Math 300 (Blok) Writing Assignment 3
Fall 2003
Use TeX to type two or more of your favorite results from mathematics, statistics or computer science that contain a good number of mathematical symbols. Type them out as they might be stated in a book.
Find a computer that has some version of TeX; for example PC TeX on PCs, OzTeX on Macs. Create your file in a simple editor, such as Notepad or Simpletext. Save your file as <filename>.tex. Typeset the file; this will produce a file called <filename>.dvi. You can view the .dvi file, and print it once you are satisfied with the result.
Due in class: October 15. Write your name on the output.
The TeX source file for ÔIn Class Writing Exercise 2Õ was:
%source file for inclass writing exercise 10/7/2003
\documentclass[12pt]{article}
\def\blank{\quad\rule{2cm}{.1mm}\quad}
\pagestyle{empty}
\begin{document}
\noindent
{\sc Math 300 (Blok) \hfill In Class Writing 2 \hfill Fall 2003}
\bigskip
\noindent
{\sc Connecting phrases:}
\smallskip
In each of the following examples fill in the blanks with a
connecting word. Examples of words that can be used are: and,
but, therefore, so, since, hence, although, however, despite this,
because, then; this list is not exhaustive. Add commas as
necessary.
\begin{enumerate}
\item It was raining \blank I didn't go biking.
\item I went to the baseball game \blank I ate a hot dog.
\item \blank the sum of the angles of a convex pentagon is
540 degrees, each angle of a regular pentagon measures 108
degrees.
\item The geometric series
$\sum_{n=1}^\infty r^n$ converges \blank $|r| < 1$.
\item The terms of the harmonic series tend to 0 \blank
the harmonic series diverges.
\item The terms of the geometric series $$\sum_{n=1}^\infty
(\frac{1}{2})^n$$ tend to 0
\blank this series converges.
\item Euler proved $\sum_{n=1}^\infty \frac{1}{n^2} =
\frac{\pi^2}{6}$ \blank $\sum_{n=1}^{500} \frac{1}{n^2}
\leq\frac{\pi^2}{6}$.
\item $\sum_{n=1}^\infty \frac{1}{n^2} < 1.7$ \blank
$\sum_{n=1}^\infty \frac{1}{n^3}$ is between 1.202 and 1.203.
\item The series $\sum_{n=1}^\infty \frac{1}{n^3}$ converges. Its
sum, \blank is not known.
\item The sum of the volumes of the blocks in the Deluxe set is less
than 1.5 ft$^3$ \blank the blocks won't fit in a box with dimensions
1.5 ft $\times$ 1 ft $\times$ 1 ft.
\item For every integer $n \geq 2$ the rectangle with vertices $n-1$,
$n$, and $\frac{1}{n^3}$ is contained in the region bounded by the
the $x$-axis, the line $x = 1$ and the graph of $f(x) =
\frac{1}{x^3}$. The rectangles are disjoint
\blank
$$\int_1^\infty \frac{1}{x^3} dx \geq \frac{1}{2^3} + \frac{1}{3^3} +
\frac{1}{4^3} + \ldots.$$
\end{enumerate}
\end{document}