Starting to add content

publication/publication.ptx

@@ -121,11 +121,11 @@
 
     <!-- Whether to knowl a particular elements is set here    -->
     <!-- Lots of elements have this possibility; see the guide -->
-      <!--<knowl
+      <knowl
         theorem="no"
         proof="yes"
         definition="no"
-        example="yes"
+        example="no"
         example-solution="yes"
         project="no"
         task="no"
@@ -140,7 +140,7 @@
         exercise-divisional="no"
         exercise-worksheet="no"
         exercise-readingquestion="no"
-      />-->
+      />
 
     <!-- Specify the theme for the html by giving names to     -->
     <!-- override defaults.  Ex:<css theme="denver"/>          -->

source/ch-Probability.ptx

@@ -12,9 +12,121 @@
   <section xml:id="sec-Set-Theory" xmlns:xi="http://www.w3.org/2001/XInclude">
     <title>Set Theory</title>
 
+    <definition xml:id="def-sample-space">
+      <statement>
         <p>
-            Text of section.
+          The <term>sample space</term>, often denoted <m>\Omega</m>, is the set of all possible results of an experiment.
+          A single result is called an <term>outcome</term>, while a collection of results is called an <term>event</term>.
         </p>
+      </statement>
+    </definition>
+
+    <example>
+      <statement>
+        <p>
+          An experiment consists of rolling a standard 6-sided die.
+          The sample space is <m>\Omega = \{1, 2, 3, 4, 5, 6\}</m>.
+          One possible event is <m>A = \{2, 4, 6\}</m>, i.e., the event that the result of the roll is even.
+        </p>
+
+        <p>
+          What would the sample space look like if we roll the die two times and recorded the results?
+        </p>
+      </statement>
+
+      <answer>
+        <p>
+          <md>
+            <mrow> \Omega = \{\amp (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), </mrow>
+            <mrow> \amp (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), </mrow>
+            <mrow> \amp (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), </mrow>
+            <mrow> \amp (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), </mrow>
+            <mrow> \amp (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), </mrow>
+            <mrow> \amp (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)\} </mrow>
+          </md>
+        </p>
+      </answer>
+    </example>
+
+    <definition xml:id="def-subset">
+      <statement>
+        <p>
+          Let <m>A</m> be a set.
+          The symbol <m>\in</m> means "is an element of", as in <m>a \in A</m>.
+          Given another set <m>B</m>, we say <m>A</m> is a <term>subset</term> of <m>B</m>, written <m>A\subset B</m>, to mean that every element of the set <m>A</m> is also an element of the set <m>B</m>.
+        </p>
+      </statement>
+    </definition>
+
+    <definition xml:id="def-set-operations">
+      <statement>
+        <p>
+          Consider sets <m>A</m> and <m>B</m>, each contained inside <m>\Omega</m>.
+          We can combine sets in a variety of ways:
+        </p>
+        <dl>
+        <li>
+          <title>Union</title>
+
+          <p>
+            The <term>union</term> of <m>A</m> and <m>B</m> is the set <m>A \cup B = \{x \mid x \in A \text{ or } x \in B\}</m>.
+          </p>
+        </li>
+
+        <li>
+          <title>Intersection</title>
+
+          <p>
+            The <term>intersection</term> of <m>A</m> and <m>B</m> is the set <m>A \cap B = \{x \mid x \in A \text{ and } x \in B\}</m>.
+          </p>
+        </li>
+
+        <li>
+          <title>Difference</title>
+
+          <p>
+            The <term>set difference</term> <m>A-B</m> is the set <m>A - B = \{x \mid x \in A \text{ and } x \notin B\}</m>.
+          </p>
+        </li>
+
+        <li>
+          <title>Complement</title>
+
+          <p>
+            The <term>complement</term> of <m>A</m> is the set <m>A^c = \{x \in \Omega \mid x \notin A\}</m>.
+          </p>
+        </li>
+
+        <li>
+          <title>Empty Set</title>
+
+          <p>
+            The <term>empty set</term>, usually written <m>\emptyset</m> or <m>\{\}</m>, is the set which contains no elements.
+          </p>
+        </li>
+        </dl>
+      </statement>
+    </definition>
+
+    <p>
+      It's useful sometimes to draw pictures representing sets...
+    </p>
+    <!-- TODO learn figures -->
+    <definition xml:id="def-disjoint">
+      <statement>
+        <p>
+          Two sets <m>A</m> and <m>B</m> are <term>disjoint</term> if <m>A \cap B = \emptyset</m>.
+        </p>
+      </statement>
+    </definition>
+
+    <definition xml:id="def-cardinality">
+      <statement>
+        <p>
+          Given a finite set <m>A</m>, the <term>cardinality</term> of <m>A</m>, written <m>|A|</m>, is the number of elements in <m>A</m>.
+        </p>
+      </statement>
+    </definition>
 
     <exercises xml:id="exercises-Set-Theory">
     <exercise>
@@ -104,10 +216,34 @@
   <section xml:id="sec-Probability" xmlns:xi="http://www.w3.org/2001/XInclude">
     <title>Definition of Probability</title>
 
+    <definition xml:id="def-probability-distribution">
+      <statement>
         <p>
-            Text of section.
+          A <term>probability distribution</term> on a sample space <m>\Omega</m> assigns probabilities to every event, satisfying the following conditions:
         </p>
 
+        <ol>
+          <li>
+            <p>
+              <m>\Pr(\Omega) = 1</m>.
+            </p>
+          </li>
+
+          <li>
+            <p>
+              <m>0 \leq \Pr(A) \leq 1</m> for any event <m>A</m>.
+            </p>
+          </li>
+
+          <li>
+            <p>
+              If <m>A \cap B = \emptyset</m>, then <m>\Pr(A\cup B) = \Pr(A) + \Pr(B)</m>.
+            </p>
+          </li>
+        </ol>
+      </statement>
+    </definition>
+
     <exercises xml:id="exercises-Probability">
     <exercise>
       <statement>

source/frontmatter.ptx

@@ -7,21 +7,21 @@
   <bibinfo>
   
     <author>
-      <personname>You</personname>
+      <personname>Andy Eisenberg</personname>
-      <department>Your department</department>
+      <department>Mathematics Department</department>
-      <institution>Your institution</institution>
+      <institution>Temple University</institution>
     </author>
     <date>
       <today />
     </date>
 
-    <website>
+    <!-- <website>
       <url href="https://pretextbook.org">My Website</url>
-    </website>
+    </website> -->
 
     <copyright>
-      <year>2020<ndash />2024</year>
+      <year>2025</year>
-      <holder>You</holder>
+      <holder>Andy Eisenberg</holder>
       <shortlicense> This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. To view a copy of this license, visit <url href="http://creativecommons.org/licenses/by-sa/4.0/" visual="creativecommons.org/licenses/by-sa/4.0"> CreativeCommons.org</url>
       </shortlicense>
     </copyright>