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 <office:meta><meta:initial-creator>Michael Zingale</meta:initial-creator><meta:creation-date>2013-01-02T12:36:14</meta:creation-date><dc:date>2018-01-22T19:51:53.931863166</dc:date><meta:editing-duration>P2DT9H35M22S</meta:editing-duration><meta:editing-cycles>126</meta:editing-cycles><meta:generator>LibreOffice/5.4.4.2$Linux_X86_64 LibreOffice_project/40$Build-2</meta:generator><meta:document-statistic meta:object-count="379"/></office:meta>
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     <text:list-level-style-bullet text:level="5" text:bullet-char="●">
      <style:list-level-properties text:space-before="2.4cm" text:min-label-width="0.6cm"/>
      <style:text-properties fo:font-family="StarSymbol" style:use-window-font-color="true" fo:font-size="45%"/>
     </text:list-level-style-bullet>
     <text:list-level-style-bullet text:level="6" text:bullet-char="●">
      <style:list-level-properties text:space-before="3cm" text:min-label-width="0.6cm"/>
      <style:text-properties fo:font-family="StarSymbol" style:use-window-font-color="true" fo:font-size="45%"/>
     </text:list-level-style-bullet>
     <text:list-level-style-bullet text:level="7" text:bullet-char="●">
      <style:list-level-properties text:space-before="3.6cm" text:min-label-width="0.6cm"/>
      <style:text-properties fo:font-family="StarSymbol" style:use-window-font-color="true" fo:font-size="45%"/>
     </text:list-level-style-bullet>
     <text:list-level-style-bullet text:level="8" text:bullet-char="●">
      <style:list-level-properties text:space-before="4.2cm" text:min-label-width="0.6cm"/>
      <style:text-properties fo:font-family="StarSymbol" style:use-window-font-color="true" fo:font-size="45%"/>
     </text:list-level-style-bullet>
     <text:list-level-style-bullet text:level="9" text:bullet-char="●">
      <style:list-level-properties text:space-before="4.8cm" text:min-label-width="0.6cm"/>
      <style:text-properties fo:font-family="StarSymbol" style:use-window-font-color="true" fo:font-size="45%"/>
     </text:list-level-style-bullet>
     <text:list-level-style-bullet text:level="10" text:bullet-char="●">
      <style:list-level-properties text:space-before="5.4cm" text:min-label-width="0.6cm"/>
      <style:text-properties fo:font-family="StarSymbol" style:use-window-font-color="true" fo:font-size="45%"/>
     </text:list-level-style-bullet>
    </text:list-style>
   </style:graphic-properties>
   <style:paragraph-properties fo:text-align="center"/>
   <style:text-properties fo:color="#ffffff" style:text-outline="false" style:text-line-through-style="none" style:text-line-through-type="none" style:font-name="Arial1" fo:font-family="Arial" style:font-family-generic="roman" style:font-pitch="variable" fo:font-size="48pt" fo:font-style="normal" fo:text-shadow="none" style:text-underline-style="none" fo:font-weight="normal" style:letter-kerning="true" style:font-name-asian="WenQuanYi Zen Hei Sharp" style:font-family-asian="&apos;WenQuanYi Zen Hei Sharp&apos;" style:font-family-generic-asian="system" style:font-pitch-asian="variable" style:font-size-asian="48pt" style:font-style-asian="normal" style:font-weight-asian="normal" style:font-name-complex="Lohit Devanagari" style:font-family-complex="&apos;Lohit Devanagari&apos;" style:font-family-generic-complex="system" style:font-pitch-complex="variable" style:font-size-complex="48pt" style:font-style-complex="normal" style:font-weight-complex="normal" style:text-emphasize="none" style:font-relief="none" style:text-overline-style="none" style:text-overline-color="font-color"/>
  </style:style>
  <style:presentation-page-layout style:name="AL0T26">
   <presentation:placeholder presentation:object="handout" svg:x="2.058cm" svg:y="1.743cm" svg:width="10.556cm" svg:height="-0.233cm"/>
   <presentation:placeholder presentation:object="handout" svg:x="15.414cm" svg:y="1.743cm" svg:width="10.556cm" svg:height="-0.233cm"/>
   <presentation:placeholder presentation:object="handout" svg:x="2.058cm" svg:y="3.612cm" svg:width="10.556cm" svg:height="-0.233cm"/>
   <presentation:placeholder presentation:object="handout" svg:x="15.414cm" svg:y="3.612cm" svg:width="10.556cm" svg:height="-0.233cm"/>
   <presentation:placeholder presentation:object="handout" svg:x="2.058cm" svg:y="5.481cm" svg:width="10.556cm" svg:height="-0.233cm"/>
   <presentation:placeholder presentation:object="handout" svg:x="15.414cm" svg:y="5.481cm" svg:width="10.556cm" svg:height="-0.233cm"/>
  </style:presentation-page-layout>
  <style:presentation-page-layout style:name="AL1T1">
   <presentation:placeholder presentation:object="title" svg:x="2.058cm" svg:y="1.743cm" svg:width="23.912cm" svg:height="3.507cm"/>
   <presentation:placeholder presentation:object="outline" svg:x="2.058cm" svg:y="5.838cm" svg:width="23.912cm" svg:height="13.23cm"/>
  </style:presentation-page-layout>
 </office:styles>
 <office:automatic-styles>
  <style:page-layout style:name="PM0">
   <style:page-layout-properties fo:margin-top="0cm" fo:margin-bottom="0cm" fo:margin-left="0cm" fo:margin-right="0cm" fo:page-width="21.59cm" fo:page-height="27.94cm" style:print-orientation="portrait"/>
  </style:page-layout>
  <style:page-layout style:name="PM1">
   <style:page-layout-properties fo:margin-top="0cm" fo:margin-bottom="0cm" fo:margin-left="0cm" fo:margin-right="0cm" fo:page-width="28cm" fo:page-height="21cm" style:print-orientation="landscape"/>
  </style:page-layout>
  <style:style style:name="dp1" style:family="drawing-page">
   <style:drawing-page-properties draw:background-size="border" draw:fill="none"/>
  </style:style>
  <style:style style:name="dp2" style:family="drawing-page">
   <style:drawing-page-properties draw:background-size="border" draw:fill="solid" draw:fill-color="#c0c0c0" draw:fill-image-width="0cm" draw:fill-image-height="0cm"/>
  </style:style>
  <style:style style:name="dp3" style:family="drawing-page">
   <style:drawing-page-properties presentation:display-header="true" presentation:display-footer="true" presentation:display-page-number="false" presentation:display-date-time="true"/>
  </style:style>
  <style:style style:name="dp4" style:family="drawing-page">
   <style:drawing-page-properties presentation:background-visible="true" presentation:background-objects-visible="true" presentation:display-footer="true" presentation:display-page-number="false" presentation:display-date-time="true"/>
  </style:style>
  <style:style style:name="dp5" style:family="drawing-page">
   <style:drawing-page-properties presentation:visibility="hidden" presentation:background-visible="true" presentation:background-objects-visible="true" presentation:display-footer="true" presentation:display-page-number="false" presentation:display-date-time="true"/>
  </style:style>
  <style:style style:name="gr1" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties draw:stroke="none" draw:fill="none" draw:fill-color="#ffffff" draw:auto-grow-height="false" fo:min-height="1.397cm"/>
  </style:style>
  <style:style style:name="gr2" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties draw:stroke="none" draw:fill="none" draw:fill-color="#ffffff" draw:textarea-vertical-align="bottom" draw:auto-grow-height="false" fo:min-height="1.397cm"/>
  </style:style>
  <style:style style:name="gr3" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties draw:stroke="none" svg:stroke-color="#000000" draw:fill="none" draw:fill-color="#ffffff" draw:auto-grow-height="true" draw:auto-grow-width="false" fo:max-height="0cm" fo:min-height="0.746cm"/>
  </style:style>
  <style:style style:name="gr4" style:family="graphic">
   <style:graphic-properties style:protect="size"/>
  </style:style>
  <style:style style:name="gr5" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties draw:stroke="none" draw:fill="none" draw:textarea-horizontal-align="center" draw:textarea-vertical-align="middle" draw:color-mode="standard" draw:luminance="0%" draw:contrast="0%" draw:gamma="100%" draw:red="0%" draw:green="0%" draw:blue="0%" fo:clip="rect(0cm, 0cm, 0cm, 0cm)" draw:image-opacity="100%" style:mirror="none"/>
  </style:style>
  <style:style style:name="gr6" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties draw:stroke="none" svg:stroke-color="#000000" draw:fill="none" draw:fill-color="#ffffff" draw:auto-grow-height="true" draw:auto-grow-width="false" fo:max-height="0cm" fo:min-height="0.475cm"/>
  </style:style>
  <style:style style:name="gr7" style:family="graphic" style:parent-style-name="Object_20_with_20_no_20_fill_20_and_20_no_20_line">
   <style:graphic-properties draw:stroke="none" draw:fill="none" draw:textarea-vertical-align="middle" draw:color-mode="standard" draw:luminance="0%" draw:contrast="0%" draw:gamma="100%" draw:red="0%" draw:green="0%" draw:blue="0%" fo:clip="rect(0cm, 0cm, 0cm, 0cm)" draw:image-opacity="100%" style:mirror="none"/>
  </style:style>
  <style:style style:name="gr8" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties draw:stroke="none" svg:stroke-color="#000000" draw:fill="none" draw:fill-color="#ffffff" draw:auto-grow-height="true" draw:auto-grow-width="false" fo:max-height="0cm" fo:min-height="0.869cm"/>
  </style:style>
  <style:style style:name="gr9" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties draw:stroke="none" svg:stroke-color="#000000" draw:fill="none" draw:fill-color="#ffffff" draw:auto-grow-height="true" draw:auto-grow-width="false" fo:max-height="0cm" fo:min-height="7.451cm"/>
  </style:style>
  <style:style style:name="gr10" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties draw:stroke="none" svg:stroke-color="#000000" draw:fill="none" draw:fill-color="#ffffff" draw:auto-grow-height="true" draw:auto-grow-width="false" fo:max-height="0cm" fo:min-height="2.367cm"/>
  </style:style>
  <style:style style:name="gr11" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties draw:stroke="none" svg:stroke-color="#000000" draw:fill="none" draw:fill-color="#ffffff" draw:auto-grow-height="true" draw:auto-grow-width="false" fo:max-height="0cm" fo:min-height="1.423cm"/>
  </style:style>
  <style:style style:name="gr12" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties draw:stroke="none" svg:stroke-color="#000000" draw:fill="none" draw:fill-color="#ffffff" draw:auto-grow-height="true" draw:auto-grow-width="false" fo:max-height="0cm" fo:min-height="11.565cm"/>
  </style:style>
  <style:style style:name="gr13" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties draw:stroke="none" svg:stroke-color="#000000" draw:fill="none" draw:fill-color="#ffffff" draw:auto-grow-height="true" draw:auto-grow-width="false" fo:max-height="0cm" fo:min-height="3.454cm"/>
  </style:style>
  <style:style style:name="gr14" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties draw:fill="none" draw:textarea-vertical-align="middle" draw:auto-grow-height="false" fo:min-height="18.056cm" fo:min-width="0cm"/>
  </style:style>
  <style:style style:name="gr15" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties draw:stroke="none" svg:stroke-color="#000000" draw:fill="none" draw:fill-color="#ffffff" draw:auto-grow-height="true" draw:auto-grow-width="false" fo:max-height="0cm" fo:min-height="0.712cm"/>
  </style:style>
  <style:style style:name="gr16" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties OOoLatexArgs="26§display§\sqrt{-1}" draw:stroke="none" draw:fill="none" draw:textarea-horizontal-align="center" draw:textarea-vertical-align="middle" draw:color-mode="standard" draw:luminance="0%" draw:contrast="0%" draw:gamma="100%" draw:red="0%" draw:green="0%" draw:blue="0%" fo:clip="rect(0cm, 0cm, 0cm, 0cm)" draw:image-opacity="100%" style:mirror="none"/>
  </style:style>
  <style:style style:name="gr17" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties draw:stroke="none" svg:stroke-color="#000000" draw:fill="none" draw:fill-color="#ffffff" draw:auto-grow-height="true" draw:auto-grow-width="false" fo:max-height="0cm" fo:min-height="8.196cm"/>
  </style:style>
  <style:style style:name="gr18" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties OOoLatexArgs="26§display§\sqrt{x+1} - \sqrt{x}" draw:stroke="none" draw:fill="none" draw:textarea-horizontal-align="center" draw:textarea-vertical-align="middle" draw:color-mode="standard" draw:luminance="0%" draw:contrast="0%" draw:gamma="100%" draw:red="0%" draw:green="0%" draw:blue="0%" fo:clip="rect(0cm, 0cm, 0cm, 0cm)" draw:image-opacity="100%" style:mirror="none"/>
  </style:style>
  <style:style style:name="gr19" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties OOoLatexArgs="26§display§x = 1984" draw:stroke="none" draw:fill="none" draw:textarea-horizontal-align="center" draw:textarea-vertical-align="middle" draw:color-mode="standard" draw:luminance="0%" draw:contrast="0%" draw:gamma="100%" draw:red="0%" draw:green="0%" draw:blue="0%" fo:clip="rect(0cm, 0cm, 0cm, 0cm)" draw:image-opacity="100%" style:mirror="none"/>
  </style:style>
  <style:style style:name="gr20" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties OOoLatexArgs="26§display§\sqrt{x+1} - \sqrt{x} = 44.55 - 44.54 = 0.01" draw:stroke="none" draw:fill="none" draw:textarea-horizontal-align="center" draw:textarea-vertical-align="middle" draw:color-mode="standard" draw:luminance="0%" draw:contrast="0%" draw:gamma="100%" draw:red="0%" draw:green="0%" draw:blue="0%" fo:clip="rect(0cm, 0cm, 0cm, 0cm)" draw:image-opacity="100%" style:mirror="none"/>
  </style:style>
  <style:style style:name="gr21" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties OOoLatexArgs="24§display§\sqrt{x+1} - \sqrt{x} = (\sqrt{x+1} - \sqrt{x}) \left ( \frac{\sqrt{x+1} + \sqrt{x}}{\sqrt{x+1} + \sqrt{x}} \right ) = \frac{1}{\sqrt{x+1} + \sqrt{x}}" draw:stroke="none" draw:fill="none" draw:textarea-horizontal-align="center" draw:textarea-vertical-align="middle" draw:color-mode="standard" draw:luminance="0%" draw:contrast="0%" draw:gamma="100%" draw:red="0%" draw:green="0%" draw:blue="0%" fo:clip="rect(0cm, 0cm, 0cm, 0cm)" draw:image-opacity="100%" style:mirror="none"/>
  </style:style>
  <style:style style:name="gr22" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties OOoLatexArgs="26§display§e^x \sim S(x) = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \cdots + \frac{x^n}{n!}" draw:stroke="none" draw:fill="none" draw:textarea-horizontal-align="center" draw:textarea-vertical-align="middle" draw:color-mode="standard" draw:luminance="0%" draw:contrast="0%" draw:gamma="100%" draw:red="0%" draw:green="0%" draw:blue="0%" fo:clip="rect(0cm, 0cm, 0cm, 0cm)" draw:image-opacity="100%" style:mirror="none"/>
  </style:style>
  <style:style style:name="gr23" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties OOoLatexArgs="26§display§\frac{|x|^{n+1}}{(n+1)!} \max\{1,e^x\}" draw:stroke="none" draw:fill="none" draw:textarea-horizontal-align="center" draw:textarea-vertical-align="middle" draw:color-mode="standard" draw:luminance="0%" draw:contrast="0%" draw:gamma="100%" draw:red="0%" draw:green="0%" draw:blue="0%" fo:clip="rect(0cm, 0cm, 0cm, 0cm)" draw:image-opacity="100%" style:mirror="none"/>
  </style:style>
  <style:style style:name="gr24" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties OOoLatexArgs="26§display§e^{-24} = \left (e^{-1} \right )^{24} \Longrightarrow S(-24) = S(-1)^{24}" draw:stroke="none" draw:fill="none" draw:textarea-horizontal-align="center" draw:textarea-vertical-align="middle" draw:color-mode="standard" draw:luminance="0%" draw:contrast="0%" draw:gamma="100%" draw:red="0%" draw:green="0%" draw:blue="0%" fo:clip="rect(0cm, 0cm, 0cm, 0cm)" draw:image-opacity="100%" style:mirror="none"/>
  </style:style>
  <style:style style:name="gr25" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties OOoLatexArgs="26§display§V = \frac{4}{3} \pi (r_r^3 - r_l^3)" draw:stroke="none" draw:fill="none" draw:textarea-horizontal-align="center" draw:textarea-vertical-align="middle" draw:color-mode="standard" draw:luminance="0%" draw:contrast="0%" draw:gamma="100%" draw:red="0%" draw:green="0%" draw:blue="0%" fo:clip="rect(0cm, 0cm, 0cm, 0cm)" draw:image-opacity="100%" style:mirror="none"/>
  </style:style>
  <style:style style:name="gr26" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties OOoLatexArgs="26§display§V = \frac{4}{3}\pi \Delta r (r_l^2 + r_l r_r + r_r^2)" draw:stroke="none" draw:fill="none" draw:textarea-horizontal-align="center" draw:textarea-vertical-align="middle" draw:color-mode="standard" draw:luminance="0%" draw:contrast="0%" draw:gamma="100%" draw:red="0%" draw:green="0%" draw:blue="0%" fo:clip="rect(0cm, 0cm, 0cm, 0cm)" draw:image-opacity="100%" style:mirror="none"/>
  </style:style>
  <style:style style:name="gr27" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties OOoLatexArgs="26§display§|x - y| &lt; \epsilon" draw:stroke="none" draw:fill="none" draw:textarea-horizontal-align="center" draw:textarea-vertical-align="middle" draw:color-mode="standard" draw:luminance="0%" draw:contrast="0%" draw:gamma="100%" draw:red="0%" draw:green="0%" draw:blue="0%" fo:clip="rect(0cm, 0cm, 0cm, 0cm)" draw:image-opacity="100%" style:mirror="none"/>
  </style:style>
  <style:style style:name="gr28" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties OOoLatexArgs="26§display§x = y" draw:stroke="none" draw:fill="none" draw:textarea-horizontal-align="center" draw:textarea-vertical-align="middle" draw:color-mode="standard" draw:luminance="0%" draw:contrast="0%" draw:gamma="100%" draw:red="0%" draw:green="0%" draw:blue="0%" fo:clip="rect(0cm, 0cm, 0cm, 0cm)" draw:image-opacity="100%" style:mirror="none"/>
  </style:style>
  <style:style style:name="gr29" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties draw:stroke="none" draw:fill="none" fo:min-height="0.713cm"/>
  </style:style>
  <style:style style:name="gr30" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties OOoLatexArgs="28§display§\left (&#x0a;\begin{array}{ccc}&#x0a; 1 &amp; 2 &amp; 3 \\&#x0a;  4 &amp; 5 &amp; 6&#x0a;\end{array}&#x0a;\right )" draw:stroke="none" draw:fill="none" draw:textarea-horizontal-align="center" draw:textarea-vertical-align="middle" draw:color-mode="standard" draw:luminance="0%" draw:contrast="0%" draw:gamma="100%" draw:red="0%" draw:green="0%" draw:blue="0%" fo:clip="rect(0cm, 0cm, 0cm, 0cm)" draw:image-opacity="100%" style:mirror="none"/>
  </style:style>
  <style:style style:name="gr31" style:family="graphic" style:parent-style-name="objectwithoutfill">
   <style:graphic-properties svg:stroke-width="0.051cm" svg:stroke-color="#ff0000" draw:marker-start-width="0.279cm" draw:marker-end="Short_20_line_20_Arrow" draw:marker-end-width="0.381cm" draw:fill="none" draw:textarea-vertical-align="middle" fo:padding-top="0.15cm" fo:padding-bottom="0.15cm" fo:padding-left="0.275cm" fo:padding-right="0.275cm"/>
  </style:style>
  <style:style style:name="gr32" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties OOoLatexArgs="28§display§f^\prime (x) = \lim_{h\rightarrow 0} \frac{f(x+h) - f(x)}{h}" draw:stroke="none" draw:fill="none" draw:textarea-horizontal-align="center" draw:textarea-vertical-align="middle" draw:color-mode="standard" draw:luminance="0%" draw:contrast="0%" draw:gamma="100%" draw:red="0%" draw:green="0%" draw:blue="0%" fo:clip="rect(0cm, 0cm, 0cm, 0cm)" draw:image-opacity="100%" style:mirror="none"/>
  </style:style>
  <style:style style:name="gr33" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties OOoLatexArgs="28§display§D_h(x) = \frac{f(x + h) - f(x)}{h}" draw:stroke="none" draw:fill="none" draw:textarea-horizontal-align="center" draw:textarea-vertical-align="middle" draw:color-mode="standard" draw:luminance="0%" draw:contrast="0%" draw:gamma="100%" draw:red="0%" draw:green="0%" draw:blue="0%" fo:clip="rect(0cm, 0cm, 0cm, 0cm)" draw:image-opacity="100%" style:mirror="none"/>
  </style:style>
  <style:style style:name="gr34" style:family="graphic" style:parent-style-name="objectwithoutfill">
   <style:graphic-properties draw:stroke="dash" draw:stroke-dash="Fine_20_Dashed" draw:fill="none" draw:textarea-vertical-align="middle"/>
  </style:style>
  <style:style style:name="gr35" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties draw:stroke="none" draw:fill="none" fo:min-height="4.474cm"/>
  </style:style>
  <style:style style:name="gr36" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties draw:stroke="none" draw:fill="none" fo:min-height="1.918cm"/>
  </style:style>
  <style:style style:name="gr37" style:family="graphic" style:parent-style-name="standard">
   <style:graphic-properties draw:stroke="none" draw:fill="none" fo:min-height="3.196cm"/>
  </style:style>
  <style:style style:name="pr1" style:family="presentation" style:parent-style-name="Default-backgroundobjects">
   <style:graphic-properties draw:stroke="none" draw:fill-color="#ff3366" draw:textarea-vertical-align="middle" draw:auto-grow-height="false"/>
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  <style:style style:name="pr2" style:family="presentation" style:parent-style-name="Default-backgroundobjects">
   <style:graphic-properties draw:stroke="none" draw:fill="none" draw:fill-color="#ffffff" draw:auto-grow-height="false" fo:min-height="1.449cm"/>
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  <style:style style:name="pr3" style:family="presentation" style:parent-style-name="Default-backgroundobjects">
   <style:graphic-properties draw:stroke="none" draw:fill="none" draw:fill-color="#ffffff" draw:auto-grow-height="false" fo:min-height="1.397cm"/>
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   <style:graphic-properties draw:stroke="none" draw:fill="none" draw:fill-color="#ffffff" draw:textarea-vertical-align="bottom" draw:auto-grow-height="false" fo:min-height="1.397cm"/>
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      <text:p>Python for Scientific Computing</text:p>
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      <text:p><text:span text:style-name="T3">http://bender.astro.sunysb.edu/classes/python-science</text:span></text:p>
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      <text:p>Course Goals</text:p>
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        <text:p>Simply: to learn how to use python to do</text:p>
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         <text:list-item>
          <text:p>Numerical analysis</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Data analysis</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Plotting and visualizations</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Symbol mathematics</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Write applications</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>...</text:p>
         </text:list-item>
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      <text:p>Class Participation</text:p>
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        <text:p>We&apos;ll learn by interactively trying out some ideas and looking at code</text:p>
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         <text:list-item>
          <text:p>I want to learn from all of you—share you experiences and expertise</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T4">We&apos;ll use slack to communicate out of class</text:span></text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T5">Everyone should have received an invite to our slack: </text:span><text:span text:style-name="T5"><text:a xlink:href="https://python-sbu.slack.com/" xlink:type="simple">https://python-sbu.slack.com</text:a></text:span><text:span text:style-name="T5"><text:s/></text:span></text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Try out ideas and report to the class what you&apos;ve learned</text:p>
        <text:list>
         <text:list-item>
          <text:p>You should have an installation of python on your laptop</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Alternately, you can use the Virtual SINC site on campus, which has Anaconda Python installed</text:p>
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      <text:p>Slack</text:p>
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        <text:p>Log onto our slack as soon as possible</text:p>
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          <text:p>If you didn’t get an invite, e-mail me, and I’ll add you</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Slack is a web-based team chat tool</text:p>
        <text:list>
         <text:list-item>
          <text:p>I’ve setup a number of channels for us to focus our discussions</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Everyone is expected to participate</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T6">Your course grade is based on your participation </text:span></text:p>
        <text:list>
         <text:list-item>
          <text:p>I have a simple script(<text:a xlink:href="https://github.com/zingale/slack_grader" xlink:type="simple">https://github.com/zingale/slack_grader</text:a> ) that I’ll use for grading</text:p>
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           <text:list-item>
            <text:p>Good contributions will get a comment on the slack, counting as “+1” </text:p>
           </text:list-item>
           <text:list-item>
            <text:p>The script will record these points over the semester</text:p>
           </text:list-item>
           <text:list-item>
            <text:p>Help, by using slack reactions for useful comments from your classmates</text:p>
           </text:list-item>
          </text:list>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>In “free” mode, slack only keeps 10k messages—I don’t think we’ll go over that during the semester</text:p>
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      <text:p>Why Slack?</text:p>
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        <text:p>One of the goals of this class is to teach you tools that are used by computational science groups</text:p>
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       <text:list-item>
        <text:p>Slack has gained enormous adoption by research groups over the past few years</text:p>
        <text:list>
         <text:list-item>
          <text:p>We’ll see how to integrate github repos to it, so everyone can keep on top of code developments</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>It’s easy to post code snippets in conversations</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>There are lots of integrations that are available to extend its usefulness</text:p>
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      <text:p>Why Python?</text:p>
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        <text:p><text:span text:style-name="T7">Very high-level language</text:span></text:p>
        <text:list>
         <text:list-item>
          <text:p>Provides many complex data-structures (lists, dictionaries, ...) </text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Your code is shorter than a comparable algorithm in a compiled language</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T7">Many powerful libraries to perform complex tasks</text:span></text:p>
        <text:list>
         <text:list-item>
          <text:p>Parse structured inputs files</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>send e-mail</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>interact with the operating system</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>make plots</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>make GUIs</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>do scientific computations</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>...</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T7">Easy to prototype new tools</text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T7">Cross-platform and Free</text:span></text:p>
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      <text:p>Why Python?</text:p>
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        <text:p><text:span text:style-name="T7">Dynamically-typed</text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T7">Object-oriented foundation</text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T7">Extensible</text:span> (easy to call Fortran, C/C++, ...)</text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T7">Automatic memory management</text:span> (garbage collection)</text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T7">Ease of readability</text:span> (whitespace matters)</text:p>
        <text:p/>
        <text:p>... and for this course ...</text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T4">Very widely adopted in the scientific community</text:span></text:p>
        <text:list>
         <text:list-item>
          <text:p>Mostly due to the very powerful array library NumPy</text:p>
         </text:list-item>
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      <text:p><text:span text:style-name="T8">(xkcd)</text:span></text:p>
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     <draw:text-box>
      <text:p>Installing Python</text:p>
     </draw:text-box>
    </draw:frame>
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      <text:list text:style-name="L4">
       <text:list-item>
        <text:p><text:span text:style-name="T9">Linux</text:span></text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T9">Python is probably already installed</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T9">The dependencies we need for our class should be available </text:span><text:span text:style-name="T9">through your package manager</text:span></text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T9">OS X / Windows</text:span></text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T9">The easiest way to get everything we need for class is by installing </text:span><text:span text:style-name="T9">Anaconda: </text:span><text:span text:style-name="T9"><text:a xlink:href="https://www.continuum.io/downloads" xlink:type="simple">https://www.continuum.io/downloads</text:a></text:span><text:span text:style-name="T9"><text:s/></text:span></text:p>
          <text:list>
           <text:list-item>
            <text:p><text:span text:style-name="T9">You&apos;ll have a choice of python 2.7 or 3.6—choose python 3.6</text:span></text:p>
           </text:list-item>
          </text:list>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T9">If you run into problems ask on slack (there is an “installation” </text:span><text:span text:style-name="T9">channel), or come by my office</text:span></text:p>
       </text:list-item>
      </text:list>
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     <draw:text-box>
      <text:p>Hello, World!</text:p>
     </draw:text-box>
    </draw:frame>
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      <text:list text:style-name="L4">
       <text:list-item>
        <text:p>If you have python installed properly, you can start python simply by typing <text:span text:style-name="T3">python</text:span> at your command line prompt</text:p>
        <text:list>
         <text:list-item>
          <text:p>The python shell will come up</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Our hello world program is simply:</text:p>
          <text:p><text:span text:style-name="T10">print(&quot;hello, world&quot;)</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T9">Or, in python 2 (more on this later...):</text:span></text:p>
          <text:p><text:span text:style-name="T10">print &quot;hello, world&quot;</text:span></text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
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    <presentation:notes draw:style-name="dp3">
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     <draw:text-box>
      <text:p>Communities</text:p>
     </draw:text-box>
    </draw:frame>
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       <text:list-item>
        <text:p>Many scientific disciplines have their own python communities that</text:p>
        <text:list>
         <text:list-item>
          <text:p>Provide tutorials</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Cookbooks</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Libraries to do standard analysis in the field</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>For the most part, these build on the Open nature of python</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>I&apos;ve put links on our course page to some information on the python communities for:</text:p>
        <text:list>
         <text:list-item>
          <text:p>Astronomy</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Atmospheric Science</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Biology</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Cognitive Science</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Psychology</text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T4">Let me know of any others!</text:span></text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
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     <draw:text-box>
      <text:p>Python in Astro</text:p>
     </draw:text-box>
    </draw:frame>
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      <text:list text:style-name="L4">
       <text:list-item>
        <text:p>Python is seeing rapidly increasing adoption in Astrophysics</text:p>
        <text:list>
         <text:list-item>
          <text:p>Open-source alternative to IDL</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Python for IDL users: <text:span text:style-name="T11"><text:a xlink:href="https://www.cfa.harvard.edu/~jbattat/computer/python/science/idl-numpy.html" xlink:type="simple">https://www.cfa.harvard.edu/~jbattat/computer/python/science/idl-numpy.html</text:a></text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Astropython: <text:a xlink:href="http://www.astropython.org/" xlink:type="simple">http://www.astropython.org/</text:a></text:p>
        <text:list>
         <text:list-item>
          <text:p>Lots of tutorials, links to resources, forum, ...</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Astropy mailing list: <text:a xlink:href="http://mail.scipy.org/mailman/listinfo/astropy" xlink:type="simple">http://mail.scipy.org/mailman/listinfo/astropy</text:a></text:p>
        <text:p/>
       </text:list-item>
      </text:list>
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     <draw:text-box>
      <text:p>Python in Biology</text:p>
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    </draw:frame>
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       <text:list-item>
        <text:p>Biopython (<text:a xlink:href="http://biopython.org/wiki/Main_Page" xlink:type="simple">http://biopython.org/wiki/Main_Page</text:a>) provides tools for using python for computational molecular biology and bioinformatics projects</text:p>
        <text:list>
         <text:list-item>
          <text:p>Able to parse many different bioinformatics file formats</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Access online databases</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Do analysis, operate on sequences, ...</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>See <text:span text:style-name="T12">Python—All a Scientist Needs</text:span> by J. B. Lucks (arxiv:0803.1838)</text:p>
       </text:list-item>
      </text:list>
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      <text:p>Scientific Python Stack</text:p>
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       <text:list-item>
        <text:p>Most scientific libraries in python build on the Scientific Python stack:</text:p>
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      </text:list>
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      <text:p/>
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      <text:p><text:span text:style-name="T8">(scipy.org)</text:span></text:p>
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     <draw:text-box>
      <text:p>Starters...</text:p>
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       <text:list-item>
        <text:p>Before we get into python, we&apos;ll review some of the core ideas about numerical computing</text:p>
       </text:list-item>
      </text:list>
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   <draw:page draw:name="page16" draw:style-name="dp5" draw:master-page-name="Default" presentation:presentation-page-layout-name="AL1T1">
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     <draw:text-box>
      <text:p>Basics of Computation</text:p>
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      <text:list text:style-name="L4">
       <text:list-item>
        <text:p><text:span text:style-name="T4">Computers store information and allow us to operate on it.</text:span></text:p>
        <text:list>
         <text:list-item>
          <text:p>That&apos;s basically it.</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Computers have finite memory, so it is not possible to store the infinite range of numbers that exist in the real world, so approximations are made.</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>You should have some familiarity with how computers store numbers</text:p>
        <text:list>
         <text:list-item>
          <text:p>Great floating point reference</text:p>
          <text:list>
           <text:list-item>
            <text:p><text:span text:style-name="T12">What Every Computer Scientist Should Know About Floating-Point </text:span><text:span text:style-name="T12">Arithmetic</text:span> by D. Goldberg</text:p>
           </text:list-item>
          </text:list>
          <text:p/>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
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    <presentation:notes draw:style-name="dp3">
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   <draw:page draw:name="page17" draw:style-name="dp5" draw:master-page-name="Default" presentation:presentation-page-layout-name="AL1T1">
    <draw:frame presentation:style-name="pr13" draw:layer="layout" svg:width="25.199cm" svg:height="1.957cm" svg:x="1.4cm" svg:y="0.537cm" presentation:class="title" presentation:user-transformed="true">
     <draw:text-box>
      <text:p>Integers</text:p>
     </draw:text-box>
    </draw:frame>
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      <text:list text:style-name="L4">
       <text:list-item>
        <text:p>Basic unit of information in a computer is a <text:span text:style-name="T7">bit</text:span>: 0 or 1</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>8 bits = 1 byte</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Different types of information require more bits/bytes to store.</text:p>
        <text:list>
         <text:list-item>
          <text:p>A <text:span text:style-name="T7">logical</text:span> (T or F) can be stored in a single bit.</text:p>
          <text:list>
           <text:list-item>
            <text:p>C/C++: <text:span text:style-name="T3">bool</text:span> datatype</text:p>
           </text:list-item>
           <text:list-item>
            <text:p>Fortran: <text:span text:style-name="T3">logical</text:span> datatype</text:p>
           </text:list-item>
          </text:list>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T7">Integers</text:span>: </text:p>
          <text:list>
           <text:list-item>
            <text:p>Standard in many languages is 4-bytes. <text:s/>This allows for 2<text:span text:style-name="T13">32</text:span>-1 distinct values.</text:p>
            <text:list>
             <text:list-item>
              <text:p>This can store: -2,147,483,648 to 2,147,483,647 (signed)</text:p>
              <text:list>
               <text:list-item>
                <text:p>C/C++: <text:span text:style-name="T3">int</text:span> (usually) or <text:span text:style-name="T3">int32_t</text:span></text:p>
               </text:list-item>
               <text:list-item>
                <text:p>Fortran: <text:span text:style-name="T3">integer</text:span> or <text:span text:style-name="T3">integer*4</text:span></text:p>
               </text:list-item>
              </text:list>
             </text:list-item>
             <text:list-item>
              <text:p>Or it can store: 0 to 4,294,967,295 (unsigned)</text:p>
              <text:list>
               <text:list-item>
                <text:p>C/C++: <text:span text:style-name="T3">uint</text:span> or <text:span text:style-name="T3">uint32_t</text:span></text:p>
               </text:list-item>
               <text:list-item>
                <text:p>Fortran (as of 95): <text:span text:style-name="T3">unsigned</text:span></text:p>
               </text:list-item>
              </text:list>
             </text:list-item>
            </text:list>
           </text:list-item>
          </text:list>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
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    <presentation:notes draw:style-name="dp3">
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   </draw:page>
   <draw:page draw:name="page18" draw:style-name="dp5" draw:master-page-name="Default" presentation:presentation-page-layout-name="AL1T1">
    <draw:frame presentation:style-name="pr13" draw:layer="layout" svg:width="25.199cm" svg:height="1.957cm" svg:x="1.4cm" svg:y="0.537cm" presentation:class="title" presentation:user-transformed="true">
     <draw:text-box>
      <text:p>Integers</text:p>
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      <text:list text:style-name="L4">
       <text:list-item>
        <text:list>
         <text:list-item>
          <text:p>Integers (continued): </text:p>
          <text:list>
           <text:list-item>
            <text:p>Sometimes 2-bytes. <text:s/>This allows for 2<text:span text:style-name="T13">16</text:span>-1 distinct values.</text:p>
            <text:list>
             <text:list-item>
              <text:p>This can store: -32,768 to 32,767 (signed)</text:p>
              <text:list>
               <text:list-item>
                <text:p>C/C++: <text:span text:style-name="T3">short</text:span> (usually) or <text:span text:style-name="T3">int16_t</text:span></text:p>
               </text:list-item>
               <text:list-item>
                <text:p>Fortran: <text:span text:style-name="T3">integer*2</text:span></text:p>
               </text:list-item>
              </text:list>
             </text:list-item>
             <text:list-item>
              <text:p>Or it can store: 0 to 65,535 (unsigned)</text:p>
              <text:list>
               <text:list-item>
                <text:p>C/C++: <text:span text:style-name="T3">uint16_t</text:span></text:p>
               </text:list-item>
               <text:list-item>
                <text:p>Fortran (as of 95): <text:span text:style-name="T3">unsigned*2</text:span></text:p>
               </text:list-item>
              </text:list>
             </text:list-item>
            </text:list>
           </text:list-item>
           <text:list-item>
            <text:p>Note for IDL users: the standard integer in IDL is a 2-byte integer. <text:s/>If you do </text:p>
            <text:p><text:span text:style-name="T3">i = 2</text:span></text:p>
            <text:p>that&apos;s 2-bytes. <text:s/>To get a 4-byte integer, do:</text:p>
            <text:p><text:span text:style-name="T3">i = 2l</text:span></text:p>
           </text:list-item>
          </text:list>
         </text:list-item>
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      </office:binary-data>
      <text:p/>
     </draw:image>
    </draw:frame>
    <draw:frame draw:style-name="gr6" draw:text-style-name="P14" draw:layer="layout" svg:width="3.302cm" svg:height="0.725cm" svg:x="24.26cm" svg:y="14.686cm">
     <draw:text-box>
      <text:p><text:span text:style-name="T8">(xkcd)</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr8" draw:text-style-name="P16" draw:layer="layout" svg:width="16.51cm" svg:height="1.119cm" svg:x="2.45cm" svg:y="16.51cm">
     <draw:text-box>
      <text:p><text:span text:style-name="T14">Overflow example...</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <presentation:notes draw:style-name="dp3">
     <draw:page-thumbnail draw:style-name="gr4" draw:layer="layout" svg:width="13.968cm" svg:height="10.476cm" svg:x="3.81cm" svg:y="2.123cm" draw:page-number="19" presentation:class="page"/>
     <draw:frame presentation:style-name="pr15" draw:text-style-name="P11" draw:layer="layout" svg:width="17.271cm" svg:height="12.572cm" svg:x="2.159cm" svg:y="13.271cm" presentation:class="notes" presentation:placeholder="true" presentation:user-transformed="true">
      <draw:text-box/>
     </draw:frame>
    </presentation:notes>
   </draw:page>
   <draw:page draw:name="page20" draw:style-name="dp5" draw:master-page-name="Default" presentation:presentation-page-layout-name="AL1T1">
    <draw:frame presentation:style-name="pr13" draw:layer="layout" svg:width="25.199cm" svg:height="1.957cm" svg:x="1.4cm" svg:y="0.537cm" presentation:class="title" presentation:user-transformed="true">
     <draw:text-box>
      <text:p>Overflow</text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame presentation:style-name="pr14" draw:layer="layout" svg:width="26.162cm" svg:height="16.51cm" svg:x="1.27cm" svg:y="3.556cm" presentation:class="outline" presentation:user-transformed="true">
     <draw:text-box>
      <text:p><text:span text:style-name="T3">iold = -1</text:span></text:p>
      <text:p><text:span text:style-name="T3">i = 1</text:span></text:p>
      <text:p><text:span text:style-name="T3"/></text:p>
      <text:p><text:span text:style-name="T3">type_init = type(i)</text:span></text:p>
      <text:p><text:span text:style-name="T3">print &quot;type currently: &quot;, type_init</text:span></text:p>
      <text:p><text:span text:style-name="T3"/></text:p>
      <text:p><text:span text:style-name="T3">while (i &gt; iold):</text:span></text:p>
      <text:p><text:span text:style-name="T3"><text:s text:c="4"/></text:span><text:span text:style-name="T3">print i</text:span></text:p>
      <text:p><text:span text:style-name="T3"><text:s text:c="4"/></text:span><text:span text:style-name="T3">iold = i</text:span></text:p>
      <text:p><text:span text:style-name="T3"><text:s text:c="4"/></text:span><text:span text:style-name="T3">i *= 2</text:span></text:p>
      <text:p><text:span text:style-name="T3"/></text:p>
      <text:p><text:span text:style-name="T3"><text:s text:c="4"/></text:span><text:span text:style-name="T3">if (not type(i) == type_init):</text:span></text:p>
      <text:p><text:span text:style-name="T3"><text:s text:c="8"/></text:span><text:span text:style-name="T3">print &quot;type changed, now: &quot;, type(i)</text:span></text:p>
      <text:p><text:span text:style-name="T3"><text:s text:c="8"/></text:span><text:span text:style-name="T3">break</text:span></text:p>
      <text:p><text:span text:style-name="T3"/></text:p>
      <text:p><text:span text:style-name="T3">print i</text:span></text:p>
      <text:p/>
     </draw:text-box>
    </draw:frame>
    <presentation:notes draw:style-name="dp3">
     <draw:page-thumbnail draw:style-name="gr4" draw:layer="layout" svg:width="13.968cm" svg:height="10.476cm" svg:x="3.81cm" svg:y="2.123cm" draw:page-number="20" presentation:class="page"/>
     <draw:frame presentation:style-name="pr15" draw:text-style-name="P12" draw:layer="layout" svg:width="17.271cm" svg:height="12.572cm" svg:x="2.159cm" svg:y="13.271cm" presentation:class="notes" presentation:placeholder="true" presentation:user-transformed="true">
      <draw:text-box/>
     </draw:frame>
    </presentation:notes>
   </draw:page>
   <draw:page draw:name="page21" draw:style-name="dp5" draw:master-page-name="Default" presentation:presentation-page-layout-name="AL1T1">
    <draw:frame presentation:style-name="pr13" draw:layer="layout" svg:width="25.199cm" svg:height="1.957cm" svg:x="1.4cm" svg:y="0.537cm" presentation:class="title" presentation:user-transformed="true">
     <draw:text-box>
      <text:p>Integers</text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame presentation:style-name="pr14" draw:layer="layout" svg:width="26.924cm" svg:height="16.764cm" svg:x="0.508cm" svg:y="3.556cm" presentation:class="outline" presentation:user-transformed="true">
     <draw:text-box>
      <text:list text:style-name="L4">
       <text:list-item>
        <text:p><text:span text:style-name="T15">Python allows for the date size of the integer to scale with the size of the </text:span><text:span text:style-name="T15">number: https://www.python.org/dev/peps/pep-0237/</text:span></text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T15">Initially, it is the largest value supported in hardware on a machine (64-</text:span><text:span text:style-name="T15">bits on a 64-bit machine—see </text:span><text:span text:style-name="T10">sys.maxint</text:span></text:p>
         </text:list-item>
        </text:list>
        <text:p/>
        <text:p/>
        <text:p/>
        <text:p/>
        <text:p/>
        <text:p/>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T15">This prints:</text:span></text:p>
       </text:list-item>
      </text:list>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr9" draw:text-style-name="P17" draw:layer="layout" svg:width="21.336cm" svg:height="7.701cm" svg:x="2.54cm" svg:y="7.958cm">
     <draw:text-box>
      <text:p><text:span text:style-name="T16">def fac(x):</text:span></text:p>
      <text:p><text:span text:style-name="T16"><text:s text:c="4"/></text:span><text:span text:style-name="T16">if (x == 0):</text:span></text:p>
      <text:p><text:span text:style-name="T16"><text:s text:c="8"/></text:span><text:span text:style-name="T16">return 1</text:span></text:p>
      <text:p><text:span text:style-name="T16"><text:s text:c="4"/></text:span><text:span text:style-name="T16">else:</text:span></text:p>
      <text:p><text:span text:style-name="T16"><text:s text:c="8"/></text:span><text:span text:style-name="T16">return x*fac(x-1)</text:span></text:p>
      <text:p><text:span text:style-name="T16"/></text:p>
      <text:p><text:span text:style-name="T16"/></text:p>
      <text:p><text:span text:style-name="T16">a = fac(52)</text:span></text:p>
      <text:p><text:span text:style-name="T16">print a</text:span></text:p>
      <text:p><text:span text:style-name="T16">print a.bit_length()</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr10" draw:text-style-name="P18" draw:layer="layout" svg:width="26.416cm" svg:height="2.617cm" svg:x="1.27cm" svg:y="17.259cm">
     <draw:text-box>
      <text:p><text:span text:style-name="T16">80658175170943878571660636856403766975289505440883277824000000000000</text:span></text:p>
      <text:p><text:span text:style-name="T17">226</text:span></text:p>
      <text:p><text:span text:style-name="T18"/></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr11" draw:text-style-name="P19" draw:layer="layout" svg:width="22.036cm" svg:height="1.673cm" svg:x="5.842cm" svg:y="19.004cm">
     <draw:text-box>
      <text:p><text:span text:style-name="T19">Note: python 3.x does away with the distinction between int and long altogether.</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <presentation:notes draw:style-name="dp3">
     <draw:page-thumbnail draw:style-name="gr4" draw:layer="layout" svg:width="13.968cm" svg:height="10.476cm" svg:x="3.81cm" svg:y="2.123cm" draw:page-number="21" presentation:class="page"/>
     <draw:frame presentation:style-name="pr15" draw:text-style-name="P11" draw:layer="layout" svg:width="17.271cm" svg:height="12.572cm" svg:x="2.159cm" svg:y="13.271cm" presentation:class="notes" presentation:placeholder="true" presentation:user-transformed="true">
      <draw:text-box/>
     </draw:frame>
    </presentation:notes>
   </draw:page>
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      <text:p>Real Numbers</text:p>
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       <text:list-item>
        <text:p><text:span text:style-name="T7">Floating point</text:span> format</text:p>
        <text:list>
         <text:list-item>
          <text:p>Infinite real numbers on the number line need to be represented by a finite number of bits</text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T7">Approximations made</text:span></text:p>
          <text:list>
           <text:list-item>
            <text:p>Finite number of decimal places stored, maximum range of exponents.</text:p>
           </text:list-item>
          </text:list>
         </text:list-item>
         <text:list-item>
          <text:p>Not every number can be represented. </text:p>
          <text:list>
           <text:list-item>
            <text:p>In base-2 (what a computer uses), <text:span text:style-name="T3">0.1</text:span> does not have an exact representation (see S 2.1 of Goldberg)</text:p>
           </text:list-item>
          </text:list>
         </text:list-item>
         <text:list-item>
          <text:p>There is a finite precision</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
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    <presentation:notes draw:style-name="dp3">
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     <draw:text-box>
      <text:p>Exact Representations</text:p>
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       <text:list-item>
        <text:p><text:span text:style-name="T3">0.1</text:span> as represented by a computer:</text:p>
        <text:p/>
        <text:p/>
        <text:p/>
        <text:p/>
        <text:p/>
       </text:list-item>
      </text:list>
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      <text:p><text:span text:style-name="T20">&gt;&gt;&gt; b = 0.1</text:span></text:p>
      <text:p><text:span text:style-name="T20">&gt;&gt;&gt; print(type(b))</text:span></text:p>
      <text:p><text:span text:style-name="T20">&lt;class &apos;float&apos;&gt;</text:span></text:p>
      <text:p><text:span text:style-name="T20">&gt;&gt;&gt; print(&quot;{:30.20}”.format(b))</text:span></text:p>
      <text:p><text:span text:style-name="T20"><text:s text:c="8"/></text:span><text:span text:style-name="T20">0.10000000000000000555</text:span></text:p>
      <text:p><text:span text:style-name="T20"/></text:p>
      <text:p><text:span text:style-name="T20">&gt;&gt;&gt; import sys</text:span></text:p>
      <text:p><text:span text:style-name="T20">&gt;&gt;&gt; print(sys.float_info)</text:span></text:p>
      <text:p><text:span text:style-name="T20">sys.float_info(max=1.7976931348623157e+308, max_exp=1024, max_10_exp=308, min=2.2250738585072014e-308, min_exp=-1021, min_10_exp=-307, dig=15, mant_dig=53, epsilon=2.220446049250313e-16, radix=2, rounds=1)</text:span></text:p>
      <text:p><text:span text:style-name="T20"/></text:p>
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      <text:p><text:span text:style-name="T9">Note: in python 2.x, the </text:span><text:span text:style-name="T3">type()</text:span><text:span text:style-name="T9"> statement would have returned </text:span></text:p>
      <text:p><text:span text:style-name="T9"/></text:p>
      <text:p><text:span text:style-name="T3">&lt;type &apos;float&apos;&gt;</text:span></text:p>
      <text:p><text:span text:style-name="T9"/></text:p>
      <text:p><text:span text:style-name="T9">but this really in a class, in the object-oriented sense.</text:span></text:p>
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     <draw:text-box>
      <text:p>Floating Point</text:p>
     </draw:text-box>
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       <text:list-item>
        <text:p>In the floating point format, a number is represented by a <text:span text:style-name="T7">significand</text:span> (or mantissa), and <text:span text:style-name="T7">exponent</text:span>, and a <text:span text:style-name="T7">sign</text:span>.</text:p>
        <text:list>
         <text:list-item>
          <text:p>Base 2 is used (since we are using bits)</text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T3">0.1 ~ (1 + 1</text:span><text:span text:style-name="T21">·2</text:span><text:span text:style-name="T22">-1</text:span><text:span text:style-name="T21"> + 0·2</text:span><text:span text:style-name="T23">-2</text:span><text:span text:style-name="T21"> + 0·2</text:span><text:span text:style-name="T23">-3</text:span><text:span text:style-name="T21"> + 1·2</text:span><text:span text:style-name="T23">-4</text:span><text:span text:style-name="T21"> + 1·2</text:span><text:span text:style-name="T23">-5</text:span><text:span text:style-name="T21"> </text:span><text:span text:style-name="T21">+ ...) · 2</text:span><text:span text:style-name="T23">-4</text:span></text:p>
          <text:p><text:span text:style-name="T24"/></text:p>
          <text:p><text:span text:style-name="T24"/></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T25">All significand&apos;s will start with 1, so it is not stored</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T26">Single precision:</text:span></text:p>
          <text:list>
           <text:list-item>
            <text:p><text:span text:style-name="T25">Sign: 1 bit; exponent: 8 bits; significand: 24 bits (23 stored) = 32 </text:span><text:span text:style-name="T25">bits</text:span></text:p>
           </text:list-item>
           <text:list-item>
            <text:p><text:span text:style-name="T25">Range: 2</text:span><text:span text:style-name="T27">7</text:span><text:span text:style-name="T25">-1 in exponent (because of sign) = 2</text:span><text:span text:style-name="T27">127 </text:span><text:span text:style-name="T25">multiplier ~ </text:span><text:span text:style-name="T25">10</text:span><text:span text:style-name="T27">38</text:span></text:p>
           </text:list-item>
           <text:list-item>
            <text:p><text:span text:style-name="T25">Decimal precision: ~6 significant digits</text:span></text:p>
           </text:list-item>
          </text:list>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T26">Double precision:</text:span></text:p>
          <text:list>
           <text:list-item>
            <text:p><text:span text:style-name="T25">Sign: 1 bit; exponent: 11 bits; significand: 53 bits (52 stored) = </text:span><text:span text:style-name="T25">64 bits</text:span></text:p>
           </text:list-item>
           <text:list-item>
            <text:p><text:span text:style-name="T25">Range: 2</text:span><text:span text:style-name="T27">10</text:span><text:span text:style-name="T25">-1 in exponent = 2</text:span><text:span text:style-name="T27">1023</text:span><text:span text:style-name="T25"> multiplier ~ 10</text:span><text:span text:style-name="T27">308</text:span></text:p>
           </text:list-item>
           <text:list-item>
            <text:p><text:span text:style-name="T25">Decimal precision: ~15 significant digits</text:span></text:p>
           </text:list-item>
          </text:list>
         </text:list-item>
        </text:list>
       </text:list-item>
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      <text:p><text:span text:style-name="T28">significand</text:span></text:p>
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      <text:p>Floating Point</text:p>
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       <text:list-item>
        <text:p>Overflows and underflows can still occur when you go outside the representable range. <text:s/></text:p>
        <text:list>
         <text:list-item>
          <text:p>The floating-point standard will signal these (and compilers can catch them)</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Some special numbers:</text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T7">NaN</text:span> = <text:span text:style-name="T3">0/0</text:span> or</text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T7">Inf</text:span> is for overflows, like <text:span text:style-name="T3">1/0</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Both of these allow the program to continue, and both can be trapped (and dealt with)</text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T3">-0</text:span> is a valid number, and <text:span text:style-name="T3">-0 = 0</text:span> in comparison </text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Floating point is governed by an IEEE standard</text:p>
        <text:list>
         <text:list-item>
          <text:p>Ensures all machines do the same thing</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Aggressive compiler optimizations can break the standard</text:p>
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      <text:p>Numerical Precision</text:p>
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      <text:list text:style-name="L4">
       <text:list-item>
        <text:p>Finite number of bits used to represent #s means there is a finite precision, the <text:span text:style-name="T7">machine epsilon</text:span>, <text:span text:style-name="T29">ε</text:span></text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T30">One way to find this is to ask when</text:span><text:span text:style-name="T29"> 1 + ε = 1</text:span></text:p>
          <text:p><text:span text:style-name="T29"/></text:p>
          <text:p><text:span text:style-name="T29"/></text:p>
          <text:p><text:span text:style-name="T29"/></text:p>
          <text:p><text:span text:style-name="T29"/></text:p>
          <text:p><text:span text:style-name="T29"/></text:p>
          <text:p><text:span text:style-name="T29"/></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T30">This gives</text:span><text:span text:style-name="T29"> </text:span><text:span text:style-name="T31">2.22044604925e-16</text:span></text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr17" draw:text-style-name="P23" draw:layer="layout" svg:width="23.622cm" svg:height="8.446cm" svg:x="3.048cm" svg:y="7.336cm">
     <draw:text-box>
      <text:p><text:span text:style-name="T32">x = 1.0</text:span></text:p>
      <text:p><text:span text:style-name="T32"/></text:p>
      <text:p><text:span text:style-name="T32">eps = 1.0</text:span></text:p>
      <text:p><text:span text:style-name="T32"/></text:p>
      <text:p><text:span text:style-name="T32">while (not x + eps == x):</text:span></text:p>
      <text:p><text:span text:style-name="T32"><text:s text:c="4"/></text:span><text:span text:style-name="T32">eps = eps/2.0</text:span></text:p>
      <text:p><text:span text:style-name="T32"/></text:p>
      <text:p><text:span text:style-name="T32"># machine precision is 2*eps, since that was the last </text:span></text:p>
      <text:p><text:span text:style-name="T32"># value for which 1 + eps was not 1</text:span></text:p>
      <text:p><text:span text:style-name="T32">print 2*eps</text:span></text:p>
      <text:p><text:span text:style-name="T32"/></text:p>
     </draw:text-box>
    </draw:frame>
    <presentation:notes draw:style-name="dp3">
     <draw:page-thumbnail draw:style-name="gr4" draw:layer="layout" svg:width="13.968cm" svg:height="10.476cm" svg:x="3.81cm" svg:y="2.123cm" draw:page-number="26" presentation:class="page"/>
     <draw:frame presentation:style-name="pr15" draw:text-style-name="P11" draw:layer="layout" svg:width="17.271cm" svg:height="12.572cm" svg:x="2.159cm" svg:y="13.271cm" presentation:class="notes" presentation:placeholder="true" presentation:user-transformed="true">
      <draw:text-box/>
     </draw:frame>
    </presentation:notes>
   </draw:page>
   <draw:page draw:name="page27" draw:style-name="dp5" draw:master-page-name="Default" presentation:presentation-page-layout-name="AL1T1">
    <draw:frame presentation:style-name="pr13" draw:layer="layout" svg:width="25.199cm" svg:height="1.957cm" svg:x="1.4cm" svg:y="0.537cm" presentation:class="title" presentation:user-transformed="true">
     <draw:text-box>
      <text:p>Numerical Precision</text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame presentation:style-name="pr16" draw:layer="layout" svg:width="26.924cm" svg:height="16.256cm" svg:x="0.508cm" svg:y="3.556cm" presentation:class="outline" presentation:user-transformed="true">
     <draw:text-box>
      <text:list text:style-name="L4">
       <text:list-item>
        <text:p text:style-name="P24"><text:span text:style-name="T33">This means that </text:span><text:span text:style-name="T34">most real numbers do not have an exact </text:span><text:span text:style-name="T34">representation on a computer</text:span><text:span text:style-name="T33">.</text:span></text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T30">Spacing between numbers varies with the size of numbers</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T30">Relative spacing is constant</text:span></text:p>
          <text:p><text:span text:style-name="T29"/></text:p>
          <text:p><text:span text:style-name="T29"/></text:p>
          <text:p><text:span text:style-name="T29"/></text:p>
          <text:p><text:span text:style-name="T29"/></text:p>
          <text:p><text:span text:style-name="T29"/></text:p>
          <text:p><text:span text:style-name="T29"/></text:p>
          <text:p><text:span text:style-name="T29"/></text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
     </draw:text-box>
    </draw:frame>
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     <svg:title>TexMaths</svg:title>
     <svg:desc>24§display§\mathrm{relative~roundoff~error}~ = \frac{|\mathrm{true~number} - \mathrm{computer~number}|}{|\mathrm{true~number}|} \le \epsilon§png§600§FALSE§</svg:desc>
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    <draw:frame presentation:style-name="pr13" draw:layer="layout" svg:width="25.199cm" svg:height="1.957cm" svg:x="1.4cm" svg:y="0.537cm" presentation:class="title" presentation:user-transformed="true">
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      <text:p>Round-off Error</text:p>
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       <text:list-item>
        <text:p><text:span text:style-name="T7">Round-off error</text:span> is the error arising from the fact that no every number is exactly representable in the finite precision floating point format.</text:p>
        <text:list>
         <text:list-item>
          <text:p>Can accumulate in a program over many arithmetic operations</text:p>
         </text:list-item>
        </text:list>
        <text:p/>
       </text:list-item>
      </text:list>
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      <text:p>Round-off Example 1</text:p>
     </draw:text-box>
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        <text:p>Imagine that we can only keep track of 4 significant digits</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Compute</text:p>
        <text:list>
         <text:list-item>
          <text:p>Take</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Keeping only 4 digits each step of the way, <text:s/></text:p>
          <text:p/>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T7">We&apos;ve lost a lot of precision</text:span></text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Instead, consider:</text:p>
        <text:p><text:span text:style-name="T35"/></text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Then</text:p>
        <text:p/>
       </text:list-item>
      </text:list>
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     <draw:text-box>
      <text:p><text:span text:style-name="T8">(Yakowitz &amp; Szidarovszky)</text:span></text:p>
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      <text:p/>
     </draw:image>
     <svg:title>TexMaths</svg:title>
     <svg:desc>24§display§\sqrt{1985} - \sqrt{1984} =  \frac{1}{\sqrt{1985} + \sqrt{1984}} = \frac{1}{44.55 + 44.54} = 0.01122</svg:desc>
    </draw:frame>
    <presentation:notes draw:style-name="dp3">
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      <draw:text-box/>
     </draw:frame>
    </presentation:notes>
   </draw:page>
   <draw:page draw:name="page30" draw:style-name="dp5" draw:master-page-name="Default" presentation:presentation-page-layout-name="AL1T1">
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     <draw:text-box>
      <text:p>Round-off Example 2</text:p>
     </draw:text-box>
    </draw:frame>
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     <draw:text-box>
      <text:list text:style-name="L4">
       <text:list-item>
        <text:p>Consider computing <text:span text:style-name="T3">exp(-24)</text:span> via a truncated Taylor series</text:p>
        <text:p><text:span text:style-name="T35"/></text:p>
       </text:list-item>
       <text:list-item>
        <text:p>The error in this approximation is less than</text:p>
        <text:p/>
        <text:p/>
       </text:list-item>
       <text:list-item>
        <text:p>We can compute S(-24) by adding terms until the term is less than machine precision</text:p>
        <text:list>
         <text:list-item>
          <text:p>We find <text:span text:style-name="T3">S(-24) = 3.44305354288101977E-007</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p>But <text:span text:style-name="T3">exp(-24) = 3.77513454427909773E-011</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T7">The error is far bigger than the true answer!</text:span></text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
     </draw:text-box>
    </draw:frame>
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     <draw:text-box>
      <text:p><text:span text:style-name="T8">(Yakowitz &amp; Szidarovszky)</text:span></text:p>
     </draw:text-box>
    </draw:frame>
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     </draw:image>
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    <presentation:notes draw:style-name="dp3">
     <draw:page-thumbnail draw:style-name="gr4" draw:layer="layout" svg:width="13.968cm" svg:height="10.476cm" svg:x="3.81cm" svg:y="2.123cm" draw:page-number="30" presentation:class="page"/>
     <draw:frame presentation:style-name="pr15" draw:text-style-name="P11" draw:layer="layout" svg:width="17.271cm" svg:height="12.572cm" svg:x="2.159cm" svg:y="13.271cm" presentation:class="notes" presentation:placeholder="true" presentation:user-transformed="true">
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   </draw:page>
   <draw:page draw:name="page31" draw:style-name="dp5" draw:master-page-name="Default" presentation:presentation-page-layout-name="AL1T1">
    <draw:frame presentation:style-name="pr13" draw:layer="layout" svg:width="25.199cm" svg:height="1.957cm" svg:x="1.4cm" svg:y="0.537cm" presentation:class="title" presentation:user-transformed="true">
     <draw:text-box>
      <text:p>Round-off Example 2</text:p>
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    <draw:frame draw:style-name="gr6" draw:text-style-name="P14" draw:layer="layout" svg:width="10.16cm" svg:height="0.725cm" svg:x="10.668cm" svg:y="2.033cm">
     <draw:text-box>
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      <text:p/>
     </draw:image>
    </draw:frame>
    <draw:frame draw:style-name="gr8" draw:text-style-name="P25" draw:layer="layout" svg:width="26.67cm" svg:height="1.119cm" svg:x="1.524cm" svg:y="16.51cm">
     <draw:text-box>
      <text:p><text:span text:style-name="T36">Look at the terms—we are relying on cancellation to get our result</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <presentation:notes draw:style-name="dp3">
     <draw:page-thumbnail draw:style-name="gr4" draw:layer="layout" svg:width="13.968cm" svg:height="10.476cm" svg:x="3.81cm" svg:y="2.123cm" draw:page-number="31" presentation:class="page"/>
     <draw:frame presentation:style-name="pr15" draw:text-style-name="P11" draw:layer="layout" svg:width="17.271cm" svg:height="12.572cm" svg:x="2.159cm" svg:y="13.271cm" presentation:class="notes" presentation:placeholder="true" presentation:user-transformed="true">
      <draw:text-box/>
     </draw:frame>
    </presentation:notes>
   </draw:page>
   <draw:page draw:name="page32" draw:style-name="dp5" draw:master-page-name="Default" presentation:presentation-page-layout-name="AL1T1">
    <draw:frame presentation:style-name="pr13" draw:layer="layout" svg:width="25.199cm" svg:height="1.957cm" svg:x="1.4cm" svg:y="0.537cm" presentation:class="title" presentation:user-transformed="true">
     <draw:text-box>
      <text:p>Round-off Example 2</text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame presentation:style-name="pr14" draw:layer="layout" svg:width="26.924cm" svg:height="16.256cm" svg:x="0.508cm" svg:y="3.556cm" presentation:class="outline" presentation:user-transformed="true">
     <draw:text-box>
      <text:list text:style-name="L4">
       <text:list-item>
        <text:p>Instead recognize:</text:p>
        <text:p><text:span text:style-name="T35"/></text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T3">S(-1)</text:span> is well behaved, since each term is smaller in absolute magnitude than the previous.</text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T37">S(-1) = 0.36787944117144245</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T37">S(-1)</text:span><text:span text:style-name="T38">24</text:span><text:span text:style-name="T37"> = 3.77513454427912681E-011</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T37">exp(-24) = 3.77513454427909773E-011</text:span></text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr6" draw:text-style-name="P14" draw:layer="layout" svg:width="10.16cm" svg:height="0.725cm" svg:x="10.668cm" svg:y="2.033cm">
     <draw:text-box>
      <text:p><text:span text:style-name="T8">(Yakowitz &amp; Szidarovszky)</text:span></text:p>
     </draw:text-box>
    </draw:frame>
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     <draw:text-box>
      <text:p>Round-off Example 3</text:p>
     </draw:text-box>
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      <text:list text:style-name="L4">
       <text:list-item>
        <text:p>In spherically-symmetric codes (like a stellar evolution code), it is common to compute the volume of a spherical shell as</text:p>
        <text:p/>
        <text:p/>
        <text:list>
         <text:list-item>
          <text:p>This <text:span text:style-name="T7">relies on the cancellation of two very big numbers</text:span><text:span text:style-name="T5">.</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Rewriting reduces round-off errors:</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
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      <text:p>Comparing Floating Point #s</text:p>
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        <text:p>When comparing two floating point #s, we need to be careful</text:p>
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        <text:p>If you want to check whether 2 computed values are equal, instead of asking if</text:p>
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        <text:p>it is safer to ask whether they agree to within some tolerance</text:p>
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     <draw:text-box>
      <text:p>Associative Property</text:p>
     </draw:text-box>
    </draw:frame>
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      <text:list text:style-name="L4">
       <text:list-item>
        <text:p>You learned in grade school that: (a + b) + c = a + (b + c)</text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T7">Not true with floating point</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p>You can use parenthesizes to force order of operations</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>If you want to enforce a particular association, use parenthesis</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
     </draw:text-box>
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     <draw:text-box>
      <text:p>Associative Property</text:p>
     </draw:text-box>
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      <text:list text:style-name="L4">
       <text:list-item>
        <text:p>Adding lots of numbers together can compound round-off error</text:p>
        <text:list>
         <text:list-item>
          <text:p>One solution: sort and add starting with the smallest numbers</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Kahan summation (see reading list)</text:p>
        <text:list>
         <text:list-item>
          <text:p>Algorithm for adding sequence of numbers while minimizing roundoff accumulation</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Keeps a separate variable that accumulates small errors</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Requires that the compiler obey parenthesis</text:p>
         </text:list-item>
        </text:list>
        <text:p><text:span text:style-name="T4"/></text:p>
       </text:list-item>
      </text:list>
     </draw:text-box>
    </draw:frame>
    <presentation:notes draw:style-name="dp3">
     <draw:page-thumbnail draw:style-name="gr4" draw:layer="layout" svg:width="13.968cm" svg:height="10.476cm" svg:x="3.81cm" svg:y="2.123cm" draw:page-number="36" presentation:class="page"/>
     <draw:frame presentation:style-name="pr15" draw:text-style-name="P11" draw:layer="layout" svg:width="17.271cm" svg:height="12.572cm" svg:x="2.159cm" svg:y="13.271cm" presentation:class="notes" presentation:placeholder="true" presentation:user-transformed="true">
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     </draw:frame>
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   </draw:page>
   <draw:page draw:name="page37" draw:style-name="dp5" draw:master-page-name="Default" presentation:presentation-page-layout-name="AL1T1">
    <draw:frame presentation:style-name="pr13" draw:layer="layout" svg:width="25.199cm" svg:height="1.957cm" svg:x="1.4cm" svg:y="0.537cm" presentation:class="title" presentation:user-transformed="true">
     <draw:text-box>
      <text:p>Computer Languages</text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame presentation:style-name="pr16" draw:layer="layout" svg:width="26.924cm" svg:height="16.256cm" svg:x="0.508cm" svg:y="3.556cm" presentation:class="outline" presentation:user-transformed="true">
     <draw:text-box>
      <text:list text:style-name="L4">
       <text:list-item>
        <text:p><text:span text:style-name="T39">You can write any algorithm in any programming language—they all </text:span><text:span text:style-name="T39">provide the necessary logical constructs</text:span></text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T15">However, some languages make things much easier than others</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T40">C </text:span></text:p>
          <text:list>
           <text:list-item>
            <text:p><text:span text:style-name="T11">Excellent low-level machine access (operating systems are written in C)</text:span></text:p>
           </text:list-item>
           <text:list-item>
            <text:p><text:span text:style-name="T11">Multidimensional arrays are “kludgy”</text:span></text:p>
           </text:list-item>
          </text:list>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T40">Fortran</text:span><text:span text:style-name="T15"> (Formula Translate)</text:span></text:p>
          <text:list>
           <text:list-item>
            <text:p><text:span text:style-name="T11">One of the earliest complied languages</text:span></text:p>
           </text:list-item>
           <text:list-item>
            <text:p><text:span text:style-name="T11">Large code base of legacy code</text:span></text:p>
           </text:list-item>
           <text:list-item>
            <text:p><text:span text:style-name="T11">Modern Fortran offers many more conveniences than old Fortran</text:span></text:p>
           </text:list-item>
           <text:list-item>
            <text:p><text:span text:style-name="T11">Great support for arrays</text:span></text:p>
           </text:list-item>
          </text:list>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T40">Python</text:span></text:p>
          <text:list>
           <text:list-item>
            <text:p><text:span text:style-name="T11">Offers many high-level data-structures (lists, dictionaries, arrays)</text:span></text:p>
           </text:list-item>
           <text:list-item>
            <text:p><text:span text:style-name="T11">Great for quick prototyping, analysis, experimentation</text:span></text:p>
           </text:list-item>
           <text:list-item>
            <text:p><text:span text:style-name="T11">Increasingly popular in scientific computing</text:span></text:p>
           </text:list-item>
          </text:list>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
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    </draw:frame>
    <presentation:notes draw:style-name="dp3">
     <draw:page-thumbnail draw:style-name="gr4" draw:layer="layout" svg:width="13.968cm" svg:height="10.476cm" svg:x="3.81cm" svg:y="2.123cm" draw:page-number="37" presentation:class="page"/>
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     </draw:frame>
    </presentation:notes>
   </draw:page>
   <draw:page draw:name="page38" draw:style-name="dp5" draw:master-page-name="Default" presentation:presentation-page-layout-name="AL1T1">
    <draw:frame presentation:style-name="pr13" draw:layer="layout" svg:width="25.199cm" svg:height="1.957cm" svg:x="1.4cm" svg:y="0.537cm" presentation:class="title" presentation:user-transformed="true">
     <draw:text-box>
      <text:p>Computer Languages</text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame presentation:style-name="pr16" draw:layer="layout" svg:width="26.924cm" svg:height="16.256cm" svg:x="0.508cm" svg:y="3.556cm" presentation:class="outline" presentation:user-transformed="true">
     <draw:text-box>
      <text:list text:style-name="L4">
       <text:list-item>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T40">IDL</text:span><text:span text:style-name="T15"> </text:span></text:p>
          <text:list>
           <text:list-item>
            <text:p><text:span text:style-name="T11">Proprietary</text:span></text:p>
           </text:list-item>
           <text:list-item>
            <text:p><text:span text:style-name="T11">Great array language</text:span></text:p>
           </text:list-item>
           <text:list-item>
            <text:p><text:span text:style-name="T11">Modern (like object-oriented programming) features break the “clean-</text:span><text:span text:style-name="T11">ness” of the language</text:span></text:p>
           </text:list-item>
          </text:list>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T11">C++</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T11">Others</text:span></text:p>
          <text:list>
           <text:list-item>
            <text:p><text:span text:style-name="T11">Ruby, Perl, shell scripts, ...</text:span></text:p>
           </text:list-item>
          </text:list>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
     </draw:text-box>
    </draw:frame>
    <presentation:notes draw:style-name="dp3">
     <draw:page-thumbnail draw:style-name="gr4" draw:layer="layout" svg:width="13.968cm" svg:height="10.476cm" svg:x="3.81cm" svg:y="2.123cm" draw:page-number="38" presentation:class="page"/>
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     </draw:frame>
    </presentation:notes>
   </draw:page>
   <draw:page draw:name="page39" draw:style-name="dp5" draw:master-page-name="Default" presentation:presentation-page-layout-name="AL1T1">
    <draw:frame presentation:style-name="pr13" draw:layer="layout" svg:width="25.199cm" svg:height="1.957cm" svg:x="1.4cm" svg:y="0.537cm" presentation:class="title" presentation:user-transformed="true">
     <draw:text-box>
      <text:p>Computer Languages</text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame presentation:style-name="pr16" draw:layer="layout" svg:width="26.924cm" svg:height="16.256cm" svg:x="0.508cm" svg:y="3.556cm" presentation:class="outline" presentation:user-transformed="true">
     <draw:text-box>
      <text:list text:style-name="L4">
       <text:list-item>
        <text:p><text:span text:style-name="T7">Compiled languages</text:span> (Fortran, C, C++, ...)</text:p>
        <text:list>
         <text:list-item>
          <text:p>Compiled into machine code—machine specific</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Produce faster code (no interpretation is needed)</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Can offer lower level system access (especially C)</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T7">Interpreted languages</text:span> (python, IDL, perl, Java (kind-of) ...)</text:p>
        <text:list>
         <text:list-item>
          <text:p>Not converted into machine code, but instead interpreted by the interpreter</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Great for prototyping</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Can modify itself while running</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Platform independent</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Often has dynamic typing and scoping</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Many offer garbage collection</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
     </draw:text-box>
    </draw:frame>
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     <draw:text-box>
      <text:p><text:span text:style-name="T8">http://en.wikipedia.org/wiki/Interpreted_language</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <presentation:notes draw:style-name="dp3">
     <draw:page-thumbnail draw:style-name="gr4" draw:layer="layout" svg:width="13.968cm" svg:height="10.476cm" svg:x="3.81cm" svg:y="2.123cm" draw:page-number="39" presentation:class="page"/>
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    </presentation:notes>
   </draw:page>
   <draw:page draw:name="page40" draw:style-name="dp5" draw:master-page-name="Default" presentation:presentation-page-layout-name="AL1T1">
    <draw:frame presentation:style-name="pr13" draw:layer="layout" svg:width="25.199cm" svg:height="1.957cm" svg:x="1.4cm" svg:y="0.537cm" presentation:class="title" presentation:user-transformed="true">
     <draw:text-box>
      <text:p>Computer Languages</text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame presentation:style-name="pr16" draw:layer="layout" svg:width="26.924cm" svg:height="16.256cm" svg:x="0.508cm" svg:y="3.556cm" presentation:class="outline" presentation:user-transformed="true">
     <draw:text-box>
      <text:list text:style-name="L4">
       <text:list-item>
        <text:p><text:span text:style-name="T7">Vector languages</text:span></text:p>
        <text:list>
         <text:list-item>
          <text:p>Some languages are designed to operate on entire arrays at once (python + NumPy, many Fortran routines, IDL, ...)</text:p>
          <text:list>
           <text:list-item>
            <text:p>For interpreted languages, getting reasonable performance requires operating on arrays instead of explicitly writing loops</text:p>
            <text:list>
             <text:list-item>
              <text:p>Low level routines are written in compiled language and do the loop behind the scenes</text:p>
             </text:list-item>
            </text:list>
           </text:list-item>
           <text:list-item>
            <text:p>We&apos;ll see this in some detail when we discuss python</text:p>
           </text:list-item>
          </text:list>
         </text:list-item>
         <text:list-item>
          <text:p>Next-generation computing = GPUs ?</text:p>
          <text:list>
           <text:list-item>
            <text:p>Hardware is designed to do the same operations on many pieces of data at the same time</text:p>
           </text:list-item>
          </text:list>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
     </draw:text-box>
    </draw:frame>
    <presentation:notes draw:style-name="dp3">
     <draw:page-thumbnail draw:style-name="gr4" draw:layer="layout" svg:width="13.968cm" svg:height="10.476cm" svg:x="3.81cm" svg:y="2.123cm" draw:page-number="40" presentation:class="page"/>
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    </presentation:notes>
   </draw:page>
   <draw:page draw:name="page41" draw:style-name="dp5" draw:master-page-name="Default" presentation:presentation-page-layout-name="AL1T1">
    <draw:frame presentation:style-name="pr13" draw:layer="layout" svg:width="25.199cm" svg:height="1.957cm" svg:x="1.4cm" svg:y="0.537cm" presentation:class="title" presentation:user-transformed="true">
     <draw:text-box>
      <text:p>Object-Oriented Languages</text:p>
     </draw:text-box>
    </draw:frame>
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      <text:list text:style-name="L4">
       <text:list-item>
        <text:p><text:span text:style-name="T7">Python is an object-oriented language</text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Think of an object as a container that holds both data and functions (methods) that know how to operate on that date.</text:p>
        <text:list>
         <text:list-item>
          <text:p>Objects are build from a datatype called a class—you can create as many instances (objects) from a class as memory allows</text:p>
          <text:list>
           <text:list-item>
            <text:p>Each object will have its own memory allocated</text:p>
           </text:list-item>
          </text:list>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Objects provide a convenient way to package up data </text:p>
        <text:list>
         <text:list-item>
          <text:p>In Fortran, think of a derived type that also has it&apos;s own functions</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>In C, think of a struct that, again, also has it&apos;s own functions</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Everything, even integers, etc. is an object</text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T10">1 + 2</text:span> will be interpreted as <text:span text:style-name="T10">(1).__add__(2)</text:span> in python</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
     </draw:text-box>
    </draw:frame>
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   <draw:page draw:name="page42" draw:style-name="dp5" draw:master-page-name="Default" presentation:presentation-page-layout-name="AL1T1">
    <draw:frame presentation:style-name="pr13" draw:layer="layout" svg:width="25.199cm" svg:height="1.957cm" svg:x="1.4cm" svg:y="0.537cm" presentation:class="title" presentation:user-transformed="true">
     <draw:text-box>
      <text:p>Programming Paradigms</text:p>
     </draw:text-box>
    </draw:frame>
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     <draw:text-box>
      <text:p><text:span text:style-name="T8">(Wikipedia)</text:span></text:p>
     </draw:text-box>
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    </presentation:notes>
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    <draw:frame presentation:style-name="pr13" draw:layer="layout" svg:width="25.199cm" svg:height="1.957cm" svg:x="1.4cm" svg:y="0.537cm" presentation:class="title" presentation:user-transformed="true">
     <draw:text-box>
      <text:p>Arrays and Memory Layout</text:p>
     </draw:text-box>
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       <text:list-item>
        <text:p>Building block of many numerical methods</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Row vs. Column major: A(m,n)</text:p>
        <text:list>
         <text:list-item>
          <text:p>First index is called the row</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Second index is called the column</text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T7">Multi-dimensional arrays are flattened into a one-dimensional </text:span><text:span text:style-name="T7">sequence for storage</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Row-major (C, python): rows are stored one after the other</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Column-major (Fortran, matlab): columns are stored one after the other</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Ordering matters for:</text:p>
        <text:list>
         <text:list-item>
          <text:p>Passing arrays between languages</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Deciding which index to loop over first</text:p>
         </text:list-item>
        </text:list>
        <text:p/>
       </text:list-item>
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     <draw:text-box>
      <text:p><text:span text:style-name="T28">Row major</text:span></text:p>
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     <draw:text-box>
      <text:p><text:span text:style-name="T28">Column major</text:span></text:p>
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     <draw:text-box>
      <text:p>Roundoff vs. Truncation Error</text:p>
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       <text:list-item>
        <text:p>Roundoff error is just one of the errors we deal with</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Translating continuous mathematical expressions into discrete forms introduces <text:span text:style-name="T7">truncation error</text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Consider the Taylor series expansion for sine:</text:p>
        <text:p/>
        <text:p/>
       </text:list-item>
       <text:list-item>
        <text:p>If x is small, then we can neglect the higher-order terms (we truncate the series). <text:s/>This introduces an error.</text:p>
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      <text:p/>
     </draw:image>
     <svg:title>TexMaths</svg:title>
     <svg:desc>24§display§\sin(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} + \ldots</svg:desc>
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      <draw:text-box/>
     </draw:frame>
    </presentation:notes>
   </draw:page>
   <draw:page draw:name="page45" draw:style-name="dp5" draw:master-page-name="Default" presentation:presentation-page-layout-name="AL1T1">
    <draw:frame presentation:style-name="pr13" draw:layer="layout" svg:width="25.199cm" svg:height="1.957cm" svg:x="1.4cm" svg:y="0.537cm" presentation:class="title" presentation:user-transformed="true">
     <draw:text-box>
      <text:p>Roundoff vs. Truncation Error</text:p>
     </draw:text-box>
    </draw:frame>
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     <draw:text-box>
      <text:list text:style-name="L4">
       <text:list-item>
        <text:p>Roundoff error is just one of the errors we deal with</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Translating continuous mathematical expressions into discrete forms introduces <text:span text:style-name="T7">truncation error</text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Consider the definition of a derivative:</text:p>
        <text:p/>
        <text:p/>
       </text:list-item>
       <text:list-item>
        <text:p>We can&apos;t take the limit to 0. <text:s/>Our discrete version will be:</text:p>
        <text:p/>
        <text:p/>
       </text:list-item>
       <text:list-item>
        <text:p>If we choose h small enough, this should be a good approximation.</text:p>
       </text:list-item>
      </text:list>
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    </draw:frame>
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     <draw:text-box>
      <text:p><text:span text:style-name="T8">(Yakowitz &amp; Szidarovszky)</text:span></text:p>
     </draw:text-box>
    </draw:frame>
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      <text:p><text:span text:style-name="T41">Truncation error dominates</text:span></text:p>
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      <text:p><text:span text:style-name="T41">Roundoff error dominates</text:span></text:p>
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      <text:p>Potential Topics</text:p>
     </draw:text-box>
    </draw:frame>
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      <text:list text:style-name="L4">
       <text:list-item>
        <text:p><text:span text:style-name="T15">General python</text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T15">Advanced python / special modules</text:span></text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T11">Regular expressions</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T11">Command line/input file parsing</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T11">Filesystem operations</text:span></text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T40">NumPy</text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T40">SciPy</text:span><text:span text:style-name="T15"> and numerical methods</text:span></text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T11">Integration</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T11">ODEs</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T11">Curve fitting/optimization</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T11">Interpolation</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T11">Signal processing (FFT)</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T11">Linear algebra</text:span></text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
     </draw:text-box>
    </draw:frame>
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     <draw:text-box>
      <text:list text:style-name="L4">
       <text:list-item>
        <text:p><text:span text:style-name="T15">Plotting / visualization</text:span></text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T42">matplotlib</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T42">MayaVi</text:span></text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T15">Workflow management with </text:span><text:span text:style-name="T40">IPython</text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T15">Extending python w/ Fortran and C/C++</text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T15">Symbolic math with </text:span><text:span text:style-name="T40">SymPy</text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T15">Writing python applications</text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T15">GUI programming</text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T15">Unit testing</text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T15">Git/github</text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T43">Others? </text:span></text:p>
       </text:list-item>
      </text:list>
     </draw:text-box>
    </draw:frame>
    <presentation:notes draw:style-name="dp3">
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     <draw:text-box>
      <text:p>Who Are We?</text:p>
     </draw:text-box>
    </draw:frame>
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      <text:list text:style-name="L4">
       <text:list-item>
        <text:p>Physics</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Ecology &amp; Evolution</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Sociology</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Biology / Applied Ecology / Evolution</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Cognitive Science</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Integrative Neuroscience</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Applied Math &amp; Statistics</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Mechanical Engineering</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Psychology</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Marine and Atmospheric Science</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Earth &amp; Space Science—Geoscience </text:p>
       </text:list-item>
      </text:list>
     </draw:text-box>
    </draw:frame>
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     <draw:page-thumbnail draw:style-name="gr4" draw:layer="layout" svg:width="13.968cm" svg:height="10.476cm" svg:x="3.81cm" svg:y="2.123cm" draw:page-number="48" presentation:class="page"/>
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     <draw:text-box>
      <text:p>What Do You Want To Learn?</text:p>
     </draw:text-box>
    </draw:frame>
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      <text:list text:style-name="L4">
       <text:list-item>
        <text:p>From your posts (in some order by popularity):</text:p>
        <text:list>
         <text:list-item>
          <text:p>Replace R / matlab (most popular)</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>General (scientific) programming</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Data analysis</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Plotting &amp; Visualization (including 3-d visualization)</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Interacting with experiments (a la PsychoPy)</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>High performance computing</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Curve / parameter fitting</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>General scripting / glue for C + Fortran programs</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
     </draw:text-box>
    </draw:frame>
    <presentation:notes draw:style-name="dp3">
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      <text:p>Python Shell</text:p>
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       <text:list-item>
        <text:p>This is the standard (and most basic) interactive way to use python</text:p>
        <text:list>
         <text:list-item>
          <text:p>Runs in a terminal window</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Provides basic interactivity with the python language</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Simply type <text:span text:style-name="T3">python</text:span> (or <text:span text:style-name="T3">python3</text:span>) at your command prompt</text:p>
        <text:list>
         <text:list-item>
          <text:p>You can scroll back through the history using the arrows</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
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      <text:p>IPython Shell</text:p>
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       <text:list-item>
        <text:p>Type <text:span text:style-name="T44">ipython</text:span> (or <text:span text:style-name="T39">ipython3</text:span>) at your prompt</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Like the standard shell, this runs in a terminal, but provides many conveniences (type <text:span text:style-name="T44">%quickref</text:span> to see an overview)</text:p>
        <text:list>
         <text:list-item>
          <text:p>Scrollback history preserved between sessions</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Built-in help with ?</text:p>
          <text:list>
           <text:list-item>
            <text:p>function-name?</text:p>
           </text:list-item>
           <text:list-item>
            <text:p>object?</text:p>
           </text:list-item>
          </text:list>
         </text:list-item>
         <text:list-item>
          <text:p>Magics (<text:span text:style-name="T10">%lsmagic</text:span> lists all the magic functions)</text:p>
          <text:list>
           <text:list-item>
            <text:p><text:span text:style-name="T20">%run script</text:span>: runs a script </text:p>
           </text:list-item>
           <text:list-item>
            <text:p><text:span text:style-name="T20">%timeit</text:span>: times a command</text:p>
           </text:list-item>
           <text:list-item>
            <text:p>Lots of magics to deal with command history (including <text:span text:style-name="T20">%history</text:span>)</text:p>
           </text:list-item>
          </text:list>
         </text:list-item>
         <text:list-item>
          <text:p>Tab completion</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Run system commands (prefix with a !)</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Last 3 output objects are referred to via _, __, ___</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
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      <text:p>Jupyter Notebooks</text:p>
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       <text:list-item>
        <text:p>A web-based environment that combines code and output, plots, plain text/stylized headings, LaTeX, ...</text:p>
        <text:list>
         <text:list-item>
          <text:p>Notebooks can be saved and shared</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Viewable on the web via: http://nbviewer.ipython.org/</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Provides a complete view of your entire workflow</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Start with <text:span text:style-name="T45">jupyter</text:span><text:span text:style-name="T46"> </text:span><text:span text:style-name="T45">notebook</text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p>I&apos;ll provide notebooks for a lot of the lectures to follow so you can play along on your own</text:p>
        <text:list>
         <text:list-item>
          <text:p>The best way to learn is to experiment—download the notebooks and play around</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Discuss anything you don&apos;t understand in the discussion forum</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
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      <text:p>Python Scripts</text:p>
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       <text:list-item>
        <text:p>Scripts are a non-interactive means of writing python code</text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T3">filename.py</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Can be executable by adding:</text:p>
          <text:p><text:span text:style-name="T3">#!/usr/bin/env python</text:span></text:p>
          <text:p><text:span text:style-name="T47">as the first line and setting the executable bit for the file</text:span></text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T9">This is also the way that you write python modules that can be </text:span><text:span text:style-name="T3">import</text:span><text:span text:style-name="T9">-ed into other python code (more on that later...)</text:span></text:p>
       </text:list-item>
      </text:list>
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      <text:p>Python 2.x vs. Python 3</text:p>
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        <text:p>See <text:a xlink:href="https://wiki.python.org/moin/Python2orPython3" xlink:type="simple">https://wiki.python.org/moin/Python2orPython3</text:a></text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Mostly about cleaning up the language and making things consistent</text:p>
        <text:list>
         <text:list-item>
          <text:p>e.g. <text:span text:style-name="T3">print</text:span> is a statement in python 2.x but a function in 3.x</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Some trivial differences</text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T3">.pyc</text:span> are now stored in a <text:span text:style-name="T3">__pycache__</text:span> directory</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Some gotyas:</text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T3">1/2</text:span> will give different results between python 2 and 3</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>It&apos;s possible to write code that works with both python 2 and 3—often we will do so by <text:span text:style-name="T3">import</text:span>ing from <text:span text:style-name="T3">__future__</text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T19">We will focus on python 3.x</text:span></text:p>
       </text:list-item>
      </text:list>
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      <text:p>Python 2.x vs. Python 3</text:p>
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        <text:p>Write for both</text:p>
        <text:list>
         <text:list-item>
          <text:p>In python 2.6+, do </text:p>
          <text:p><text:span text:style-name="T3">from __future__ import print_function</text:span> </text:p>
          <text:p>and then use the new <text:span text:style-name="T3">print()</text:span> style</text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T3">exec cmd</text:span> becomes <text:span text:style-name="T3">exec(cmd)</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Some small changes to how <text:span text:style-name="T3">__init__.py</text:span> are done (more on this later)</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>One some systems, you can have python 2.x and 3.x installed side by side</text:p>
        <text:list>
         <text:list-item>
          <text:p>May need to install packages twice, e.g. <text:span text:style-name="T3">python-numpy</text:span> and <text:span text:style-name="T3">python3-numpy</text:span></text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
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      <text:p>Class Organization</text:p>
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       <text:list-item>
        <text:p>We’ll work mostly with Jupyter notebooks from now one (with a few exceptions)</text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T6">Each week, I’ll ask you to work through some notebooks on your </text:span><text:span text:style-name="T6">own, outside of class</text:span></text:p>
        <text:list>
         <text:list-item>
          <text:p>These will always be posted on the class website</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Great opportunity to ask questions on slack</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>The hope is that we’ll get a lot of the basic concepts for the week covered by working through the notebooks</text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T6">In class, we’ll work on some exercises together</text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p>We’ll fine-tune some of this as we go through the semester</text:p>
       </text:list-item>
      </text:list>
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      <text:p>Let’s Play</text:p>
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       <text:list-item>
        <text:p>There are a number of notebooks on our website to demonstrate some core ideas</text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T4">Data types</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T4">Advanced data types</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T4">Control flow</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T4">Functions</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T4">Classes</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T4">Modules</text:span></text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
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      <text:p>Lists vs. Arrays</text:p>
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       <text:list-item>
        <text:p>Lists (note that python lists are not implemented as a simple linked-list: <text:s/>see <text:span text:style-name="T11"><text:a xlink:href="http://docs.python.org/2/faq/design.html#how-are-lists-implemented" xlink:type="simple">http://docs.python.org/2/faq/design.html#how-are-lists-implemented</text:a></text:span><text:s/>)</text:p>
        <text:list>
         <text:list-item>
          <text:p>Implemented as a variable-length array</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Can store multiple different datatypes in a single list</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Easy to add items to the end (increasing list length)</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Accessing <text:span text:style-name="T3">a[i]</text:span> is independent of list length (unlike a traditional linked list)</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Arrays:</text:p>
        <text:list>
         <text:list-item>
          <text:p>Generally used for fixed-length, homogeneous data</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Less overhead than a list</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>We&apos;ll use a special array library (NumPy) for performance later</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
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      <text:p>Intro to Python: Functions</text:p>
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      <text:list text:style-name="L4">
       <text:list-item>
        <text:p>No distinction between functions and procedures/subroutines</text:p>
        <text:list>
         <text:list-item>
          <text:p>Always return something. <text:s/>If not explicitly set, then None</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Can have default values for arguments, optional arguments, <text:s/>variable number of arguments</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Can return multiple values, objects</text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T4">Function examples...</text:span></text:p>
       </text:list-item>
      </text:list>
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      <text:p>Intro to Python: Classes</text:p>
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      <text:list text:style-name="L4">
       <text:list-item>
        <text:p><text:span text:style-name="T7">Classes</text:span> are a fundamental concept of object-oriented programming</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>An <text:span text:style-name="T7">object</text:span> is an instance of a class</text:p>
        <text:list>
         <text:list-item>
          <text:p>Carries data (state) and has methods that can act on that data</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Objects are easy to pass around </text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Simplest use is just as a container to carry associated data together (similar to a struct in C)</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>Inheritance, operator overloading, ... all supported. <text:s/>See the tutorial.</text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T4">Classes example...</text:span></text:p>
       </text:list-item>
      </text:list>
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      <text:p>Intro to Python: Modules</text:p>
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       <text:list-item>
        <text:p><text:span text:style-name="T7">Modules</text:span> are a collection of python statements, functions, variables, grouped together in a file ending with .py</text:p>
        <text:list>
         <text:list-item>
          <text:p>Can be <text:span text:style-name="T7">import</text:span>ed to be used by any routine</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>Python includes a host of useful modules </text:p>
         </text:list-item>
         <text:list-item>
          <text:p>You can define your own. <text:s/>Python will look in the current directory and then in the PYTHONPATH</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Modules have their own <text:span text:style-name="T7">namespace</text:span></text:p>
        <text:list>
         <text:list-item>
          <text:p>Variables (even global variables) don&apos;t clash with those with the same name in the importing program</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>You can change the name of a module on import or import it into the current namespace (*). <text:s/></text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>General practice: put all the imports at the top of your code</text:p>
       </text:list-item>
      </text:list>
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      <text:p>Intro to Python: Modules</text:p>
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      <text:list text:style-name="L4">
       <text:list-item>
        <text:p>Example: <text:span text:style-name="T3">myprofile.py</text:span>—a simple timing module for measuring code performance</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>In the <text:span text:style-name="T4">python</text:span> shell:</text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T3">import myprofile</text:span></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T3">help(myprofile)</text:span></text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Note that this module can also be run on its own</text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T3">if __name__ == &quot;__main__&quot;: </text:span><text:span text:style-name="T47">clause at the end</text:span></text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T48">Let&apos;s look at an example of using this module in a notebook</text:span></text:p>
       </text:list-item>
      </text:list>
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      <text:p>Intro to Python: Exceptions</text:p>
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       <text:list-item>
        <text:p><text:span text:style-name="T7">Exceptions</text:span> are raised if an action you tried (e.g. opening a file) fails. <text:s/></text:p>
        <text:list>
         <text:list-item>
          <text:p>Left alone, the code will abort, printing the exception</text:p>
         </text:list-item>
         <text:list-item>
          <text:p>You can catch the exception, and take appropriate action to fix the situation </text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p>Built-in exceptions have particular names that let you check for specific failure modes</text:p>
        <text:list>
         <text:list-item>
          <text:p>Allows you to write robust code for other users</text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T4">Exceptions example...</text:span></text:p>
       </text:list-item>
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      <text:p>Intro to Python: I/O</text:p>
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      <text:list text:style-name="L4">
       <text:list-item>
        <text:p>Basic I/O</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>File I/O</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>CSV reading</text:p>
       </text:list-item>
       <text:list-item>
        <text:p>INI file reading</text:p>
       </text:list-item>
      </text:list>
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      <text:p>Caveats</text:p>
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      <text:list text:style-name="L4">
       <text:list-item>
        <text:p><text:span text:style-name="T15">Slicing (we&apos;ll look at this with arrays soon)</text:span></text:p>
       </text:list-item>
       <text:list-item>
        <text:p><text:span text:style-name="T15">Function defaults: default values are only evaluated once. <text:s/></text:span></text:p>
        <text:list>
         <text:list-item>
          <text:p><text:span text:style-name="T11">From python tutorial:</text:span></text:p>
          <text:p><text:span text:style-name="T49"/></text:p>
          <text:p/>
          <text:p/>
          <text:p/>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T11">Prints:</text:span></text:p>
          <text:p><text:span text:style-name="T50"/></text:p>
          <text:p><text:span text:style-name="T49"/></text:p>
         </text:list-item>
         <text:list-item>
          <text:p><text:span text:style-name="T11">Correct way:</text:span></text:p>
         </text:list-item>
        </text:list>
       </text:list-item>
      </text:list>
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      <text:p text:style-name="P28"><text:span text:style-name="T51">def f(a, L=[]):</text:span></text:p>
      <text:p text:style-name="P28"><text:span text:style-name="T51"><text:s text:c="4"/></text:span><text:span text:style-name="T51">L.append(a)</text:span></text:p>
      <text:p text:style-name="P28"><text:span text:style-name="T51"><text:s text:c="4"/></text:span><text:span text:style-name="T51">return L</text:span></text:p>
      <text:p text:style-name="P28"><text:span text:style-name="T51"/></text:p>
      <text:p text:style-name="P28"><text:span text:style-name="T51">print f(1)</text:span></text:p>
      <text:p text:style-name="P28"><text:span text:style-name="T51">print f(2)</text:span></text:p>
      <text:p text:style-name="P28"><text:span text:style-name="T51">print f(3)</text:span></text:p>
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      <text:p text:style-name="P28"><text:span text:style-name="T51">[1]</text:span></text:p>
      <text:p text:style-name="P28"><text:span text:style-name="T51">[1, 2]</text:span></text:p>
      <text:p text:style-name="P28"><text:span text:style-name="T51">[1, 2, 3]</text:span></text:p>
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      <text:p text:style-name="P28"><text:span text:style-name="T51">def f(a, L=None):</text:span></text:p>
      <text:p text:style-name="P28"><text:span text:style-name="T51"><text:s text:c="4"/></text:span><text:span text:style-name="T51">if L is None:</text:span></text:p>
      <text:p text:style-name="P28"><text:span text:style-name="T51"><text:s text:c="8"/></text:span><text:span text:style-name="T51">L = []</text:span></text:p>
      <text:p text:style-name="P28"><text:span text:style-name="T51"><text:s text:c="4"/></text:span><text:span text:style-name="T51">L.append(a)</text:span></text:p>
      <text:p text:style-name="P28"><text:span text:style-name="T51"><text:s text:c="4"/></text:span><text:span text:style-name="T51">return L</text:span></text:p>
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