Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica ® [Hardcover]

Sriram Pemmaraju (Author), Steven Skiena (Author)

Book Description

ISBN-10: 0521806860 | ISBN-13: 978-0521806862 | Publication Date: December 8, 2003

With examples of all 450 functions in action plus tutorial text on the mathematics, this book is the definitive guide to Experimenting with Combinatorica, a widely used software package for teaching and research in discrete mathematics. Three interesting classes of exercises are provided--theorem/proof, programming exercises, and experimental explorations--ensuring great flexibility in teaching and learning the material. The Combinatorica user community ranges from students to engineers, researchers in mathematics, computer science, physics, economics, and the humanities. Recipient of the EDUCOM Higher Education Software Award, Combinatorica is included with every copy of the popular computer algebra system Mathematica.

Editorial Reviews

Review

"This book is the definitive reference guide to Combinatorica -- an extension of the popular computer software, Mathematica -- with examples of the 450 combinatorics functions. The authors developed the newest version of this software that has dramatic improvements in graphical processing performance, representation, visualization, and many brand new functions...This book is highly recommended. It is a well organized and readable textbook for beginners and intermediate students." Leonardo

Book Description

Experimenting with Combinatorica, a widely used software package for teaching and research in discrete mathematics, provides an exciting new way to learn combinatorics and graph theory. With examples of all 450 functions in action plus tutorial text on the mathematics, this book is the definitive guide to Combinatorica. Three interesting classes of exercises are provided -- theorem/proof, programming exercises, and experimental explorations, providing great flexibility in teaching and learning the material.The Combinatorica user community ranges from students to engineers to researchers in mathematics, computer science, physics, economics, and the humanities. Combinatorica, which has received the EDUCOM Higher Education Software Award, is included with every copy of the popular computer algebra system Mathematica.

Product Details

• Hardcover: 494 pages
• Publisher: Cambridge University Press (December 8, 2003)
• Language: English
• ISBN-10: 0521806860
• ISBN-13: 978-0521806862
• Product Dimensions: 9.7 x 8.7 x 1.1 inches
• Shipping Weight: 2.7 pounds
• Average Customer Review: 3.3 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #1,841,638 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

4 of 4 people found the following review helpful:

5.0 out of 5 stars It fills a Mathematica niche to perfection, October 28, 2009

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
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This review is from: Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica ® (Hardcover)

This book has two primary uses, as a reference for the Combinatorica extension to Mathematica or as a textbook in a course in combinatorics and graph theory where Mathematica is extensively used. In both cases it is the best resource on the market. Combinatorica is an extremely powerful package that allows for very sophisticated operations to be performed in combinatorics and on graphs. However, there is no coverage of other areas of discrete mathematics.
The structure of the book is that it is split up into sections. For each section, there is a short textual description of the operation, a section of code illustrating the appropriate function(s) and the output from that code. The output is sometimes in the form of a textual listing and at other times an actual diagram. A complete listing of the functions and their actions is given in an appendix.
While this book is not one that could be used in a general course in discrete mathematics, it is an exceptional example of one that fills a niche to perfection. If you have any interest in doing combinatoric or graphing operations with Mathematica, then you have to look no further.

Published in Journal of Recreational Mathematics, reprinted with permission.

7 of 9 people found the following review helpful:

3.0 out of 5 stars Way too specialized to be a stand alone discrete math text, November 17, 2009

By 

Jaime Moreno (Farmersville,CA) - See all my reviews
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Amazon Verified Purchase

This review is from: Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica ® (Hardcover)

I think the best parts of this book was the illustration overleafs for each chapter. There are some pretty cool images created using Combinatorica and Mathematica. I got this book to help me with my Discrete math course and with that in mind it wasn't as helpful as I thought it would be. I think the reason is that it's really a book about Combinatorica and how to use it with Mathematica and how the latest version is faster and how the functions were written. So in order to use it effectively you have to already be quite familiar with discrete math and graph theory to use this. There are plenty of examples to try and play with though if you can get them to run. I used Mathematica 7 and I would get a lot of obsolete command warnings or errors when trying to run the examples from the book. The book website says they have an updated version of Combinatorica but I didn't try that. Also, there are some exercises but no answers provided for any of them. There is also a complete listing of all the Combinatorica in the book but no clear indication if it's now included with the latest version of Mathematica which would be helpful. I don't see how this book could be used as a primary text for a discrete math course unless you had an excellent instructor to add all the material the book is missing and to walk you though putting the example in the book to best use. It makes more sense as a laboratory type book. This book will appeal most to those that use Mathematica with discrete math and find the documentation lacking or want to find out how the Combinatorica functions were programmed. Will also appeal to the more visual people like myself. I figured visualizing the different discrete math structures would help me solve my discrete math problems but the effort getting it to work in mathematica negates the extra time spent. If you are using it just to supplement a discrete math course as I did you probably won't benefit as much.
I must admit it was kind fun seeing Mathematica choke up on trying to spit out a 20x20 gridgraph! Never seen it do that before on my quadcore pc.

4 of 5 people found the following review helpful:

1.0 out of 5 stars Does not get past frustrating., June 25, 2011

By 

Anthony Knape "Anthony" (nowhere in Texas) - See all my reviews

Amazon Verified Purchase

This review is from: Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica ® (Paperback)

This is a giant frustrating experience. A high percentage of the examples do not work in current versions of Mathematica (7 and 8). Particularly in the very, very beginning of the book when the reader is just trying to get anything to work, there is pitiful effort to update the user experience by both Wolfram and Combinatorica.com. The only problem, THIS is all that there is. Your only guide to Combinatorica on Mathematica. Amazon needs to add a ZERO STAR choice. Perhaps even negative stars. So here it is 'one star' for lack of effort. No bona fide updates on the websites.

Shame on Wolfram. Shame on Pemmaraju and Skiena.

The problems that I see are as follows.

1) The dictionary problem. To understand Table, See Sum and Products. To understand Sum and Products, See Iterator Notation. To understand Iterator Notation, See Repetitive Operators 'Do Loops'.

2) Mathematica makes heavy use of parametric overloading. Sometimes it works with one parameter. Sometimes 2 parameters. Sometimes 3 parameters. Sometimes 4. So the examples that you see make use of many different syntax structures but this is only cryptically explained.

3) You would buy 'Computational Discrete Mathematics' to do combinatorics. Duh. But before you can understand the syntax in the book, you need to know these sections in Mathematica: "Some General Notations and Conventions", "Sums and Products", "Making Tables of Values", "Repetitive Operators 'Do Loops', "Symbolic Calculations", "Iterator Notation" and "Mathematics and Algorithms". Otherwise you just go in circles. Cut and paste code. Break the code. Have no clue. Cut and paste more code.

4) A lot of the code as mentioned was written for versions long ago.

5) If you experience trouble because of the previous 4 reasons, but you need to do combinatorics, then you will find this book helpful - A beginners guide to Mathematica by David M. McMahon, Daniel M. Topa. You can read it on Google Books and still understand a lot of it even though select pages are omitted.

6) To invoke the Combinatorica Package

Do not use <<DiscreteMath `Combinatorica`
Do not use << Combinatorica`
Do not use Needs["Combinatorica`"]

DO USE `Combinatorica
At least this will get you started.

Below this point is my original rant. But you should understand my point already.

Be aware that once you are in `Combinatorica you will break other functionality of Mathematica. I will document some of these soon.

Next Google 'mathematica compatibility guide' find the updates for DiscreteMath and Graphics. Note the changes that affect many commands in (Pemmaraju/Skiena, 2006).

Next Google 'Mathematica 8 Documentation'. Save this link because you will need to come back often.

Next Google 'combinatorica package tutorial'. A lot of what you want to do has new commands. The only way that I can figure out what to do is to Google each command. In particular, do not use ShowGraph. Instead Google 'mathematica 8 butterfly graph' and you will see something like below. (But you may have to close you Mathematica program. And then reopen Mathematica and paste in the code.) It is random. The Google query pattern is Mathematica 8 + Noun of the thing you want to create. Many/most of the Method Commands used in the book have changed.

This worked for me.

{ButterflyGraph[1], ButterflyGraph[2]}

Table[ButterflyGraph[2, b, PlotLabel -> Row[{"base", b}, "-"]], {b, 2,
3}]

It actually works. So page 10 In(26) would be {ButterflyGraph[3]}

But this is just one of the patterns. In other places it will be different. In closing, this scenario would be bad for an open source product. I think we are all paying for Mathematica and paying for "Computational Discrete Mathematics", so (in my mind) this irritated rant has some justification. I don't think I should have to waste days of my time. I'm not getting paid. So why aren't the people who are getting paid not taking any ownership for their products?