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<h4>Gaussian Elimination</h4>
<br>In the Integer Factoring Lab, the assignment says
<br> <span style="color: rgb(51, 51, 51);">Try out your procedure on N = 2419 by calling find candidates(N, </span><b style="box-sizing: border-box; color: rgb(51, 51, 51);">primeset</b><span style="color: rgb(51, 51, 51);">(32))</span>
<span style="color: rgb(51, 51, 51);">
<br>but should say
<br></span><span style="color: rgb(51, 51, 51);"> Try out your procedure on N = 2419 by calling find candidates(N, </span><b style="box-sizing: border-box; color: rgb(51, 51, 51);">primes</b><span style="color: rgb(51, 51, 51);">(32)).<br></span>
<br>Also, in the lab stencil, the spec for the procedure find_candidates(N, primeset) states that the output should be a list but the output should be a tuple.
<br><h4><br></h4>
<h4>Dimension</h4>In the video lecture <i>Dimension: Dual representation of vector spaces</i>, I give a definition for the <i>dual</i> of a vector space. I should have called that the <i>annihilator</i> of a vector space; the dual of a vector space is something different.
<br>
<br>In the Perspective Lab,
<br><ul>
<li>In Section 2, I say that <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-1-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-1"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 132%;"><span style="position: absolute; clip: rect(28.8px 18480px 46.1px -8.4px); top: -40px; left: 0px;"><span class="mrow" id="MathJax-Span-2"><span class="msubsup" id="MathJax-Span-3"><span style="display: inline-block; position: relative; width: 16.4px; height: 0px;"><span style="position: absolute; clip: rect(28.8px 18480px 43.2px -8.4px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-4" style="font-family: MathJax_Math; font-style: italic;">c</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 8px;"><span class="mn" id="MathJax-Span-5" style="font-size: 70.7%; font-family: MathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.2px; vertical-align: -4.1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-1">c_3</script> goes to the top-right corner of the whiteboard but I mean the top-left corner.</li>
<li>In the top-view diagram in Section 4, I use <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-2-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 132%;"><span style="position: absolute; clip: rect(24.2px 18480px 45.8px -8.3px); top: -40px; left: 0px;"><span class="mrow" id="MathJax-Span-7"><span class="msubsup" id="MathJax-Span-8"><span style="display: inline-block; position: relative; width: 16.4px; height: 0px;"><span style="position: absolute; clip: rect(24.2px 18480px 43.2px -8.3px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-9" style="font-family: MathJax_Math; font-style: italic;">b</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 8px;"><span class="mn" id="MathJax-Span-10" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 17.6px; vertical-align: -3.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-2">b_1</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-3-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 132%;"><span style="position: absolute; clip: rect(24.2px 18480px 46.1px -8.3px); top: -40px; left: 0px;"><span class="mrow" id="MathJax-Span-12"><span class="msubsup" id="MathJax-Span-13"><span style="display: inline-block; position: relative; width: 16.4px; height: 0px;"><span style="position: absolute; clip: rect(24.2px 18480px 43.2px -8.3px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-14" style="font-family: MathJax_Math; font-style: italic;">b</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 8px;"><span class="mn" id="MathJax-Span-15" style="font-size: 70.7%; font-family: MathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 17.9px; vertical-align: -4.1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-3">b_3</script> but I mean <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-4-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-16"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 132%;"><span style="position: absolute; clip: rect(28.8px 18480px 45.8px -8.4px); top: -40px; left: 0px;"><span class="mrow" id="MathJax-Span-17"><span class="msubsup" id="MathJax-Span-18"><span style="display: inline-block; position: relative; width: 16.4px; height: 0px;"><span style="position: absolute; clip: rect(28.8px 18480px 43.2px -8.4px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-19" style="font-family: MathJax_Math; font-style: italic;">c</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 8px;"><span class="mn" id="MathJax-Span-20" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -3.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-4">c_1</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-5-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-21"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 132%;"><span style="position: absolute; clip: rect(28.8px 18480px 46.1px -8.4px); top: -40px; left: 0px;"><span class="mrow" id="MathJax-Span-22"><span class="msubsup" id="MathJax-Span-23"><span style="display: inline-block; position: relative; width: 16.4px; height: 0px;"><span style="position: absolute; clip: rect(28.8px 18480px 43.2px -8.4px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-24" style="font-family: MathJax_Math; font-style: italic;">c</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 8px;"><span class="mn" id="MathJax-Span-25" style="font-size: 70.7%; font-family: MathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.2px; vertical-align: -4.1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-5">c_3</script>.</li>
<li>In Section 5, we write <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-6-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-26"><span style="display: inline-block; position: relative; width: 87px; height: 0px; font-size: 132%;"><span style="position: absolute; clip: rect(20.1px 18480px 43.4px -8.4px); top: -40px; left: 0px;"><span class="mrow" id="MathJax-Span-27"><span class="mi" id="MathJax-Span-28" style="font-family: MathJax_Math; font-style: italic;">H<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.1px;"></span></span><span class="mo" id="MathJax-Span-29" style="font-family: MathJax_Main; padding-left: 5.1px;">=</span><span class="msubsup" id="MathJax-Span-30" style="padding-left: 5.1px;"><span style="display: inline-block; position: relative; width: 32.4px; height: 0px;"><span style="position: absolute; clip: rect(23.8px 18480px 43px -8.4px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-31" style="font-family: MathJax_Math; font-style: italic;">A</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -48.2px; left: 14px;"><span class="texatom" id="MathJax-Span-32"><span class="mrow" id="MathJax-Span-33"><span class="mo" id="MathJax-Span-34" style="font-size: 70.7%; font-family: MathJax_Main;">−</span><span class="mn" id="MathJax-Span-35" style="font-size: 70.7%; font-family: MathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span><span class="mi" id="MathJax-Span-36" style="font-family: MathJax_Math; font-style: italic;">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.8px;"></span></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.3px; vertical-align: -1.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-6">H=A^{-1}C</script> instead of <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-7-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-37"><span style="display: inline-block; position: relative; width: 88px; height: 0px; font-size: 132%;"><span style="position: absolute; clip: rect(20.3px 18480px 43.4px -8.4px); top: -40px; left: 0px;"><span class="mrow" id="MathJax-Span-38"><span class="mi" id="MathJax-Span-39" style="font-family: MathJax_Math; font-style: italic;">H<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.1px;"></span></span><span class="mo" id="MathJax-Span-40" style="font-family: MathJax_Main; padding-left: 5.1px;">=</span><span class="msubsup" id="MathJax-Span-41" style="padding-left: 5.1px;"><span style="display: inline-block; position: relative; width: 33.6px; height: 0px;"><span style="position: absolute; clip: rect(24px 18480px 43.4px -8.1px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-42" style="font-family: MathJax_Math; font-style: italic;">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.8px;"></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -48px; left: 15.2px;"><span class="texatom" id="MathJax-Span-43"><span class="mrow" id="MathJax-Span-44"><span class="mo" id="MathJax-Span-45" style="font-size: 70.7%; font-family: MathJax_Main;">−</span><span class="mn" id="MathJax-Span-46" style="font-size: 70.7%; font-family: MathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span><span class="mi" id="MathJax-Span-47" style="font-family: MathJax_Math; font-style: italic;">A</span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -1.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-7">H=C^{-1}A</script>. </li>
</ul>
<h4>The Matrix</h4>In the video lecture <i>What is a Matrix?</i>, the solution to the <i>transpose </i>quiz has <code>.F</code> where it should have <code>.f</code><br><br>In the video lecture <i>The Matrix: Matrix Inverse</i>, I stated as a proposition: <br> "Suppose the matrix product <i>AB</i> is defined. Then <i>AB</i> is an invertible matrix if and only if both <i>A</i> and <i>B</i> are invertible matrices."<br>Only one direction of this statement is true. It should read: <br> "Suppose the matrix product AB is defined. If <i>A</i> and <i>B</i> are invertible then <i>AB</i> is invertible."<br><h4>The Vector Space: Linear Combinations</h4>In the video lecture, the solution to the <i>Lights Out</i> problem should be <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-8-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-48"><span style="display: inline-block; position: relative; width: 238px; height: 0px; font-size: 132%;"><span style="position: absolute; clip: rect(24.7px 18480px 46.6px -8.4px); top: -40px; left: 0px;"><span class="mrow" id="MathJax-Span-49"><span class="msubsup" id="MathJax-Span-50"><span style="display: inline-block; position: relative; width: 20.4px; height: 0px;"><span style="position: absolute; clip: rect(28.8px 18480px 43.2px -8.4px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-51" style="font-family: MathJax_Math; font-style: italic;">α</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 12px;"><span class="mn" id="MathJax-Span-52" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span><span class="mo" id="MathJax-Span-53" style="font-family: MathJax_Main; padding-left: 5.1px;">=</span><span class="mn" id="MathJax-Span-54" style="font-family: MathJax_Main; padding-left: 5.1px;">0</span><span class="mo" id="MathJax-Span-55" style="font-family: MathJax_Main;">,</span><span class="msubsup" id="MathJax-Span-56" style="padding-left: 3.1px;"><span style="display: inline-block; position: relative; width: 20.4px; height: 0px;"><span style="position: absolute; clip: rect(28.8px 18480px 43.2px -8.4px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-57" style="font-family: MathJax_Math; font-style: italic;">α</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 12px;"><span class="mn" id="MathJax-Span-58" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span><span class="mo" id="MathJax-Span-59" style="font-family: MathJax_Main; padding-left: 5.1px;">=</span><span class="mn" id="MathJax-Span-60" style="font-family: MathJax_Main; padding-left: 5.1px;">1</span><span class="mo" id="MathJax-Span-61" style="font-family: MathJax_Main;">,</span><span class="msubsup" id="MathJax-Span-62" style="padding-left: 3.1px;"><span style="display: inline-block; position: relative; width: 20.4px; height: 0px;"><span style="position: absolute; clip: rect(28.8px 18480px 43.2px -8.4px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-63" style="font-family: MathJax_Math; font-style: italic;">α</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 12px;"><span class="mn" id="MathJax-Span-64" style="font-size: 70.7%; font-family: MathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span><span class="mo" id="MathJax-Span-65" style="font-family: MathJax_Main; padding-left: 5.1px;">=</span><span class="mn" id="MathJax-Span-66" style="font-family: MathJax_Main; padding-left: 5.1px;">0</span><span class="mo" id="MathJax-Span-67" style="font-family: MathJax_Main;">,</span><span class="msubsup" id="MathJax-Span-68" style="padding-left: 3.1px;"><span style="display: inline-block; position: relative; width: 20.4px; height: 0px;"><span style="position: absolute; clip: rect(28.8px 18480px 43.2px -8.4px); top: -40px; left: 0px;"><span class="mi" id="MathJax-Span-69" style="font-family: MathJax_Math; font-style: italic;">α</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span><span style="position: absolute; top: -37.2px; left: 12px;"><span class="mn" id="MathJax-Span-70" style="font-size: 70.7%; font-family: MathJax_Main;">4</span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span></span><span class="mo" id="MathJax-Span-71" style="font-family: MathJax_Main; padding-left: 5.1px;">=</span><span class="mn" id="MathJax-Span-72" style="font-family: MathJax_Main; padding-left: 5.1px;">1</span></span><span style="display: inline-block; width: 0px; height: 40px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 17.9px; vertical-align: -4.6px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-8">\alpha_1=0, \alpha_2=1, \alpha_3=0, \alpha_4=1</script>.
<h4>Politics</h4>
<p>Versions of politics_lab.zip downloaded before July 9 at 11:40pm EDT have an erroneous newline in the <code>create_voting_dict()['Clinton']</code> example. To make this doctest pass, please remove the newline in the array, or just download the latest ZIP
file if you haven't started the lab yet.</p>
<h4>Vec class</h4>
<p>For a few hours after release on Monday, July 8, there was a bug in our grader for the equality test on Vecs. It's fixed now.</p>
<h4>Python Lab</h4>
<p>Tasks in Python Lab that require you to write a comprehension won't work if the comprehension is split over multiple lines. Our apologies for that! Please put each comprehension on a single line of the stencil file.</p>
<h4>HW0, preliminary version</h4>
<p>Some students who went to the course web site before the official launch downloaded a version of hw0.zip that was preliminary. You would probably notice this: the stencil file hw0.py has fifteen problems instead of ten. If this happened to you, my apologies!
Please rename your current hw0.py, download the official version of hw0.zip, and move or copy the files it contains into your matrix
<br>folder. Then copy your answers from the old, renamed hw0.py file into the new one, and submit your solutions in the usual way.</p>
<h4>The Function</h4>
<p>On a slide titled 'The function', the example at the bottom of the slide might be misleading. I should have included more tuples such as ((1,1,),1), ((1,2,)1),((2,1),2), and ((3,1),3). I just listed some examples of tuples in this infinite set (using
"..." to indicate there were more) but this might have confused some people.</p>
<p>In slides titled 'The function' and 'The function: Composition', the diagrams showing the Caesar cypher mistakenly showed Z mapping to B. the letter Z should map to C, as indicated by the text on the slide 'The function'.</p>
<p>In a slide titled 'Set terminology and notation: Cartesian product', there was a spurious (3, clubs) in the set.</p>
<h4>Course Map</h4>
<pre><code>If MA=B where M is invertible
then Row A = Col A</code></pre>
<p>should be replaced with</p>
<pre><code>If MA=B where M is invertible
then Row A = Row B</code></pre>
<p>We've updated the map on the course web site.</p>
</div>
<hr>
<div>
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</div>
<div style="float:right;text-align:right;font-size:10px;">
Created Tue 2 Jul 2013 7:41 AM PDT (UTC -0700)<br>
Last Modified Sun 1 Sep 2013 12:33 PM PDT (UTC -0700) </div>
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