Knowledge (XXG)

Mirrors and Reflections

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86:. Part IV, "the highlight in this book", proves the classification of finite reflection groups and of root systems. The final part of the book studies in more detail and through more elementary methods the three-dimensional finite reflection groups and the symmetries of the regular 101:
is aimed at undergraduate mathematics students, and uses an intuitive and heavily visual approach suitable for that level. its readers are expected to already have a solid background in
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recommends the book, both as a textbook for a "capstone" undergraduate course, and as individual reading for students interested in this topic.
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is divided into five major parts, with two appendices. The first part provides background material in affine geometric spaces,
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and Anna Borovik and published in 2009 by Springer in their Universitext book series. The Basic Library List Committee of the
282: 292: 52: 48: 59:. The second part introduces the definitions of reflection systems and reflection groups, the special case of 90:. Appendices provide suggestions for mathematical visualization, and list hints and solutions for exercises. 134: 29: 259: 25: 224: 263: 220: 137:, 1990). However, these take a more algebraic and less geometric view of the subject than 79: 71: 56: 102: 60: 276: 169: 110: 106: 75: 87: 64: 215: 121:
There are several other standard textbooks on reflection groups, including
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has recommended its inclusion in undergraduate mathematics libraries.
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Mirrors and Reflections: The Geometry of Finite Reflection Groups
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is an undergraduate-level textbook on the geometry of
123:Groupes et algèbres de Lie, Chapitres 4, 5 et 6 204: 202: 200: 198: 196: 194: 141:, and are less accessible to undergraduates. 8: 129:(L. C. Grove and C. T. Benson, 1985), and 164: 162: 160: 158: 156: 154: 243: 241: 239: 237: 235: 233: 150: 209:Chlouveraki, Maria (2011), "Review of 78:of reflection groups, including their 74:, and uses them as the basis for some 7: 131:Reflection Groups and Coxeter Groups 186:Mathematical Association of America 34:Mathematical Association of America 16:Undergraduate mathematics textbook 14: 70:Part III of the book concerns 1: 248:Ellers, Erich W., "Review of 53:arrangements of hyperplanes 309: 49:geometric transformations 127:Finite Reflection Groups 250:Mirrors and Reflections 211:Mirrors and Reflections 176:Mirrors and Reflections 139:Mirrors and Reflections 99:Mirrors and Reflections 45:Mirrors and Reflections 288:2009 non-fiction books 94:Audience and reception 283:Mathematics textbooks 30:Alexandre V. Borovik 28:. It was written by 84:parabolic subgroups 135:James E. Humphreys 125:(Bourbaki, 1968), 293:Reflection groups 72:Coxeter complexes 26:reflection groups 300: 267: 266: 245: 228: 227: 206: 189: 188: 166: 80:length functions 57:polyhedral cones 308: 307: 303: 302: 301: 299: 298: 297: 273: 272: 271: 270: 247: 246: 231: 208: 207: 192: 168: 167: 152: 147: 119: 96: 61:dihedral groups 42: 17: 12: 11: 5: 306: 304: 296: 295: 290: 285: 275: 274: 269: 268: 229: 190: 170:Karaali, Gizem 149: 148: 146: 143: 118: 115: 103:linear algebra 95: 92: 41: 38: 15: 13: 10: 9: 6: 4: 3: 2: 305: 294: 291: 289: 286: 284: 281: 280: 278: 265: 261: 257: 256: 251: 244: 242: 240: 238: 236: 234: 230: 226: 222: 218: 217: 212: 205: 203: 201: 199: 197: 195: 191: 187: 183: 179: 177: 171: 165: 163: 161: 159: 157: 155: 151: 144: 142: 140: 136: 132: 128: 124: 117:Related works 116: 114: 112: 111:Gizem Karaali 108: 104: 100: 93: 91: 89: 85: 81: 77: 73: 68: 66: 62: 58: 54: 50: 46: 39: 37: 35: 31: 27: 23: 22: 253: 249: 214: 210: 181: 175: 172:(May 2010), 138: 130: 126: 122: 120: 107:group theory 98: 97: 76:group theory 69: 65:root systems 44: 43: 20: 19: 18: 182:MAA Reviews 174:"Review of 109:. Reviewer 88:icosahedron 277:Categories 264:1193.20001 216:MathSciNet 145:References 105:and some 225:2561378 55:,, and 262:  255:zbMATH 223:  63:, and 40:Topics 82:and 260:Zbl 252:", 213:", 51:,, 279:: 258:, 232:^ 221:MR 219:, 193:^ 184:, 180:, 153:^ 67:. 178:" 133:(

Index

reflection groups
Alexandre V. Borovik
Mathematical Association of America
geometric transformations
arrangements of hyperplanes
polyhedral cones
dihedral groups
root systems
Coxeter complexes
group theory
length functions
parabolic subgroups
icosahedron
linear algebra
group theory
Gizem Karaali
James E. Humphreys






Karaali, Gizem
"Review of Mirrors and Reflections"
Mathematical Association of America



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