Groups: A Path to GeometryCambridge University Press, 3 set 1987 - 242 pagine Following the same successful approach as Dr. Burn's previous book on number theory, this text consists of a carefully constructed sequence of questions that will enable the reader, through participation, to study all the group theory covered by a conventional first university course. An introduction to vector spaces, leading to the study of linear groups, and an introduction to complex numbers, leading to the study of Möbius transformations and stereographic projection, are also included. Quaternions and their relationships to 3-dimensional isometries are covered, and the climax of the book is a study of the crystallographic groups, with a complete analysis of these groups in two dimensions. |
Sommario
III | 1 |
IV | 7 |
V | 8 |
VI | 9 |
VII | 11 |
VIII | 12 |
IX | 19 |
XI | 20 |
LV | 119 |
LVI | 123 |
LVII | 124 |
LVIII | 126 |
LIX | 128 |
LX | 132 |
LXI | 133 |
LXII | 134 |
XII | 23 |
XIV | 26 |
XV | 33 |
XVII | 35 |
XVIII | 40 |
XIX | 43 |
XX | 50 |
XXI | 52 |
XXII | 53 |
XXIII | 57 |
XXIV | 60 |
XXVI | 61 |
XXVII | 62 |
XXVIII | 72 |
XXX | 74 |
XXXI | 77 |
XXXII | 84 |
XXXIV | 85 |
XXXV | 88 |
XXXVI | 91 |
XXXVIII | 92 |
XXXIX | 93 |
XL | 97 |
XLI | 98 |
XLII | 99 |
XLIII | 101 |
XLIV | 103 |
XLVI | 104 |
XLVII | 105 |
XLVIII | 110 |
L | 112 |
LI | 114 |
LII | 116 |
LIII | 117 |
LIV | 118 |
LXIII | 136 |
LXIV | 143 |
LXVI | 145 |
LXVII | 148 |
LXVIII | 152 |
LXX | 153 |
LXXI | 155 |
LXXII | 162 |
LXXIV | 163 |
LXXV | 167 |
LXXVI | 173 |
LXXVII | 174 |
LXXVIII | 175 |
LXXIX | 178 |
LXXX | 182 |
LXXXI | 183 |
LXXXII | 184 |
LXXXIII | 185 |
LXXXIV | 188 |
LXXXVI | 190 |
LXXXVII | 191 |
LXXXVIII | 199 |
LXXXIX | 200 |
XC | 201 |
XCI | 205 |
XCII | 209 |
XCIII | 210 |
XCIV | 211 |
XCV | 213 |
XCVI | 225 |
XCVIII | 227 |
XCIX | 237 |
239 | |
Altre edizioni - Visualizza tutto
Parole e frasi comuni
1-dimensional subspace 2-centres 3-cycles a₁ angle Answers to chapter aẞ automorphism axes b₁ b₂ ba² ba³ bijection C₂ called centre circle complex numbers conjugacy class contains cosets cycles cyclic group Deduce defined Definition denote determine direct isometries direct product eigenvalue eigenvectors equivalence relation fixed points frieze group function geometrically glide-reflection group G group homomorphism group of isometries group of rotational group with point half-turn Historical note identity intersection inverse isometries fixing isomorphic kernel linear transformation mapping matrix Möbius group Möbius plane Möbius transformation nonsingular normal subgroup one-one opposite isometry orbit permutations perpendicular point group prove quaternions quotient group real line real numbers reflection with axis right coset rotational symmetries shear Sp(u sphere stabiliser stereographic projection subgroup of G subset tangent Theorem qn tion transformation of V₂(R translation group transpositions V₂(F vector space wallpaper group
Brani popolari
Pagina vi - coset' appears in the literature from 1910. However, the theorem attributed to Lagrange, that the order of a subgroup divides the order of the group...
Riferimenti a questo libro
Human Symmetry Perception and Its Computational Analysis Christopher W. Tyler Anteprima non disponibile - 2002 |
Proofs and Fundamentals: A First Course in Abstract Mathematics Ethan D. Bloch Anteprima non disponibile - 2000 |