
Here is a list of all significant changes that were made between the original printing and the printing of 2008. An asterisk (*) marks technical errors that are not merely typographical:
 page ix, bottom line
 change 'that that' to 'that'
 page 4, line 8 of the displayed program
 indent this line one more notch
 page 6, line 1
 change '(596)' to '(569)'
 page 9, line 7 from the bottom
 the first left parenthesis should be larger
 page 17, line 4
 change 'Intermèdiaire' to 'Intermédiaire'
 page 18, line 8
 change ',16' to ', 16'
 page 30, line 6 from the bottom
 insert $^\bullet$ after the fourth R
 page 53, line 3 from the bottom
 change 'manuscript (Tehran: 1972)' to 'Acta Informatica 3 (1973), 3741.'
 page 63, bottom line
 change 'follows' to 'follow'
 page 66, in formula (12)
 change the rightmost occurrence of '$p_i$' to '$p_j$'
 page 74, line 20
 change 'Mathematiques' to 'Mathématiques'
 *page 75, lines 7 and 8 from the bottom
 change '$U_{n1}$' to '$U_{n2}$'
 page 75, last two lines
 change '(Preprint, November 1999).' to: [Electronic Journal of Combinatorics 7 (2000), #R44]. The sequence $S_n(2)$ was introduced by A. Cayley in Philosophical Magazine (4) 13 (1857), 245248.
 *page 103, line 16
 change '$a_m1$' to '$a_{m1}$'
 page 108, line 14 from the bottom
 change 'approaph' to 'approach'
 page 134, line 7
 change '$F(a_1\ldots a_{l1}k$' to '$F(a_1\ldots a_{l1}k)$'
 page 145, line 7 from the bottom
 change 'is is' to 'is'
 page 147, bottom line
 change '1999' to '2000'
 page 159, line 14
 change '(2.2) and (3.2)' to '(2.2) and (2.3)'
 page 176, line 4 from the bottom
 change 'with same' to 'with the same'
 page 187, line 5 from the bottom
 change 'á la' to 'à la'
 page 194, line 4
 change '(see' to '[see'
 page 205, line 3
 change ' [Originally' to '[Originally'
 *page 230, line 10 from the bottom
 change '$1/(4pqz)$' to '$1/(4pq)$'
 page 231, line 4
 change 'M_p(n)' to 'M_n(p)'
 page 240, line 9 from the bottom
 change '$x_1+$' to '$x_1$'
 *page 240, line 7 from the bottom
 change '$x_1+2x_{d1}$' to '$x_1+x_{d2}+2x_{d1}$'
 page 243, line 14
 change 'and and' to 'and'
 page 263, line 6 from the bottom
 change '$g_n(t,y)$' to '$g_n(t,y)\,dt$'
 *page 269, equation (4.18)
 change '$x^{m+n}\over m!$' to '$x^{m+n}\over(m+n)!$'
 page 288, line 6
 change '$1\over3$).' to '$1\over3$.)'
 page 292, line 5 from the bottom
 change '$2\over3$ .' to '$2\over3$.'
 page 293, line 7 from the bottom
 change 'on $n$ elements' to 'of $\{1,2,\ldots,n\}$'
 page 294, line 8 from the bottom
 change 'permutation on' to 'permutation of'
 page 295, lines 13 and 14 from the bottom
 change 'on' to 'of' [thrice]
 page 296, line 11
 change 'permutation on' to 'permutation of'
 *page 307, line 1
 change 'n\le N^{t+dt}' to 'n\le N'
 page 319, line 8
 this line should have equation number (6.13)
 page 332, lines 6 and 10
 change 'log' to 'ln'
 page 333, line 11
 the equation number '(B.3)' should be flush right
 page 336, line 6
 change '289]' to '289].'
 page 338, line 4
 change '1970' to '1968'
 *page 338, several corrections to the formulas
 line 9, righthand side should be $\ln\ln N+\sum{c_k\over(\ln N)^k}$.
line 10, $a_1=\gamma1$
line 11, $a_k=(k1)!\Bigl({\gamma_0\over0!}+\cdots+{\gamma_{k1}\over(k1)!} 1$
line 5 should say just 'also'
line 3 should say '$\gamma$' instead of '$3\gamma$' *page 366, line 4 from the bottom
 change '$f_n$' to '$d_n$'
 page 372, line 1
 change '])' to ']'
 page 380, line 6
 insert closing quotes after the second comma
 *page 380, line 6 from the bottom
 change '$o(1)$' to '$o(n^{1/2})$'
 page 381, lines 8 and 9
 change '$=$' to '$\sim$'
 page 382, line 5 from the bottom
 the first left parenthesis should be larger
 *page 382, line 5 from the bottom
 change '(1)' to '(1)'
 page 383, bottom line
 change '$=$' to '$\sim$'
 page 384, lines 5 and 6 from the bottom
 change 'know the asymptotic value' to 'know the value'
 page 388, line 4 from the bottom
 change '$=$' to '$\sim$'
 *page 399, line 10 from the bottom
 change '$A(a,1,0)$' to '$A(a,1)$'
 *page 402, line 6 from the bottom
 change '$C(z)^k$' to '$C(z)^n$
 *page 403, line 4
 change '$x\ge y$' to '$x\le y$'
 *page 410, replacement for lines 15 and 16
 else if $x_1>x_2+1=x_3+2$ then max$(x_3,x_j)$
else $g_{j1}(x_2,\ldots,x_j)$
[Also delete the footnote on this page.] *page 411, lines 6 and 7
 change '$g_{a+1}$' to '$f$' [twice]
 page 411, line 6 from the bottom
 change 'twice' to 'thrice' [once]
 page 414, lines 16 and 17
 change 'to appear.]' to '283300].'
 page 414, line 23
 change 'a paper in preparation.' to 'in Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics (Kluwer, 2001), 231242.'
 *page 414, replacement for the final paragraph
 The author's original formulation of Theorem 4 was incorrect, but a correct definition of the function $g_j(x_1,\ldots,x_j)$ was found in May 2000 by Thomas A. Bailey as he was working with John R. Cowles on Open Problem 4. As of June 2000, ACL2 has verified the corrected version of Theorem 4 when $2\le m\le 7$.
 page 466, line 3 from the bottom
 change ', to appear, apply' to '47 (2000), 905911, have applied'
 page 469, line 9
 change 'p_{nk}z^k' to 'p_{nk}z^n'
 page 478, line 15
 change ').' to ')'
 page 500, last three lines
 change 'But the optimum procedure for sorting 13, 14,' to 'Marcin Peczarski [ESA 2002, to appear] extended Wells's method to prove that merge is actually unbeatable when $n=13$. But the optimum procedure for sorting 14,'
 page 502, line 2
 change 'of of' to 'of'
 page 503, line 7 from the bottom
 change 'Intermèdiaire' to 'Intermédiaire'
 page 504, new copy to follow the references
 Addendum Strictly speaking, an addition chain should specify the sets of integers $\{j(i,q) \mid 1\le q\le r(i)\}$ as well as the sequence of vectors $C$, because the latter does not uniquely define the former.
 page 519, lines 4, 5, 6, 7, 8
 the asterisks should be the typewriter font, as on line 1
 page 523, line 18
 change 'difficlut' to 'difficult'
 page 532, line 9
 change 'whose is' to 'whose bandwidth is'
 page 532, lines 11 and 12
 change ' (Extended abstract),...9099' to ', Journal of Computer and System Sciences 60 (2000), 510539'
 page 535, line 9 from the bottom
 change 'the the' to 'the'
 page 543, line 12
 change 'is traditionally known as' to 'was in fact defined and named by J. L. Carter in his Ph.D. dissertation, On the Existence of a Projective Plane of Order Ten (Berkeley, California: Mathematics Department, University of California, 1974). It is also known as the problem of'
 page 551, line 13
 change '$(.11001\ldots{})$' to '$(.11001\ldots{})_2$'
 *page 556, line 13 from the bottom
 change 'transcendental' to 'irrational'
 *page 557, line 3 from the bottom
 change '$\mu\ge0$' to '$\mu>m$'
 *page 557, line 2 from the bottom
 change '$\sum_{m=0}^\mu$' to '$\sum_{m=0}^{\mu1}$'
 *page 581, line 9 from the bottom
 change '$F_{j+1}$' to '${1\over2}F_{j+1}$'
 *page 582, line 21
 change '(5.24)' to '(5.25)'
 page 602, line 5
 change '12861291' to '12861291'
 *page 603, new paragraph to follow line 8
 Conversely, if $F(x)$ is a polynomial distribution with rational coefficients for which $F'(x)$ has no irrational roots, Guy Kindler and Dan Romik have shown that $F(x)$ can be generated by an fsg; this completes the solution of problem (v). [``On distributions computable by random walks on graphs,'' SIAM Journal on Discrete Mathematics 17 (2004), 624633.]
 page 605, first entry in left column
 change '37' to '37.'
 page 607, Cantor entry in the left column
 change 'Philip' to 'Philipp'
 page 607, new entry
 Carter, John Lawrence, 543.
 page 608, right column
 change 'Dellac, H.' to 'Dellac, Hippolyte'
 page 609, left column
 change 'Dirichlet, Peter' to 'Dirichlet, Johann Peter'
 page 610, entry for free trees
 change '531532, 533' to '531533'
 page 610, entry for Gauss
 change 'Gau8' to 'Gauß' and 'Johann Friedrich' to 'Johann Friderich'
 page 612, new entry
 Kindler, Guy, 603.
 page 613, entry for LISP
 add page 116
 page 616, new entry
 Peczarski, Marcin Piotr, 500.
 page 617, new entry
 Romik, Dan, 603.
 page 618, left column
 Rustin, Randall Dennis, 53.
 page 620, entry for trees, free
 change '531532, 533' to '531533'
 page 621, entry for Vinogradov
 change the Russian spelling from 'Vinogradob' to 'Vinogradov'
 page 621, entry for Wrench
 change '191192, 193' to '191193'