Wednesday, September 12, 2018

New in Version 3.5 of Applied Discrete Structures

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:

In exercises:
  • replaced 2.4 exercises 5 and 6 with lattice paths exercises
  • added exercise 6 to section 4.1
  • added bakery exercise at end of section 5.1
  • added exercise #11 to 11.4
  • exercise change 11.7 new #5, old #5 moved to #10
  • changed exercise 4 of 13.4

Also, there is a new section (12.6)  on  linear equations mod 2.

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.