Important Code Error, p. 451

There is an error in the file on disk and in the book re KempeChain1. The following is correct. The ReplacePart call in book is incorrect.

KempeChain1[{v1_,vv2_},coloring_List]:=(answer=coloring;chold={};chain={v1};
While[(success=(Flatten[{vv2}]⋂chain=={}))&&chain≠chold,{chold,chain}={chain,Union[chain,Union@@(Neighbors1[gadj,#,coloring,coloring[[Flatten[{v1,vv2}]]]]&)/@chain]}];
If[success,
Do[answer=ReplacePart[answer,j->Complement[coloring[[Flatten[{v1,vv2}]]],{answer[[j]]}][[1]]],{j,chain}];
answer, False]);

Misc. other points

Thanks to Allan Stenger for several of these.

p. 507. The discussion of Apery and ζ(3) is a little odd. It was not really expected that ζ(2n+1) is a rational multiple of (π^(2n+1)). The outstanding question is where ζ(2n+1) are all irrational. And Apery showed this in the case of ζ(3). See Klee-Wagon. The code following should be fixed to, to eliminate π.

p. 28, line -2 of section:  "whose coefficients" -> "whose values"

p. 48 line 3 of section: ...alternate in sign and, when x is large, have very large values for a while, before shrinking down to small values.

p. 456. Line mising: Add “col =”. This makes code following work.
e20=ErreraCloned[20];
col=FourColoring[e20,Method->KempeKittell]

p. 472.  The True should be False. I changed the code to make it try more random restarts (30 vs. 15) so as to avoid the one bad case in this experiment (#79).

p. 476, line 13:  highest-order -> lowest-order since the error terms are of form n^-4,  n^-6, etc.

p. 478 line 7:  1+ni should be  n+i

p. 557. There are two references labeled [AW], namely Adamchik & Wagon
and Atwood & Wagon
Make Atwood [AW1 and fix in Chapter ...5?

p. 86, last line of code:
{{i, 0, "i"}, 0, frames - 1, 1}  is what it should be. The 0 before frames was missing.

Missing reference: 

[Far] Frank Farris, Wheels on wheels on wheels -- surprising symmetry, Mathematics Magazine 69 (1996) 185-189.

[Pin] J. Pintz, On Legendre's prime number formula, American Mathematical Monthly 87 (1980) 733–735.

p. 453. Code should have FourColoring1
And the code for KempeChain1 has a bad bug. Fix is in the chapter.

From Marvin Schafer

Chapter 1, Plotting, has, in essence:

f[n_] := Last[DeleteCases[IntegerDigits[n!], 0]];
freqs = Sort[Tally[Table[f[n], {n, 0, 1000}]]];
BarChart[Last /@ freqs, ChartLabels -> Placed[ Last /@ freqs, Top], 
 PlotRange -> {0, 320}, Epilog -> Text[2, {0.5, 20}]]

which properly places a 2 centered over the very low bar that shows a count of 2 for the value 1.

To mirror this in version 8, the Epilog has to be changed to the coordinate {1,20}, i.e., the properly executing sequence becomes:

f[n_] := Last[DeleteCases[IntegerDigits[n!], 0]];
freqs = Sort[Tally[Table[f[n], {n, 0, 1000}]]];
BarChart[Last /@ freqs, ChartLabels -> Placed[ Last /@ freqs, Top], 
 PlotRange -> {0, 320}, Epilog -> Text[2, {1, 20}]]

v 8 issues

In chapter 17, throughout (i.e., in the MapColoring package and in the text) the full word AdjacencyGraph should be replaced by AdjacencyGraphFromMap.

Style sheet issues

All the file on disk were done in a style sheet called BookSW9. Probably I should have had them all in Default for simplicity. If you want the BookSW9 style sheet, just ask me (wagon@macalester.edu).