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mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman","serif";} </style> <![endif]--> <meta http-equiv="Content-Language" content="en-us"><!--[if gte mso 9]><xml> <o:shapedefaults v:ext="edit" spidmax="1026"/> </xml><![endif]--><!--[if gte mso 9]><xml> <o:shapelayout v:ext="edit"> <o:idmap v:ext="edit" data="1"/> </o:shapelayout></xml><![endif]--></head> <body style="" lang="EN-US" link="blue" vlink="purple"> <div class="WordSection1"> <p class="MsoPlainText" style="text-align: center;" align="center"><span style="font-size: 24pt; font-family: &quot;Times New Roman&quot;,&quot;serif&quot;;">KPM-MEC Seminars, April 2014<o:p></o:p></span></p> <p class="MsoPlainText"><span style="font-family: &quot;Courier New&quot;;"><u1:p>&nbsp;</u1:p></span></p> <p class="style3">I am thrilled to be invited to spend time in Bogor, Indonesia talking with students, teachers and parents. I am very grateful to my host Ridwan Saputra of the <a href="http://www.kpmseikhlasnya.com/home">Mathematics Education Clinic</a> for this invitation. </p> <p class="style3">Below is a list of topics I expect to discuss. </p> <p class="style1"><span class="style21"><u><span style="font-size: 13.5pt;"><a href="PlacevalueProblems.pdf">Place Value Problems</a> </span></u></span><span class="style21"><span style="font-size: 13.5pt;">is an essay on the representation of rational and irrational numbers in our standard powers of 10 <span class="GramE">notation</span>. The sister essay Fusing Dots should be read soon after this one. In PVP we explore problems with digits. For example why do the two-digit numbers </span></span><span class="SpellE"><span class="style51"><span style="font-size: 13.5pt;">ab</span></span></span><span class="GramE"><span class="style21"><span style="font-size: 13.5pt;">&nbsp; and</span></span></span> <span class="SpellE"><span class="style61"><span style="font-size: 13.5pt;">ba</span></span></span><span class="style21"><span style="font-size: 13.5pt;"> always differ by a multiple of 9.</span></span><u1:p></u1:p></p> <p class="style1"><span class="style21"><span style="font-size: 13.5pt;"><a href="../Indonesia/FusingDots.pdf">Fusing Dots</a>, also known as Exploding Dots, is the beautiful idea of <a href="http://www.jamestanton.com/">James <span class="SpellE">Tanton</span></a>. We use it here to create exotic number systems: Fibonacci, base phi, Cantor (aka factorial), fractional and negative base.&nbsp;</span></span></p><p class="style1"><span class="style21"><span style="font-size: 13.5pt;"><a href="Divisors.pdf">Divisor Problems</a> involve finding the number and the nature of the divisors of a composite integer. </span></span></p> <p class="style1"><span class="style21"><span style="font-size: 13.5pt;"><a href="Digit%20problems.pdf"><span class="GramE">Problems with Digits</span></a><span class="GramE"> is</span> a set of problems designed to reinforce the place-value ideas of the first two essays. These are harder problems that might not be introduced in the course.</span></span><o:p></o:p></p> <p class="style3"><u1:p><a href="KenKenMathworks2.pdf">KenKen</a> is a puzzle I love. </u1:p></p> <p class="MsoNormal"><span class="style21"><span style="font-size: 13.5pt;"><a href="../Indonesia/BigBoxProblems.pdf">Boxes and Cubes</a> is an essay on visualizing geometric configurations. For example suppose all six faces on an n x n x n cube composed of n cubed unit cubes are painted red. How many of the cubes have some red paint on them?</span></span><span style=""> <o:p></o:p></span></p> <p class="style1"><span class="style21"><span style="font-size: 13.5pt;">The central topic in many undergraduate discrete math courses is counting, and these two papers focus on that topic<span class="GramE">:</span></span></span><span style="font-size: 13.5pt;"><br> <span class="style21"><a href="counting.pdf">Counting Problems</a> is a set of problems about counting the number of samples taken from a population when we can answer the two questions, Does order matter? <span class="GramE">and</span> Are we allowed to repeat an item? This is a terrific topic for students interested in competitions (very popular in the United States).&nbsp;</span></span></p> <p class="style1"><span class="style21"><span style="font-size: 13.5pt;"><a href="../Indonesia/Bugs.pdf">Bug Problems</a><u1:p> is a collection of problems involving a bug that crawls around the plane with a fixed itinerary. Questions like where is the bug after 2012 minutes and when will the bug get to a certain point are typical. The level of mathematical maturity needed is slightly higher for this topic.</u1:p></span></span></p> <p class="style1"><span class="style21"><span style="font-size: 13.5pt;"><u1:p>Here's a short paper with <a href="ThreeProblems.pdf">three problems</a>, one counting and two place value related. </u1:p></span></span></p> <p class="MsoNormal"><span style=""><o:p>&nbsp;</o:p></span></p> </div> </body></html>