can still offer
you a few hints: 1) Look through the chapter that corresponds to your homework
and see if the “Cosmic Calculation” parallels your assignment question; 2) A
significant number of calculations involve a “rate equation” (e.g., distance =
speed x time, where speed is the rate in this case);
3) Look for common themes to previous assignments (e.g., the inverse square law
implicitly, if not explicitly, appears throughout the text); and 4) Take a look
at Appendix B – “Useful Formulas”.

** Data** – Once you have a formula, usually you will
have one unknown (which is what you will be solving for) and you will need to
plug in numbers for the other variables. Often the problem itself will tell you
what these numbers are. However, you will not necessarily be given everything
up front; you will be expected to look for “standard” data in a table or
similar arrangement.

** Powers
of 10 and Units** – Once
you have your formula and your numbers, you cannot simply plug in and
calculate. You need to be sure that you have everything in compatible units and
if not, you will need to convert accordingly. Also, you can save yourself a lot
of grief if (under certain circumstances) you work with numbers expressed in
powers of ten (or scientific notation). You are expected to know how to do all
this. However, if your skills in these topics are a bit rusty, consult Appendix
C, “A Few Mathematical Skills”, for an excellent review.

** Significant Digits** – More often than not, your calculations
will not end in “nice” numbers (e.g., an integer like 2). When this occurs, it
is only natural to ask how many digits should be reported. From a scientific
point of view, the number of digits to report is determined by the precision of
the data being used and the mathematical operations being employed (e.g., see http://members.aol.com/profchm/sig_fig.html
or http://en.wikipedia.org/wiki/Significant_Digits).
However, you will not need to know all these details for reporting your
calculations. Instead, use one of the following two “rules” depending on
whether or not

__No Statement of Desired Significant Digits__: Use 5 significant digits in all calculations and report your answers to five significant digits.__Stated Significant Digits__: Use 5 significant digits in all calculations and report your answers in the number of significant digits requested.

** Making
Sense and Getting Help** –
Once you obtain an answer, always ask yourself if the answer makes sense. For
example, one way to do this is to go back to your formula and replace the
values of the variables with values that are expressed in scientific notation
with only one significant digit. You should then be able to do the calculation
on a piece of paper and get an order-of-magnitude answer to compare to the
value you obtained from a calculator. If they are not in the same ballpark,
this is a sign that you need to check your math (both on the calculator and on
the paper). Another way to test an answer is by using common sense. If you are
asked to determine the mass of a fictitious planet orbiting our Sun and you end
up deriving a mass 10 times more massive than the Sun, then you probably made
an error somewhere.

Finally, the Sierra College Tutoring Centers,
located in the LRC of both the Rocklin and Grass Valley campuses (also http://www.sierracollege.edu/StudentServices/tutorTesting/index.html),
are a valuable resource for obtaining help with math and science homework.
Also, your instructor is very willing to help outside of class – all you need
to do is ask.