To test your LaTeX skills, please try the following tasks. You should be able to use the ALPHA editor to prepare your files, and OZTEX to process them.
1) Create a document containing two paragraphs of text. using italic and boldface fonts for a few words. Process the document through OZTEX and then view the DVI file.
2) In your document, add a paragraph that includes a list. The list may be unordered, numbered, or a description list. Here is an example:
Voronoi tessellations, which are the topic of one of the REU projects,
are also known as:
* Thiessen polygons, for geographers;
* Dirichlet tiles;
* Meijering regions, for crystallographers.
They have been "reinvented" many times.
3) Write a paragraph that uses math symbols and formulas, both as part of the text, and as separate, displayed math. For example:
An identity is a statement that is true for any angle theta, such as
sin^2(theta) + cos^2(theta) = 1
whereas, in most cases, an equation which we may symbolize as
f(theta)=0 is only true for a few selected values of theta. For
instance, the equation
tan(alpha) = 1
is only true for special alpha values
alpha = pi/4, 5pi/4, ...
(You should try to get a real Greek theta and alpha, of course!)
4) Figure out how to typeset the following (meaningless) formula:
sqrt ( x^12 + 1 )
-------------------- = Integral ( from -12 to lambda+1 ) tan(x) dx
y + y
1 23
Again, use a real lambda! Try to put space between tan(x) and
dx. And try to make the tan in tan(x) come out
in a proper font.
5) Set up the following table:
-------------------------------------------------------
| Angle | Degrees | Cosine | Comment
-------------------------------------------------------
| | o | |
| 0 | 0 | 1.0 | Looks like 3 o'clock.
-------------------------------------------------------
| | o | |
| pi/4 | 45 | sqrt(2)/2 | The sine is the same.
-------------------------------------------------------
| | o | |
| pi | 90 | 0.0 | Noon.
-------------------------------------------------------
6) Use MATLAB to create a graph of
y = sin ( ( x - 1 ) * ( x - 3 ) )
from 0 <= x <= 6. Save the graph as an EPS file, and then include
it in your document using a FIGURE.
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