Errata which have been fixed in the 2nd printing are marked with a *. To the best of my knowledge, all errata are fixed in the 2nd edition.
News: The 2nd edition is now available at amazon.com or from the Johns Hopkins University Press. (All royalties go directly to charity - half to the Sage Foundation to support open-source mathematical software development, and half to the Earth Island Institute, an environmental organization with projects all over the world.)
Thanks to those readers who emailed or snail-mailed me some of the following errata. In particular, I'd like to thank Jamie Adams, Lewis Nowitz, David Youd, Roger Johnson, Jaap Scherphuis, Michael Hoy, Tom Davis, John Rood, Trevor Irwin, Stephen Lepp, Mark Edwards, Carl Patterson, Peter Neumann (seven pages!), Bill Zeno, Herbert Kociemba, Alastair Farrugia, Matthew Lewis, and Christopher Tuffley.
General comments:
[1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0] [1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0] [0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0] [1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1] [1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0] [0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0] [0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0] [0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0] [0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0] [0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0] [0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0] [0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 1] [1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1] [0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0] [0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1] [0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1]
My apologies to David Singmaster.
They can be solved by using x15=
0 | 0 | 0 | 1 | 1 |
1 | 0 | 1 | 0 | 1 |
1 | 0 | 1 | 1 | 0 |
0 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 1 |
1 | 1 | 0 | 1 | 1 |
0 | 0 | 1 | 0 | 1 |
1 | 0 | 1 | 1 | 0 |
1 | 0 | 1 | 0 | 0 |
0 | 0 | 0 | 0 | 1 |
0 | 1 | 1 | 1 | 0 |
1 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 |
1 | 0 | 1 | 0 | 1 |
1 | 0 | 0 | 0 | 1 |
0 | 1 | 1 | 1 | 0 |
0 | 0 | 1 | 0 | 0 |
|
|
|
ix, 8 | the previous | a previous |
xiii, -8 | solved | was motivated by |
6, -6 | not a subset of a finite set | not finite |
6, -1 | it's | its |
14, 11 | fg | fog = fg |
14, -6 | |S| = |T|. | |S| = |T| < infinity.. |
15, 8 | f:S --> Z | f:Z-->S |
16, -9,-8 | linear transformations | matrices |
19, -11 | k = m | k = m+1 |
19, -11 | a_{ij} | (AB)_{ij} |
19, -9 | row of | column of |
20, -1 | det(Aij) | det(Aij)aij |
21, 2 | or | and |
22, -3 | 21 | 23 |
22, -18 | (s,t) belongs to S | (s,t) belongs to R |
*26, 19 | Exactly one | Each one |
*26, 20 | 30 | 103=1000 |
*26, -9 | and | an |
*26, -3 | an | and |
27, 12 | object | objects |
27, -12 | n, n-1, ..., n-m | n, n-1, ..., n-m+1 |
27, -10 | poker hands | "ordered poker hands" |
27, -8 | 52*51*50*49*48*47 = 14658134400 = (1.4...)x1010 | 52*51*50*49*48 = 311875200 = (3.1...)x108 |
28, 5 | an combination | a combination |
28, 13-14 | right ... left | left ... right |
31, 15 | Ss | Sc |
33, -13 | a point of points | a collection of points |
33, -6 | It's | Its |
37, 10 | chapter 8 | chapter 9 (see Theorem 9.3.1) |
37, 15 | then | are distinct then |
38, 15 | Si | Ai |
43, -18 | (n,an) | (n,an-1) |
42, 9-10 | row | column |
43, -14 | (bn,n) | (bn-1,n) |
*45, 23 | a(ab)2 | (ab)2a |
*45, 26 | a(ab)2 | (ab)2a |
*46, 5 | ka(ab)2 | k(ab)2a |
*46, 7 | k2a(ab)2 | k2(ab)2a |
47, -1 | five | four |
50, -10 | radians | (degrees) |
51, 2 | closed geodesic path | closed path |
*52, -9 | f1 | f1r1 |
*61, 18 | 120 degrees | 72 degrees |
67, 1 | {i,j,k}. | {i,j,k}, and x doesn't equal y. |
68, -9 | D2n | Dn |
70, -5 | o : G x G x G | G x G ---> G |
72, -9 | What didn't | Why didn't |
76, 16 | such that | and a place token p_{i+1} such that |
*76, -3 | {1,3,6} | {1,3,4} |
*76, -2 | {3,6} | {3,4} |
77, -2 | (Lagrange) | ("Lagrange's Theorem") |
78, 7 | x in G. | x in G. (Exercise: verify this.) |
78, 8 | "so" | "(see Ponderable 2.3.3), so" |
*78, -9 | "...belongs to G" | "...belongs to Z(G)" |
79, 13 | identifies | identified |
79, -4 | likelyhood | likelihood |
*80, 4 | MD2 | MF2 |
*80, -6 | ...showed to there ... | ...showed that there ... |
*82, top diagram | label "8" (resp., "6") on cube | label "6" (resp., "8") on cube |
84, -14 | ... substitutions | ... des substitutions |
84, -3 | gh=1 | gh=g |
86, 5 | g in G_* | d \geq 0 |
*87, 2 | clases | classes |
*87, 10-11 | g*x*g^{-1} | g*y*g^{-1} |
88, -10 | left action | right action |
88, -5 | right | left |
88, -3 | on the right | on the left |
89, 5 | right action | left action |
89, 15 | send | sent |
89, 18 | are | induce |
89, 19 | (though not all are)! | . |
89, 21 | In other words, | Roughly speaking, |
89, 21-22 | group acting on a set at `random' | `random` finite group acting primitively on a finite set |
89, 24 | corners | corner |
89, -1, -2 | (a), (b) | (b), (c) |
91, 18 | set of consisting | set consisting |
*92, -6 | right face | down face |
93, 17 | sbgroup | subgroup |
93, lines 24,25 | groups | subgroups |
94, 15 | both and | both an |
95, 8-9 | Then ... G = H* ... maximal). Thus p either ... | Then G = H* ... maximal). This implies p either ... |
95, 10 | In either case, the result ... hypothesis. | The result ... hypothesis. |
95, 13 | (Lagrange) | ("Lagrange's Theorem") |
*96, 13 | a(ab)2 | (ab)2a |
99, 8 | organisational | organizational |
99, -13 | choosen | chosen |
99, -11 | always be ... is), | be ... is) is 1, |
*99, -7 | .5 | 1 |
99, -7 | always | be |
99, -6 | always be solved. | be solved is 1. |
100, 18 | and shall | and |
*101, 14 | (M-1)(N-1) | N(M-1)+M(N-1) |
*101, section 6.3.1 | Merlin's magic | 3x3 light's out |
104, 5 | for some | provided |
*104, 7 | Ei,j in MN | Ei,j in MMxN |
*105, -8 | omit "Merlin's magic and" | |
105, 3 | 2 | 3 |
105, 4 | 3 | 4 |
105, 5 | 4 | 5 |
106, -7 | = 0 | \not= 0 |
107, -20 | effectivly | effectively |
107, -14 | intorduce | introduce |
107, -9 | \cdot F | \cdot : F |
107, -4,-3 | the vector \vec{0}=(0,0,...,0)\in V satisfies | there is a vector \vec{0}\in V satisfying |
109, 15 | if multiplicity | of multiplicity |
109, -16 | matrix | square diagonalizable matrix |
110, 17 | is upper-triangular. The number of non-zero entries on the diagonal | is reduced. The number of non-zero rows |
111, -2 | reculangular | rectangular |
111, -1 | Aien | Alien |
*112, figure 6.5.5 | The outer pentagon (numbers 7-11) should be rotated clockwise 36 degrees with respect to the rest. | |
*114, 10 | matrix T | see above |
*114, -5 | 15 | 16 |
*114, -3 | is 1 | is 0 |
*114, -2 | are initial | are no initial |
116, 11 | eminating | emanating |
117, 8 | who | whom |
117, 9 | laywer | lawyer |
117, -6 | v's | v |
*117, -2 | (1 2) , (2 3) | (1,2) , (2,3) |
119, -21 | Micheal | Michael |
120, -12 | who | whom |
122, 6 | We can ... path p, | Let a path p on puz(Gamma) to be a sequence of moves |
122, 7 | n <= 1 | n >= 1 |
122, 14 | of paths based | of closed paths based |
*122, 12 | 14-15 puzzle | 15 puzzle |
123, 1 | has | has at most |
125, 9 | vertices | edges |
126, line -7,-6,-5 | symmetric | symmetry |
127, -12 | (1/2)(...||^2 + ||.. | (1/4)(...||^2 - ||.. |
127, -1 | transpose identity. | transpose |
128, 9 | *B | *A |
128, 10 | if an | if and |
129, 3-4 | In particular, ... invertible. | The matrix A is invertible since, by definition, its inverse is ^tA. |
132, 8 | permutations of | permutations in |
132, 17 | permutations of | permutations in |
132, 17 | A5 x S5 | A5 x C2 |
138, 1 | E. Jordan | C. Jordan |
139, 12 | X x X | X x X - Delta (where Delta = {(x,x) | x in X}) |
139, 17 | belonging to X | belonging to X, xi <> xj |
139, 17 | for each | provided |
139, -15 | group | permutation group |
139, -11 | [R] | [DiMo], Theorem 7.6A |
141, lines 4,5 | , and in ... i,j,k. | , as in section 5.1. |
*141, 20,21 | left, right | right, left (resp.) |
*141, 23 | Let g | Let x |
141, -8 | concept | concepts |
141, lines -7, -6 | finite groups | finite simple groups |
142, 9 | three cubes | two cubes |
142, -14 | for all 1 <= i <= n | provided 1 <= i <= n |
142, -1 | for all 1 <= j <= n | provided 1 <= j <= n |
143, 2 | <= 1 | <= n |
145, 4 | E. Galois | Ruffini and Abel |
146, 11 | who | whom |
146, -15 | normal groups | normal subgroups |
147, -21 | isomomorphism | isomorphism |
147, -1 | isomorphism between | isomorphism |
150, -14 | H acts on X. Note | Note, H acts on X and |
150, -4 | is an element | are elements |
150, -3 | any element other element of E | each other |
*156, 3 | somwhat | somewhat |
*156, -1 | H1 x H2 | H1 xphi H2 |
157, -19 | colun | column |
158, -2,-1 | (x,y) | g |
158, -1 | (-x,-y) | -g |
161, 10 | group arose | group, originally arose |
*163, -14 | n | n-1 |
*163, -12 | n=2 | n=3 |
164, 15 | Rubik's cube. | Rubik's cube which does not contain a basic move followed by its inverse |
165, 9 | , however | . However, |
165, 18 | occurance | occurence, |
165, -10 | cardiality | cardinality |
166, -10 | who | whom |
166, -6 | R | The letter script-R |
166, -5 | realtions | relations |
166, -3 | relations R | relations script-R |
*170, 4-5 | should be a horizonal line separating cases 15,16 | |
172, -13 | (a) | . |
172, -11,-10 | , and in ... {i,j,k}. | , as in section 5.1. |
*178, 1 | lu, and bu | lu, bl, and bu |
*180, 3, 4, 7, 8 | corner | edge |
*180, 4 | vertex | edge |
*180, 5 | vertices | edges |
*180, 17 | (0,1,0,0,0,1,1,0,0,1,0,0) | (0,1,0,0,0,0,0,0,0,1,0,0) |
180, -1 | (SV wr C38)x(SE wr C212) | (C3 wrSV )x(C2 wr SE) |
181, 1-2 | C38xSVx C38xSV | C38xSVx C212xSE |
185, 12-13 | allows us to count its elements easier. | enables us to determine the size of this group. |
186, -1 | isomomorphism | isomorphism |
188, -2 | of (non-trivial) | of |
189, 9 | haiku | poem |
193, 8 | x1e1 +...xn en | x1e1 +...+xn en |
194, 15 | More generally, let | Let |
194, lines 21, -10 | e2i-2 | e2i-1 |
195, 6 | < F,U > .... | < sigma(F),sigma(U) > isom S7, < rho(F),rho(U) > isom PGL2(F5), |
198, -6 | fractions | fractional |
201, 3 | enties | entries |
201, lines -12, -14, -16 | polyhedra | polyhedron |
205, 7 | undeground | underground |
215, -13 | SE wr C2 | C2 wr SE |
216, -2 | G | G_1 |
216, -2 | G | G_1 |
217, 1 and 4 | G | G_1 |
217, 14-16 | Theorem 13.5.1 | see above |
217, 18 | possible | possible in G |
217, -9 | up | down |
223, -15 | isocahedron | icosahedron |
224, -13 | in his PhD thesis. | a year after his Docteur es Sciences thesis in 1859. |
225, -18 | stating | containing |
225, -11 | A8, A12 | A7, A11 |
229, -8 | Matheiu | Mathieu |
230, lines -18,-17,-7 | isocahedron | icosahedron |
230, -14 | many experts thought they had classified all finite simple groups | some experts thought all finite simple groups had been classified |
231, lines 7,8,11 | parallelpiped | parallelepiped |
231, 20 | giving the first proof | giving one of the first proofs |
232, -1 | [R], ch. 9 | [DM], Theorem 7.6A |
251, -11 | Berlekamp | E. Berlekamp |
*253, 17 | D. Hofstatler | D. Hofstater |
*253, 17 | Metamathematical Themas | Metamagical Themas |
259, 14 | E. Jordan | C. Jordan |