tag:blogger.com,1999:blog-51459449511438313202018-09-16T21:01:33.392-07:00Applied Discrete StructuresKen Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.comBlogger48125tag:blogger.com,1999:blog-5145944951143831320.post-79741446372781114982018-09-12T07:30:00.002-07:002018-09-12T07:30:30.035-07:00New in Version 3.5 of Applied Discrete Structures<div><div><span style="font-family: Helvetica;"><span style="font-size: 12px;">The latest version of Applied Discrete Structures (3.5) has a few differences from the previous version. Here is a list of the most significant changes:</span></span></div><div><span style="font-family: Helvetica;"><span style="font-size: 12px;"><br /></span></span></div><div><span style="font-family: Helvetica;"><span style="font-size: 12px;">In exercises:</span></span></div><ul style="font-family: Helvetica; font-size: 12px;"><li><span style="background-color: rgba(255, 255, 255, 0);">replaced 2.4 exercises 5 and 6 with lattice paths exercises</span></li><li><span style="background-color: rgba(255, 255, 255, 0);">added exercise 6 to section 4.1</span></li><li><span style="background-color: rgba(255, 255, 255, 0);">added bakery exercise at end of section 5.1</span></li><li><span style="background-color: rgba(255, 255, 255, 0);">added exercise #11 to 11.4</span></li><li><span style="background-color: rgba(255, 255, 255, 0);">exercise change 11.7 new </span><a class="issue-link js-issue-link" data-error-text="Failed to load issue title" data-id="221836361" data-permission-text="Issue title is private" data-url="https://github.com/klevasseur/ads/issues/5" href="https://github.com/klevasseur/ads/pull/5" style="background-color: rgba(255, 255, 255, 0); box-sizing: border-box; text-decoration: none;">#5</a><span style="background-color: rgba(255, 255, 255, 0);">, old </span><a class="issue-link js-issue-link" data-error-text="Failed to load issue title" data-id="221836361" data-permission-text="Issue title is private" data-url="https://github.com/klevasseur/ads/issues/5" href="https://github.com/klevasseur/ads/pull/5" style="background-color: rgba(255, 255, 255, 0); box-sizing: border-box; text-decoration: none;">#5</a><span style="background-color: rgba(255, 255, 255, 0);"> moved to #10</span></li><li><span style="background-color: rgba(255, 255, 255, 0);">changed exercise 4 of 13.4</span></li></ul></div><div style="font-family: Helvetica; font-size: 12px;"><span style="background-color: rgba(255, 255, 255, 0);"><br /></span></div><div style="font-family: Helvetica; font-size: 12px;"><span style="background-color: rgba(255, 255, 255, 0);">Also, there is a new section (12.6) on linear equations mod 2.</span></div><br class="Apple-interchange-newline" />Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-34244165584424348382018-07-31T05:37:00.000-07:002018-07-31T05:37:44.757-07:00The Ternary Number SystemEvery integer is the sum of distinct signed powers of three. That this is true is nice non-elementary, yet accessible, induction proof. It's not an exercise in <i><a href="http://discretemath.org/" target="_blank">Applied Discrete Structures</a></i>, but could be given as a challenge to your students. The code implements the ideas of the proof, so it serves as a hint (or a solution?)<br /><br />Several years ago, I had a WebMathematica page that computed the ternary representation of an integer. That page is no longer in existence, and I discovered that it several broken links to it were on sequence pages of The On-Line Encyclopedia of Integer Sequences, such as sequence <a href="https://oeis.org/A072998" target="_blank">A072998</a>. As a replacement, I created a SageMath interact (similar to a Wolfram Demonstration).<br /><br />The SageMath interact converts integers from 1 to 1000 to the ternary number system. It is contained within a Sage Cell, so anyone can view and tinker with the code. Any suggestions for improving it are welcome!<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/--KlDgZFkhzk/W2BWyAlwCfI/AAAAAAAAcU4/k_imlV46lZcd7ANymLOwnJ70d0d-mGTWQCLcBGAs/s1600/Screen%2BShot%2B2018-07-31%2Bat%2B8.31.02%2BAM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="778" data-original-width="1574" height="196" src="https://3.bp.blogspot.com/--KlDgZFkhzk/W2BWyAlwCfI/AAAAAAAAcU4/k_imlV46lZcd7ANymLOwnJ70d0d-mGTWQCLcBGAs/s400/Screen%2BShot%2B2018-07-31%2Bat%2B8.31.02%2BAM.png" width="400" /></a></div><br />Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-3862679685270595962018-07-01T08:04:00.000-07:002018-07-01T08:04:10.626-07:00New version (3.5), Custom versions<span style="font-family: Times, Times New Roman, serif;">Version 3.5 of Applied Discrete Structures is now in full distribution in all three formats, html, pdf and print. The full 16 chapters with solutions to half of the exercises runs over 600 pages. For those who use the html format, the length doesn’t matter much; however, for the print and even the pdf format it may be desirable to have only a subset the chapters or sections. </span><br /><span style="font-family: Times, Times New Roman, serif;"><br /></span><span style="font-family: Times, Times New Roman, serif;">I’ve been distributing the book in two parts, corresponding to content that is normally covered in our two semester sequence at UMass Lowell (Chapters 1-10 in Part 1- Fundamentals; Chapters 11-16 in Part II- Algebraic Structures). Not many people buy these print versions, but I prefer the lighter books. I don’t use them all that frequently since I tend to use html in class, but still use them to record typos (finally getting less frequent!) and making notes for improvements. </span><br /><span style="font-family: Times, Times New Roman, serif;"><br /></span><span style="font-family: Times, Times New Roman, serif;">One of the nice things about PreTeXt is that it’s quite easy to create custom versions. If anyone would like some subset of the book in any format, let me know and I’ll create it. The only glitch I foresee is that if a reference is made to a non-included part of the text, a broken link will appear. I think that can be handled minimal extra work. </span><br /><span style="font-family: Times, Times New Roman, serif;"><br /></span><h3><span style="font-family: Times, Times New Roman, serif;">Significant Additions in Version 3.5</span></h3><div style="color: #454545; font-stretch: normal; line-height: normal;"><span style="font-family: Times, Times New Roman, serif;">Section 2.4: new exercises 5 and 6 on lattice paths</span></div><div style="color: #454545; font-stretch: normal; line-height: normal;"><span style="font-family: Times, Times New Roman, serif;">Section 5.1: added exercise 8 motivating the definition of matrix multiplication </span></div><div style="color: #454545; font-stretch: normal; line-height: normal;"><span style="font-family: Times, Times New Roman, serif;">Section 11.4: added exercise 11 on inverting a linear function. </span></div><div style="color: #454545; font-stretch: normal; line-height: normal; min-height: 23.5px;"><span style="font-family: Times, Times New Roman, serif;"><br /></span></div><br /><div style="color: #454545; font-stretch: normal; line-height: normal;"><span style="font-family: Times, Times New Roman, serif;">New section: 12.6 Linear Equations over the Integers Mod 2</span></div>Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-6448053926852837422018-03-25T13:01:00.003-07:002018-03-25T13:10:17.162-07:00New Section: Linear Equations mod 2<html xmlns="http://www.w3.org/1999/xhtml"><head> <link href="https://faculty.uml.edu/math/math_style.css" rel="stylesheet" type="text/css"></link> <script type="text/x-mathjax-config"> MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}}); </script><script async="" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.3/latest.js?config=TeX-MML-AM_CHTML"></script><body lang="EN-US"> The next version of Applied Discrete Structures will include a new section, 12.6, on systems of linear equations over \(\mathbb{Z}_2\). We work with these systems in the coding theory section (15.5) but it was presumed that students could figure out how to solve these systems on the fly. That is often the case, but some students had difficulties.<br /> <br />A pdf of the most recent draft of the new section is available at <a href="https://discretemath.org/Section_12_6_V2.pdf">https://discretemath.org/Section_12_6_V2.pdf</a> </body></head></html>Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-76612036313030667532017-06-05T07:42:00.000-07:002017-06-05T07:42:41.306-07:00Version 3.3, WeBWork collectionTwo bits of news:<br /><br />Version 3.3 of Applied Discrete Structures are available now in all three formats, HTML, PDF, and Print. <br /><br />The full print version is 588 pages, so I've resisted including WeBWork exercises, although there are a few in the HTML version. I really don't see the utility of WeBWork in print or pdf, so I've decided to develop a separate WeBWork problems document in Mathbook XML..oops, <b>PreTeXt</b> (see a <a href="https://groups.google.com/forum/?fromgroups#!topic/mathbook-xml-support/6cAu4bD7334" target="_blank">recent announcement</a>). A preliminary version that is mostly based on problems from the National Problem Library (NPL) and is at <a href="http://faculty.uml.edu/klevasseur/webwork_ads/preface-1.html">http://faculty.uml.edu/klevasseur/webwork_ads/preface-1.html</a>. <br /><br />GitHub repository is <span style="background-color: white; font-family: Menlo; font-size: 14px;"><a href="https://github.com/klevasseur/webwork_ads.git">https://github.com/klevasseur/webwork_ads.git</a></span><br /><br />The coverage is uneven and I'd welcome contributions of problems in areas that are light. Once the problem lists have been fully edited, short descriptions will be added since the problems themselves reside in knowls. Right now the descriptions are just the addresses of the problems within the NPL.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-qUvN5snnj-k/WTVtGaD5UAI/AAAAAAAAWFU/nBCq1sWsqn8sKRVJDH0WMace6fjOnLavwCLcB/s1600/Screen%2BShot%2B2017-06-05%2Bat%2B10.38.42%2BAM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1138" data-original-width="1600" height="227" src="https://2.bp.blogspot.com/-qUvN5snnj-k/WTVtGaD5UAI/AAAAAAAAWFU/nBCq1sWsqn8sKRVJDH0WMace6fjOnLavwCLcB/s320/Screen%2BShot%2B2017-06-05%2Bat%2B10.38.42%2BAM.png" width="320" /></a></div>Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-65922111520503023652016-12-31T07:09:00.000-08:002016-12-31T07:09:20.336-08:00Conversion to MathBook XML is Complete!<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-uNhbEhLDkK4/WGfDAk1KaII/AAAAAAAAT7k/E4tFJOQYDIkP26Z1g_93xb5Ccb-ObATyACEw/s1600/screen.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="310" src="https://4.bp.blogspot.com/-uNhbEhLDkK4/WGfDAk1KaII/AAAAAAAAT7k/E4tFJOQYDIkP26Z1g_93xb5Ccb-ObATyACEw/s400/screen.png" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">HTML front page</td></tr></tbody></table><br /><br />It took about a year, but <b>Applied Discrete Structures </b>is completely converted to <a href="https://mathbook.pugetsound.edu/" target="_blank">MathBook XML</a>. The source code has been converted to both HTML and LaTeX, available at <a href="http://faculty.uml.edu/klevasseur/ads2" target="_blank">http://faculty.uml.edu/klevasseur/ads2</a>. The main site also has a link to the source code on GitHub. For the minority who prefer hard copy the main site also has links to lulu.com. You can buy Part 1 (Chapters 1-10), Part 2 (Chapters 11-16), or the combined Parts 1 and 2.<br /><div class="separator" style="clear: both; text-align: center;"><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-S3ajy6mhep4/WGfDAY5mTmI/AAAAAAAAT7g/us69jkK_r10xrSCPDTDP56HkrxUsT8tKgCEw/s1600/cover.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://4.bp.blogspot.com/-S3ajy6mhep4/WGfDAY5mTmI/AAAAAAAAT7g/us69jkK_r10xrSCPDTDP56HkrxUsT8tKgCEw/s200/cover.jpg" width="153" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Cover to the full print version.</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">The content is essentially the same previous versions, but there are several improvements/features in the new version. </div><ul><li>The pdf version is extensively hyperlinked and the HTML version has <a href="http://aimath.org/knowlepedia/" target="_blank">knowl</a> links.</li><li>Sage notes have been expanded, and the HTML version includes live, editable Sage cells.</li><li>There is a table of notation and an index. </li><li>An appendix on algorithms has been expanded to include a section on the Invariant Relation Theorem. </li><li>A few <a href="http://webwork.maa.org/" target="_blank">WeBWork</a> exercises have been added to the HTML version, with an eye toward adding many more in the future. </li></ul><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-Rb3LTzNhzog/WGfDArVf0VI/AAAAAAAAT7o/3osFon9nPOA8E8VmdMffCEJ4_4I-usrNgCEw/s1600/ww.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="258" src="https://1.bp.blogspot.com/-Rb3LTzNhzog/WGfDArVf0VI/AAAAAAAAT7o/3osFon9nPOA8E8VmdMffCEJ4_4I-usrNgCEw/s400/ww.png" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">A WeBWork exercises embedded in Section 15.3.</td></tr></tbody></table><br />Two significant deletions: Mathematica notes have been removed, and the introduction to Logic Design section of Chapter 13 has been left out for now. I've had trouble finding a good utility for drawing simple logical gates. This is on the to-do list.<br /><br />There are several other things my to-do list. They include more a user survey, better web tracking, more WeBWork, and better cover art (I'm in a rut with the cover design!). Some students have requested background information on dictionaries and iterables. I may try writing up short introductions to these topics if I can find a way to integrate math into the discussion, or maybe I'll just point a good tutorial if I can find one I like.<br /> <br />Happy NewYear!<br /><br /><br /><br />Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-65768599647803989842016-04-30T10:57:00.001-07:002016-09-06T04:08:50.974-07:00Chapters 1-3 and Algorithms Appendix converted to MathBook XMLThe first three chapters of <b>Applied Discrete Structures</b> have been converted to MathBook XML. There will be some adjustments to be made (like adding solutions to many of the exercises) but these chapters are in pretty good shape. <br /><br />At the request of Rob Krueger (Concordia U.), I've also updated and converted the short appendix on Algorithms that we had in the 1989 edition. I added a section on the Invariant Relation Theorem that I've been meaning to write up for a while. Having the ability to include Sage Cells into the text really enhances the html version.<br /><br />The html version is available at <a href="http://faculty.uml.edu/klevasseur/ads2" target="_blank">http://faculty.uml.edu/klevasseur/ads2</a><br /><br />After finals and a few other chair related tasks (64 days left as I type this!), I'll make a LaTex version available.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-gSaDKDhEsv8/VyTxBHLbgVI/AAAAAAAAAsI/3Y5iGzMZ_Zsyph3yHC0S9EhlLhQDEz8tgCLcB/s1600/while-flow.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="270" src="https://3.bp.blogspot.com/-gSaDKDhEsv8/VyTxBHLbgVI/AAAAAAAAAsI/3Y5iGzMZ_Zsyph3yHC0S9EhlLhQDEz8tgCLcB/s320/while-flow.png" width="320" /></a></div><br />Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-66303103591331400042016-01-04T08:42:00.001-08:002016-01-04T09:04:53.007-08:00Chapter 1 of ADS using Mathbook XML<br /><div><span style="font-family: 'Open Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif;">A reformatting of Chapter 1: Set Theory of </span><em style="font-family: 'Open Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif;">Applied Discrete Structures</em><span style="font-family: 'Open Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif;"> was just completed using </span><a href="http://mathbook.pugetsound.edu/" style="font-family: 'Open Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif;" target="_blank">Mathbook XML</a><span style="font-family: 'Open Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif;">, an application for authors of scientific articles, textbooks and monographs initiated by Rob Beezer, U. of Puget Sound.</span></div><div><span style="font-family: 'Open Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif;"><br /></span></div><div><div><div style="font-family: 'Open Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif; line-height: 1.25em; margin-bottom: 1.25em;">The chapter was converted by exporting the Mathematica Notebook to XML and then making many adjustments by hand to Mathbook XML. I wanted to do this as a learning process. Next, I want to explore ways to convert remaining <i>Mathematica</i> Notebooks using their natural structure with regular expressions. Whether that works out remains to be seen.</div></div><div><span style="font-family: 'Open Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif;">The source code for Chapter 1 and some abbreviated front matter was converted to html and can be viewed at </span><a href="http://faculty.uml.edu/klevasseur/ads-html/" style="font-family: 'Open Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif;" target="_blank">http://faculty.uml.edu/klevasseur/ads-html/ </a><span style="font-family: Open Sans, Helvetica Neue, Helvetica, Arial, sans-serif;">. One of the advantages of this conversion is that the html sizes nicely to whatever you view it on, from a phone to a desktop browser. Also it will be the easy to convert to LaTeX and other formats.</span></div><div><span style="font-family: Open Sans, Helvetica Neue, Helvetica, Arial, sans-serif;"><br /></span></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-MvEqolnkzfA/VoV-w-mXNkI/AAAAAAAAAq0/SEh19gG_ybk/s1600/Screen%2BShot%2B2015-12-31%2Bat%2B2.14.39%2BPM.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="312" src="http://2.bp.blogspot.com/-MvEqolnkzfA/VoV-w-mXNkI/AAAAAAAAAq0/SEh19gG_ybk/s400/Screen%2BShot%2B2015-12-31%2Bat%2B2.14.39%2BPM.png" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">A first look at the new format.</td></tr></tbody></table></div>Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com1tag:blogger.com,1999:blog-5145944951143831320.post-85867193145905496272015-11-17T12:22:00.000-08:002016-01-04T09:05:31.401-08:00Developments in Open Source Textbooks: mathbook XML<b>Rob Beezer</b> at University of Puget Sound is spearheading the development of <b><a href="http://mathbook.pugetsound.edu/index.html" target="_blank">MathBook XML</a></b>, which is "a lightweight XML application for authors of scientific articles, textbooks and monographs." I'm seriously considering a conversion from <i>Mathematica</i> Notebooks to this new format. <br /><br />I spend a bit of time playing with the current version this week and converted a very small web page with a few sage cells. Then I <a href="http://faculty.uml.edu/klevasseur/ADS2/sage/sage_cell_graphs/" target="_blank">exported to html</a>.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-OZFSOSbGvYc/VkuLIF-z9RI/AAAAAAAAAqY/QIwxEA7xaVs/s1600/Screen%2BShot%2B2015-11-17%2Bat%2B3.14.55%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="228" src="http://2.bp.blogspot.com/-OZFSOSbGvYc/VkuLIF-z9RI/AAAAAAAAAqY/QIwxEA7xaVs/s320/Screen%2BShot%2B2015-11-17%2Bat%2B3.14.55%2BPM.png" width="320" /></a></div><br /><br />It wasn't obvious to me what code should appear in the output field of the sage sections, which would be all graphics in this case. It isn't a problem for the html version since the cells can be evaluated. <a href="http://faculty.uml.edu/klevasseur/ADS2/sage/sage_cell_graphs/sage_graphs.pdf" target="_blank">Converted to LaTeX</a>, the lack of output is a problem, but it still looks good.<br /><div><div><br /></div><div><br /></div></div>Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-69150505256729315282015-11-12T04:14:00.000-08:002016-01-04T09:50:50.836-08:002015 Economic Impact - rough estimates.<h2><span style="color: blue;">2015 Economic Impact of <i>Applied Discrete Structures</i></span></h2><br />We had a event on campus where open source textbooks were one of the featured subjects, so I took the opportunity to put together the numbers for the economic impact of <i>Applied Discrete Structures</i> (<i>ADS</i>) for the calendar year 2015. <br /><br /><h2><span style="font-size: small;">UML Impact</span></h2>It's fairly easy to identify the impact here at UML. I counted 405 students who took the first semester of our discrete math sequence (new course numbers MATH.3210/3220 Discrete Structures I/II). I continue to assume that the average cost of our previous text with a mix of new/used purchases would be $140. If 90% use the pdf and save the whole amount and the rest buy the hard copy of <i>ADS. </i> That translates to a savings of about $55,000 for UML students in 2015.<br /><br /><h2><span style="font-size: small;">Outside Impact</span></h2>The impact on students outside of UML is tougher to estimate. I know of 14 adoptions in 2015, but have no idea how many more there were. Working from just what I know, and assuming 25 students per adoptions with the same assumptions about the alternate book and hard copy usage, I come up with around $47,000.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-zdNoC2uSFC4/VkSB_97ZyEI/AAAAAAAAAqA/hTGjLb74S9I/s1600/100K.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="84" src="http://4.bp.blogspot.com/-zdNoC2uSFC4/VkSB_97ZyEI/AAAAAAAAAqA/hTGjLb74S9I/s200/100K.jpg" width="200" /></a></div><br /><h2><span style="font-size: small;">Conclusion</span></h2>Combining these two amounts, I'm confident we've saved students over $100,000 in 2015. If you used <i>ADS</i> and are not on the <a href="http://applied-discrete-structures.wiki.uml.edu/adoptions" target="_blank">adoption list</a>, please <a href="mailto:kenneth_levasseur@uml.edu" target="_blank">let me know</a> so that I can update my estimate.<br /><br /><br />Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com4tag:blogger.com,1999:blog-5145944951143831320.post-19940278804111932842015-08-24T11:44:00.000-07:002015-11-12T18:11:05.322-08:00Code for Spanning Trees in a Sage Cell It's been over a year since I've posted to this blog, mostly because I've been busy being department chair. As I type this, I've got 313 days left on my term. So the end is almost in sight. I posted a page with code for computing the spanning trees of a graph a while ago on <a href="http://faculty.uml.edu/klevasseur/ads2/sage_cell/sage_cell.html">http://faculty.uml.edu/klevasseur/ads2/sage_cell/sage_cell.html</a> but I'm not sure how much use it's had.<br /><br />Here is a video that shows how to use this resource:<br /><br /><video controls="" height="360" width="480"> <source src="http://faculty.uml.edu/klevasseur/ADS2/videos/sage_spanning_trees/sage_spanning_trees.mp4" type="video/mp4"></source>Your browser does not support the video tag. </video><br />A comment from who finds this resource useful will make it more likely that I will find the time to add more!<br />Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-88662479522380915292014-01-22T08:00:00.001-08:002014-01-22T08:02:50.723-08:00Update from JMM2014: WeBWork, LaTeX, and Sage CellsI was in Baltimore for a couple of days last week and concentrated on talks related to open source texts and software. I spoke in one of the sessions on open source texts, outlining this project.<br /><br />There were three main things I added to my "to do" list based on the talks I attended.<br /><ol><li>Start developing problem sets for <b>WeBWork</b>. To that end, I've arranged for out WeBWork server at UMass Lowell to updated, and once that's done I hope to get started on developing problems.</li><li>Start the process of converting our book to <b>LaTeX</b>. One of the talks, by David Farmer, convinced me that getting our "source content" into a mainstream format is the way to go.</li><li>Embedded <b>Sage Cells</b> seem to be a good to introduce the use of Sage in mathematics. I hope to gradually add content in that form to our web page. I did a short test page showing how to create graphs at <a href="http://faculty.uml.edu/klevasseur/ads2/sage_cell/sage_cell_graphs.html">http://faculty.uml.edu/klevasseur/ads2/sage_cell/sage_cell_graphs.html</a></li></ol><div>This should keep me busy for a while!</div><div><br /></div><div>By the way, the Baltimore Convention Center is next door to Camden Yards and also near the birthplace of Babe Ruth.</div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-KSJmmBqZipw/Ut_qhlQ3wwI/AAAAAAAAAMc/eOAk_-Kjxyg/s1600/IMG_4207.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-KSJmmBqZipw/Ut_qhlQ3wwI/AAAAAAAAAMc/eOAk_-Kjxyg/s1600/IMG_4207.jpg" height="400" width="300" /></a></div><div><br /></div>Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-39467520276535061872013-12-30T06:07:00.000-08:002013-12-30T06:08:13.981-08:00Open Source Math Texts at the 2014 JMMThere are going to be sessions on open source math texts at the 2014 Joint Math Meetings in Baltimore January 15-18. The sessions are on Friday January 17 , 8-10:55 and 3-4:55. I'm speaking on our text, <b>Applied Discrete Structures</b>. Because of a family obligation, I requested a late time, and I got the last time slot in the afternoon session, at 4:40. My Title is "What a Difference 30 Years Makes! -Adventures in Mathematics Textbook Publishing." The sessions will be in Room 349 of the Baltimore Convention Center.<br /><br />I'd love to meet up with anyone who has been using our book!<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://www.jointmathematicsmeetings.org/images/JMMMD2014-web-header.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="55" src="http://www.jointmathematicsmeetings.org/images/JMMMD2014-web-header.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="http://upload.wikimedia.org/wikipedia/commons/a/ac/Baltimore_Convention_Center_2005.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://upload.wikimedia.org/wikipedia/commons/a/ac/Baltimore_Convention_Center_2005.jpeg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br />Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-8816526832592367302013-04-23T08:00:00.001-07:002013-04-23T11:34:18.011-07:00<h2>A sphere in binary 11-space</h2><div>In my discrete math class this week, did an example of a code that encodes three bits to eleven bits and can correct all two-bit errors. This particular code was not meant to be particularly optimal, but for one particular example I ran with 3,000,000 bits, the number of errors was roughly 1/4 of what was predicted by the probabilities, given that two bit errors can be corrected. There were 38 failures instead of a predicted 155. This is no mystery since the packing of spheres in {0,1}^11 wasn't expected to be all that tight, and three bit errors can often be corrected. </div><div><br /></div><div>The encoding function is </div> (a, b, c) ----> (a, b, c, a + b, a + c, b + c, a + b + c, a + b, a + c, b + c, a + b + c)<br /><div><br /></div><div><br /></div><div>To get an visualize the situation, I create the graph below. The vertices are some of the points in the code space: the sphere of radius three centered around one of the code words. The color coding is</div><div><ul><li>Yellow: the code word - I used the zero word, but the space is symmetric everywhere.</li><li>Blue: points one unit from the code word</li><li>Green: points two units from the code word</li><li>Brown: points three units from the code word and further that three units from all other code words.</li><li>Red: points three units from the code word but also three units from another code word.</li></ul><div>So all but the Red points, if received, will correct to the most likely transmitted word. Only the Red ones are questionable and there is no most likely correction.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-2LHAQqICkfE/UXagHrvuyFI/AAAAAAAAAJY/CuMBGyjkJtY/s1600/Sphere3of3to11code.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="633" src="http://1.bp.blogspot.com/-2LHAQqICkfE/UXagHrvuyFI/AAAAAAAAAJY/CuMBGyjkJtY/s640/Sphere3of3to11code.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div></div></div>Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-5271311444916739682013-04-22T05:24:00.000-07:002013-04-23T08:04:32.900-07:00<h2>The Economic Impact of <i>Applied Discrete Structures</i>.</h2><div>I've been starting to collect data to document the economic impact of <a href="http://faculty.uml.edu/klevasseur/ads2/" target="_blank">Applied Discrete Structures</a>. In a class using our text, the cost to a student ranges from $0, if he/she uses the pdf, to $30 a hard copy of purchased. A rough estimate of the percentage students that buy a hard copy is 15%. Prior to using our text at UMass Lowell, we used a text that cost $160 new, and around $120 used. So a <i>very</i> conservative estimate of the impact on student costs would be $120 times the number of students enrolled in discrete math classes using our book. Here are the estimated student savings, also with very conservative estimates for enrollments starting Fall 2011 through the Spring 2013 semester:</div><div><br /></div><div>UMass Lowell: 300 students have saved a collective $36,000</div><div>Other Colleges: 75 students have saved a collective $9,000</div><div><br /></div><div>That's $45,000 that students have saved in the first couple of years that the book has been available. We're hoping that with increased exposure on open source textbook websites, we can dramatically increase the impact outside of UMass Lowell.</div><div><br /></div><div>So far we are listed on the following sites:</div><div><ul><li><a href="http://taste.merlot.org/opentextbooks.html" target="_blank">Merlot Open Textbook Services</a></li><li><a href="https://open.umn.edu/opentextbooks/" target="_blank">University of Minnesota Open Textbook Catalog</a></li><li><a href="http://www.aimath.org/textbooks/textbooklist.html" target="_blank">The American Institute of Mathematics </a></li><li><a href="http://linear.ups.edu/curriculum.html" target="_blank">U. of Puget Sound Open Content Math Curriculum</a></li><li><a href="http://www.collegeopentextbooks.org/" target="_blank">collegeopentextbooks.org</a></li></ul></div><div><br /></div><div><br /></div><div><br /></div>Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-40636652296186542452013-03-12T06:57:00.000-07:002013-04-23T08:05:06.854-07:00Version 2.0 is now availableVersion 2.0 of Applied Discrete Structures is now available both in pdf form and printed, from lulu.com.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-mbq-nu8qTO8/UT80EUgcDQI/AAAAAAAAAIo/3BVHKMNIdaU/s1600/ads_v2_cover.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-mbq-nu8qTO8/UT80EUgcDQI/AAAAAAAAAIo/3BVHKMNIdaU/s1600/ads_v2_cover.jpg" /></a></div>Here are a few notes on the new version:<br />• The full version is now 494 pages, with two blank pages added for the lulu version.<br />• The pdf's are still absolutely free!<br />• The prices of the full printed version and Part 2 (Chapters 11-16) are the same as before. The price of Part 1 (Chapters 1-10) has dropped by $1.<br />• The most significant change in content is in the chapter on Relations, which has been reorganized. It's logical flow is a bit smoother now, thanks to suggestions from Dan Klain. Other chapters where a few alterations have been made: Chapters 10 and 13.<br />• The pdf's now have links to the first page in each chapter in the table of contents.<br /><br /><br />For pdf copies: http://faculty.uml.edu/klevasseur/ads2/<br />For printed copied: <a href="http://www.lulu.com/shop/search.ep?type=Print+Products&contributorId=1060169&sorter=relevance-desc">lulu.com</a>Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-55581083270034695392013-02-15T05:26:00.001-08:002013-04-23T08:05:39.150-07:00Applied Discrete Structures: a three year status reportThe impetus for <i>Applied Discrete Structure</i> was my attendance at a Sage Day at the Clay Math Institute in December 2009. Al Doerr and I got our copyright back from Pearson a few months after that and so we are just about three years into this project. <br /><br />Probably the most important milestone was March of last year, when we assembled a complete version of the book and made it available for free on our web site and also for a reasonable price ($30) on lulu.com. <br /><br />In the past year there have been two other milestones:<br /><br /><ul><li>We are now listed on the American Math Institute's <a href="http://www.aimath.org/textbooks/" target="_blank">Open Textbook Initiative</a> site.</li><li>We have several outside adoptions: classes at the University of the Puget Sound, Grinnell College, Casper College and Luzurne Community College are all using our book.</li></ul><div>March seems to be a good time to update the book in anticipation of fall adoptions, so I've been working V2 of the full pdf. It's really just about ready, but I'm going to allow a bit more time pick up more errata from V1. Particular thanks to students at Luzurne CC, who have found several typos. </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-VGJRs9EjfdM/UR43VRDrDDI/AAAAAAAAAIY/e8UVHdbiXKk/s1600/2000px-Dominomatrix.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://1.bp.blogspot.com/-VGJRs9EjfdM/UR43VRDrDDI/AAAAAAAAAIY/e8UVHdbiXKk/s320/2000px-Dominomatrix.png" width="160" /></a></div><div><br /></div>Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-33082320708327990762012-11-15T15:08:00.002-08:002013-04-23T08:06:16.445-07:00Now listed with the American Institute of Mathematics <b>Applied Discrete Structures</b> is now listed among the Approved Textbooks by the American Institute of Mathematics as part of their <a href="http://www.aimath.org/textbooks/textbooklist.html">Open Textbook Initiative</a>.<br /><br /><blockquote>The American Institute of Mathematics (AIM) seeks to encourage the adoption of open source mathematics textbooks. The AIM Editorial Board has developed evaluation criteria to identify open source books that are suitable for use in traditional university courses. The Editorial Board maintains a list of Approved Textbooks which have been judged to meet these criteria. </blockquote><div class="separator" style="clear: both; text-align: center;"><a href="http://www.aimath.org/"><img border="0" src="http://4.bp.blogspot.com/-QbFT25bIdHE/UKVv9UNmvzI/AAAAAAAAAIE/RtpDXIVFX5s/s1600/aim210.gif" /></a></div><br /><br />If you're looking for a text for a college/university mathematics course, consider books on this list!Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-23509775520510695962012-11-14T11:31:00.000-08:002016-03-03T10:31:18.593-08:00Sage Trees<h1>New Sage Worksheet: Trees</h1>I was updating a few things in Chapter 10, Trees, and took the opportunity to do a few things with Sage. <a href="http://faculty.uml.edu/klevasseur/ADS2/sage/ADS2_Trees.sws">ADS2_Trees.sws</a><br><ul><li>Cataloging trees by degree sequence. </li><li>Finding a minimal spanning tree using Kruskal's algorithm. </li><li>The binary tree sorting algorithm </li></ul>Actually, the last item only uses Python.<br><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-9jO4QOJxzY4/UKPxTVZ4hoI/AAAAAAAAAH0/Q7S69IrF8p8/s1600/st.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="http://3.bp.blogspot.com/-9jO4QOJxzY4/UKPxTVZ4hoI/AAAAAAAAAH0/Q7S69IrF8p8/s320/st.png" width="205"></a></div>Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-41031939564974429182012-10-13T10:10:00.000-07:002012-10-13T10:11:03.085-07:00Video illustrating the construction of minimal spanning trees.<p>I've been tweeking Chapter 10 (Trees) and put together a short example of how to construct a minimal spanning tree for a weighted undirected graph. <hr><object width="425" height="344"><param name="movie" value="http://www.youtube.com/v/KhqmecZlToI&hl=en&fs=1"></param><param name="allowFullScreen" value="true"></param><embed src="http://www.youtube.com/v/KhqmecZlToI&hl=en&fs=1" type="application/x-shockwave-flash" allowfullscreen="true" width="425" height="344"></embed></object>Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-53465531655403439812012-08-04T06:48:00.000-07:002012-08-04T17:56:24.586-07:00Revised version of Chapter 6: Relations<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-A9I1GbHM6T8/UB0my6TWx1I/AAAAAAAAAHY/hyPYg57L6Do/s1600/Hasse.png" imageanchor="1" style="clear:right; float:right; margin-left:1em; margin-bottom:1em"><img border="0" height="198" width="320" src="http://1.bp.blogspot.com/-A9I1GbHM6T8/UB0my6TWx1I/AAAAAAAAAHY/hyPYg57L6Do/s320/Hasse.png" /></a></div> <p>A revised version of Chapter 6 is now available. It will become part of Version 2 of the larger pdf versions of Applied Discrete Structures in 2013. The most significant changes are: <ul><li>Hasse diagrams are not introduced until partial orderings are defined, avoiding some confusion that was reported with the original version of the chapter. <li>Congrence modulo m has been added as an example of an equivalence relation on the integers. </ul><a href="http://applied-discrete-structures.wiki.uml.edu/Chapter+6">Click here to get either a pdf or <i>Mathematica</i> Notebook of Chapter 6</a>Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-43714021274241713782012-04-18T10:08:00.004-07:002012-04-18T10:14:04.652-07:00Sage notebook on relationsI filled in for Al Doerr in his class this morning and he asked me to cover some material on relations. So I took that opportunity to figure out how to implement some relations in Sage. It went pretty well. One exception is that in squaring an adjacency matrix of a relation, I'd like to get a simple adjacency matrix with just 0's and 1's. The way I did the calculations, I got the numbers of different paths of length 2 connecting the vertices. That's fine except that the graphs of the squared relations become messy. If anyone knows how to fix this, I'd appreciate the help.<br /><br /><a href="http://www.sagenb.org/home/pub/4715">http://www.sagenb.org/home/pub/4715</a>Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-79597892027846378562012-04-04T10:19:00.004-07:002012-04-04T10:26:57.226-07:00Two Part Version of Applied Discrete StructuresApplied Discrete Structures is now available in either a single volume or in a two part version:<br /> Part 1 - Fundamentals<br /> Part 2 - Algebraic Structures<br />It broken according to how the two semesters of discrete math are taught at UMass Lowell. We did this for a few reasons. One is that many of our students only need to take the first semester. Also, the full version, whether as a pdf or a printed book, is quite large (484 pages). <br /><br />Information on the one and two part versions (as free pdf's or printed copies from lulu.com) is available on our web site:<br /><a href="http://faculty.uml.edu/klevasseur/ads2 ">http://faculty.uml.edu/klevasseur/ads2 </a>Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-8886312903200944742012-03-20T06:23:00.003-07:002012-03-20T06:29:10.393-07:00Change in Creative Commons LicenseIt's come to my attention that the Creative Commons License that we had posted:<br /><br /> Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License<br /><br />did not allow instructors to bundle selected chapters for distribution to students due to the "no derivatives" restriction. This wasn't our intent, in fact this is precisely what we do for instructors at UMass Lowell. To remedy the situation, the following license has been posted on our web site.<br /><br /><a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/3.0/us/"><img alt="Creative Commons License" style="border-width:0" src="http://i.creativecommons.org/l/by-nc-sa/3.0/us/88x31.png" /></a><br /><span xmlns:dct="http://purl.org/dc/terms/" href="http://purl.org/dc/dcmitype/Text" property="dct:title" rel="dct:type">Applied Discrete Structures</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="http://faculty.uml.edu/klevasseur/ads2/" property="cc:attributionName" rel="cc:attributionURL">Alan Doerr & Kenneth Levasseur</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/3.0/us/">Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License</a><br /><br />Most of the existing files still list the No Derivatives restriction a this time, but they will be updated as we proceed.Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0tag:blogger.com,1999:blog-5145944951143831320.post-5757602178128703022012-03-01T07:39:00.003-08:002012-03-01T07:41:10.714-08:00Full Text now available on lulu.comVersion 1.0 of the text, all 16 chapters with solutions to odd-numbered exercises is now available on lulu.com.<br /><br /><a href="http://www.lulu.com/commerce/index.php?fBuyContent=12627004"><img src="http://static.lulu.com/images/services/buy_now_buttons/us/book.gif?20120131141155" border="0" alt="Support independent publishing: Buy this book on Lulu."></a>Ken Levasseurhttps://plus.google.com/111805345442289204264noreply@blogger.com0