250 lines
10 KiB
HTML
Executable File
250 lines
10 KiB
HTML
Executable File
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<title>Slides for MATH 1044</title>
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<div id="latex-macros" class="hidden-content process-math" style="display:none"><span class="process-math">\(\newcommand{\N}{\mathbb N}
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\)</span></div>
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<div class="slides">
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<section><section><h1>Slides for MATH 1044</h1></section></section><section><section><h1>§ 1.1: Set Theory</h1></section><section><h3>Sample Space</h3>
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<div align="left"><article class="definition definition-like" id="def-sample-space"><h4 class="heading">
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<span class="type">Definition</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">1</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
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</h4>
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<p>The <dfn class="terminology">sample space</dfn> <span class="process-math">\(\Omega\)</span> is the set of all possible results of an experiment. A single result is called an <dfn class="terminology">outcome</dfn>. A collection of results is called an <dfn class="terminology">event</dfn>.</p></article></div></section><section><h3>Rolling Dice</h3>
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<div align="left"><article class="example example-like" id="sec-1-1-3-2"><h4 class="heading">
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<span class="type">Example</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">2</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
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</h4>
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<p>We roll a 6-sided die two times. What is <span class="process-math">\(\Omega\text{?}\)</span></p></article></div></section><section><h3>Flipping Coins</h3>
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<div align="left"><article class="example example-like" id="sec-1-1-4-2"><h4 class="heading">
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<span class="type">Example</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">3</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
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</h4>
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<p>We flip a coin three times. What is <span class="process-math">\(\Omega\text{?}\)</span></p></article></div></section><section><h3>Picking a Value</h3>
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<div align="left"><article class="example example-like" id="sec-1-1-5-2"><h4 class="heading">
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<span class="type">Example</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
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</h4>
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<p>We pick a number between 1 and 10. What is <span class="process-math">\(\Omega\text{?}\)</span></p></article></div></section><section><h3>Sets</h3>
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<div align="left"><article class="definition definition-like" id="def-subset"><h4 class="heading">
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<span class="type">Definition</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">5</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
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</h4>
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<p>Let <span class="process-math">\(A\)</span> be a set. The symbol <span class="process-math">\(\in\)</span> means "is an element of", as in <span class="process-math">\(a \in A\text{.}\)</span> Given another set <span class="process-math">\(B\text{,}\)</span> we say <span class="process-math">\(A\)</span> is a <dfn class="terminology">subset</dfn> of <span class="process-math">\(B\text{,}\)</span> written <span class="process-math">\(A\subset B\text{,}\)</span> to mean that every element of the set <span class="process-math">\(A\)</span> is also an element of the set <span class="process-math">\(B\text{.}\)</span></p></article></div></section><section><h3></h3>
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<div align="left"><article class="definition definition-like" id="def-set-operations"><h4 class="heading">
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<span class="type">Definition</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">6</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
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</h4>
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<p>Let <span class="process-math">\(A, B \subset \Omega\text{.}\)</span><dl class="description-list">
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<div>
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<dt>Union</dt>
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<dd><p>The <dfn class="terminology">union</dfn> is <span class="process-math">\(A \cup B = \{x \mid x \in A \text{ or } x \in B\}\text{.}\)</span></p></dd>
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</div>
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<div>
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<dt>Intersection</dt>
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<dd><p>The <dfn class="terminology">intersection</dfn> is <span class="process-math">\(A \cap B = \{x \mid x \in A \text{ and } x \in B\}\text{.}\)</span></p></dd>
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</div>
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<div>
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<dt>Difference</dt>
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<dd><p>The <dfn class="terminology">set difference</dfn> is <span class="process-math">\(A - B = \{x \mid x \in A \text{ and } x \notin B\}\text{.}\)</span></p></dd>
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</div>
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<div>
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<dt>Complement</dt>
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<dd><p>The <dfn class="terminology">complement</dfn> is <span class="process-math">\(A^c = \{x \in \Omega \mid x \notin A\}\text{.}\)</span></p></dd>
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</div>
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<div>
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<dt>Empty Set</dt>
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<dd><p>The <dfn class="terminology">empty set</dfn>, written <span class="process-math">\(\emptyset\)</span> or <span class="process-math">\(\{\}\text{,}\)</span> contains no elements.</p></dd>
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</div>
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</dl></p></article></div></section></section><section><section><h1>Section 1.2</h1></section><section><h3>Title 2</h3>
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<div align="left"><p>Some more text.</p></div></section></section>
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</div>
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</div></body>
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