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_region_.tex
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_region_.tex
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\message{ !name(lesson1.tex)}% LESSON ONE
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% Text following a percentage sign (%) is ignored by the typesetter.
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% In this manual, we will use such text for comments and notes.
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% You do not need to type out these comments.
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\documentclass{amsart}
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% Almost all commands start with a backslash (\).
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% amsart is short for American Mathematical Society article.
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\thispagestyle{empty}
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%We use this to prevent a page number from appearing.
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\begin{document}
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\message{ !name(lesson1.tex) !offset(-3) }
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\begin{center}
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\textbf{Lesson One: The Basics}
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\end{center}
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\textbf{Font Families}
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% One or more blank lines end a paragraph and put the typesetter on a new line.
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I \textbf{love} math!
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\LaTeX\ does \emph{not} rhyme with ``paychecks''!\\
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% The \ after \LaTeX creates a small horizontal space. Try leaving it out.
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% The \\ at the end creates additional vertical space between lines.
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% See Lesson Six for more on spacing.
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% In most cases, \emph and \textit look the same.
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\textbf{Math Enviroments, Superscripts, and Subscripts}
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The numbers 3, 4, and 5 are a Pythagorean triple because $3^2+4^2=5^2$.\\
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% The dollar signs ($) open and close the inline math environment.
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We all know that $(x^n)'=nx^{n-1}$, but what is $(x^x)'$?\\
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% Note that the typesetter ignores multiple spaces as above.
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The recursive definition for the Fibonacci numbers is
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$F_1=1$, $F_2=1$, and $F_n=F_{n-1}+F_{n-2}$ for all integers $n>2$.\\
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Compare $\frac{1}{a+b}\neq\frac{1}{a}+\frac{1}{b}$ to the following.
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$$\frac{1}{a+b}\neq\frac{1}{a}+\frac{1}{b}$$
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%The double dollar signs ($$) open and close the displayed math environment.
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We can also display it midline by using ``display-style'':
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$\displaystyle\frac{1}{a+b}\neq\frac{1}{a}+\frac{1}{b}$.\\
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% Make sure your typeset quotation marks look right!
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% To force a page break at any place in your document, you can use
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% \pagebreak or \newpage.
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\end{document}
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\message{ !name(lesson1.tex) !offset(-58) }
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lesson1-answer.tex
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lesson1-answer.tex
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% EXERCISE ONE
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\documentclass{amsart}
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\thispagestyle{empty}
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\begin{document}
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\begin{center}
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\textbf{Exercise One: The Basics}
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\end{center}
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A certain math professor will \textbf{scream} and may even \textbf{cry} if you confuse
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the Latin terms \emph{id est}, meaning ``that is to say'' and \emph{exempli
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gratia}, meaning ``for instance.'' Compare the following.\\
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I adore polynomials, \emph{e.g.}, $x^4+x^2+1$.
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I adore polynomials, \emph{i.e.}, expressions of the form
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$a_0+a_1x+a_2x^2+\dots+a_nx^n$, where $a_0, a_1, ..., a_n$ are constants and $n$ is a
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non-negative integer.\\
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Do you lie awake at night wondering what is the smallest positive integer that can be
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written as the sum of two perfect cubes in two distinct ways? Well, wonder no more:
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$$1729=10^3+9^3=12^3+1^3$$
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We all learned in first grade that $(a+b)^3\neq a^3+b^3$, but when we study modular
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arithmetic we'll find that the two \textit{are} equal in ``mod 3.''\\
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The famous mathematician Euler (rhymes with ``boiler'' \textbf{NOT} with ``ruler'') used
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the geometric series formula $a+ar+ar^2+ar^3+...=a/(1-r)$ to
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conclude the following.
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$$1-1+1-1+1-\dots = \frac{1}{2}$$
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But we know the formula only applies if $-1<r<1$, so this result is not valid.
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\end{document}
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lesson1.tex
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lesson1.tex
···
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% LESSON ONE
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% Text following a percentage sign (%) is ignored by the typesetter.
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+
% In this manual, we will use such text for comments and notes.
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+
% You do not need to type out these comments.
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+
6
+
\documentclass{amsart}
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+
% Almost all commands start with a backslash (\).
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+
% amsart is short for American Mathematical Society article.
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+
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\thispagestyle{empty}
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+
%We use this to prevent a page number from appearing.
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+
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\begin{document}
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\begin{center}
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\textbf{Lesson One: The Basics}
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\end{center}
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+
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+
\textbf{Font Families}
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+
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+
% One or more blank lines end a paragraph and put the typesetter on a new line.
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+
I \textbf{love} math!
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+
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+
\LaTeX\ does \emph{not} rhyme with ``paychecks''!\\
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+
% The \ after \LaTeX creates a small horizontal space. Try leaving it out.
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+
% The \\ at the end creates additional vertical space between lines.
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+
% See Lesson Six for more on spacing.
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+
% In most cases, \emph and \textit look the same.
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+
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\textbf{Math Enviroments, Superscripts, and Subscripts}
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+
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The numbers 3, 4, and 5 are a Pythagorean triple because $3^2+4^2=5^2$.\\
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+
% The dollar signs ($) open and close the inline math environment.
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+
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We all know that $(x^n)'=nx^{n-1}$, but what is $(x^x)'$?\\
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+
% Note that the typesetter ignores multiple spaces as above.
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+
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+
The recursive definition for the Fibonacci numbers is
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+
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$F_1=1$, $F_2=1$, and $F_n=F_{n-1}+F_{n-2}$ for all integers $n>2$.\\
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+
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Compare $\frac{1}{a+b}\neq\frac{1}{a}+\frac{1}{b}$ to the following.
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$$\frac{1}{a+b}\neq\frac{1}{a}+\frac{1}{b}$$
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+
%The double dollar signs ($$) open and close the displayed math environment.
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+
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+
We can also display it midline by using ``display-style'':
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+
$\displaystyle\frac{1}{a+b}\neq\frac{1}{a}+\frac{1}{b}$.\\
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+
% Make sure your typeset quotation marks look right!
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+
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+
% To force a page break at any place in your document, you can use
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+
% \pagebreak or \newpage.
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+
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+
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\begin{center}
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\textbf{Exercise One: The Basics}
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\end{center}
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+
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A certain math professor will \textbf{scream} and may even \textbf{cry} if you
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confuse the Latin terms \emph{id est}, meaning ``that is to say'' and
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\emph{exempli gratia}, meaning ``for instance.''
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Compare the following.\\
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I adore polynomials, \emph{e.g.}, $x^{4}+x^{2}+1$.
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I adore polynomials, \emph{i.e.}, expressions of the form
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$a_{0} + a_{1}x + a_{2}x^{2} + \dots + a_{n}x^{n}$,where $a_{0},a_{1},...,a_{n}$ are
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constants and $n$ is a non-negative integer.\\
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Do you lie awake at night wondering what is the smallest positive integer that
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can be written as the sum of the two perfect cubes in two distinct ways? Well,
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wonder no more:
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$$ 1729 = 10^{3} + 9^{3} = 12^{3} + 1^{3} $$
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We all learned in first grade that $(a + b)^{3} \neq a^{3} + b^{3}$, but when we
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study modular arithmetic we'll find that the two \emph{are} equal in ``mod 3.''
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The famous mathematician Euler (rhymes with ``boiler'' \textbf{NOT} with
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``ruler'') used the geometric series formula
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$a + ar + ar^{2} + ar^{3} + ... = a / (1 - r)$ to conclude the following
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$$ 1 - 1 + 1 - 1 + 1 - \dots = \frac{1}{2} $$
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But we know the formula only applies if -1 $<$ $r$ $<$ 1, so this result is not
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valid.
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\end{document}