Tuesday, July 31, 2018

The Ternary Number System

Every 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 Applied Discrete Structures, 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?)

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 A072998.  As a replacement, I created a SageMath interact (similar to a Wolfram Demonstration).

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!

Sunday, July 1, 2018

New version (3.5), Custom versions

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.  

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. 

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. 

Significant Additions in Version 3.5

Section 2.4: new exercises 5  and 6 on lattice paths
Section 5.1: added exercise 8 motivating the definition of matrix multiplication 
Section 11.4: added exercise 11 on inverting a linear function. 

New section: 12.6 Linear Equations over the Integers Mod 2

Sunday, March 25, 2018

New Section: Linear Equations mod 2

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.

A pdf of the most recent draft of the new section is available at https://discretemath.org/Section_12_6_V2.pdf

Monday, June 5, 2017

Version 3.3, WeBWork collection

Two bits of news:

Version 3.3 of Applied Discrete Structures are available now in all three formats, HTML, PDF, and Print.

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, PreTeXt (see a recent announcement).  A preliminary version that is mostly based on problems from the National Problem Library (NPL) and is at http://faculty.uml.edu/klevasseur/webwork_ads/preface-1.html.

GitHub repository is https://github.com/klevasseur/webwork_ads.git

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.

Saturday, December 31, 2016

Conversion to MathBook XML is Complete!

HTML front page

It took about a year, but Applied Discrete Structures is completely converted to MathBook XML.  The source code has been converted to both HTML and LaTeX, available at http://faculty.uml.edu/klevasseur/ads2.  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.

Cover to the full print version.

The content is essentially the same previous versions, but there are several  improvements/features in the new version. 
  • The pdf version is extensively hyperlinked and the HTML version has knowl links.
  • Sage notes have been expanded, and the HTML version includes live, editable Sage cells.
  • There is a table of notation and an index. 
  • An appendix on algorithms has been expanded to include a section on the Invariant Relation Theorem. 
  • A few WeBWork exercises have been added to the HTML version, with an eye toward adding many more in the future. 
A WeBWork exercises embedded in Section 15.3.

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.

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.
Happy NewYear!