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Computing the Continuous Discretely

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towards the end of the book. The book also includes open problems, of more interest to researchers in these topics. As reviewer Darren Glass writes, "Even people who are familiar with the material would almost certainly learn something from the clear and engaging exposition that these two authors
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This book is written at an undergraduate level, and provides many exercises, making it suitable as an undergraduate textbook. Little mathematical background is assumed, except for some
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of determining which amounts of money can be represented (and what is the largest non-representable amount of money) for a given system of coin values. Other topics touched on include
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calls the book "coherent and tightly developed ... accessible and engaging", and reviewer Oleg Karpenkov calls it "outstanding".
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series (Vol. 154). A second edition was published in 2015, and a German translation of the first edition by Kord Eickmeyer,
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for the difference between a sum and the corresponding integral; special polytopes including
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they contain. It was written by Matthias Beck and Sinai Robins, and published in 2007 by
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Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra
152: 72: 359: 253: 76: 167:. In this way, the topics of the book connect together geometry, 127:, both of which relate lattice counting to volume; 54: 44: 36: 107:The book begins with a motivating problem, the 8: 19: 348: 346: 344: 342: 25: 18: 275: 273: 271: 315: 313: 311: 309: 307: 239: 237: 235: 216: 71:is an undergraduate-level textbook in 418:Springer Science+Business Media books 99:, was published by Springer in 2008. 7: 20:Computing the Continuous Discretely 355:Computing the Continuous Discretely 334:Mathematical Association of America 324:Computing the Continuous Discretely 285:Computing the Continuous Discretely 249:Computing the Continuous Discretely 93:Undergraduate Texts in Mathematics 14: 320:Glass, Darren (February 2007), 97:Das Kontinuum diskret berechnen 75:, on the interplay between the 40:Matthias Beck and Sinai Robins 1: 205:List of books about polyhedra 353:Karpenkov, Oleg, "Review of 119:relating numbers of faces; 434: 117:Dehn–Sommerville equations 163:; and the enumeration of 24: 16:2007 mathematics textbook 143:and its discretization; 149:Euler–Maclaurin formula 413:2015 non-fiction books 408:2007 non-fiction books 179:Audience and reception 403:Mathematics textbooks 145:Bernoulli polynomials 115:of polytopes and the 290:Mathematical Reviews 129:generating functions 283:(2007), "Review of 125:Ehrhart polynomials 31:First edition cover 21: 281:De Loera, JesĂşs A. 245:Bayer, Margaret M. 133:Fourier transforms 83:and the number of 157:Birkhoff polytope 64: 63: 425: 372: 371: 350: 337: 336: 317: 302: 301: 277: 266: 265: 241: 230: 221: 185:complex analysis 81:convex polytopes 56:Publication date 29: 22: 433: 432: 428: 427: 426: 424: 423: 422: 378: 377: 376: 375: 352: 351: 340: 319: 318: 305: 279: 278: 269: 243: 242: 233: 222: 218: 213: 201: 181: 141:Green's theorem 105: 89:Springer-Verlag 57: 49:Springer-Verlag 32: 17: 12: 11: 5: 431: 429: 421: 420: 415: 410: 405: 400: 395: 393:Lattice points 390: 380: 379: 374: 373: 338: 303: 267: 231: 215: 214: 212: 209: 208: 207: 200: 197: 193:Margaret Bayer 180: 177: 121:Pick's theorem 104: 101: 85:lattice points 62: 61: 58: 55: 52: 51: 46: 42: 41: 38: 34: 33: 30: 15: 13: 10: 9: 6: 4: 3: 2: 430: 419: 416: 414: 411: 409: 406: 404: 401: 399: 396: 394: 391: 389: 386: 385: 383: 370: 366: 362: 361: 356: 349: 347: 345: 343: 339: 335: 331: 327: 325: 316: 314: 312: 310: 308: 304: 300: 296: 292: 291: 286: 282: 276: 274: 272: 268: 264: 260: 256: 255: 250: 247:, "Review of 246: 240: 238: 236: 232: 229: 225: 220: 217: 210: 206: 203: 202: 198: 196: 194: 189: 186: 178: 176: 174: 173:combinatorics 170: 169:number theory 166: 165:magic squares 162: 158: 154: 150: 146: 142: 138: 137:Dedekind sums 134: 130: 126: 122: 118: 114: 113:face lattices 110: 102: 100: 98: 94: 90: 86: 82: 78: 74: 70: 69: 59: 53: 50: 47: 43: 39: 35: 28: 23: 358: 354: 329: 323: 288: 284: 252: 248: 219: 190: 182: 161:permutohedra 109:coin problem 106: 96: 67: 66: 65: 330:MAA Reviews 322:"Review of 382:Categories 369:1339.52002 263:1114.52013 228:1147.52300 211:References 388:Polytopes 191:Reviewer 153:zonotopes 91:in their 45:Publisher 199:See also 123:and the 73:geometry 299:2271992 398:Volume 367:  360:zbMATH 297:  261:  254:zbMATH 226:  188:use." 171:, and 159:, and 155:, the 147:; the 135:, and 103:Topics 77:volume 37:Author 60:2007 365:Zbl 357:", 287:", 259:Zbl 251:", 224:Zbl 79:of 384:: 363:, 341:^ 332:, 328:, 306:^ 295:MR 293:, 270:^ 257:, 234:^ 175:. 131:, 326:"

Index


Springer-Verlag
geometry
volume
convex polytopes
lattice points
Springer-Verlag
Undergraduate Texts in Mathematics
coin problem
face lattices
Dehn–Sommerville equations
Pick's theorem
Ehrhart polynomials
generating functions
Fourier transforms
Dedekind sums
Green's theorem
Bernoulli polynomials
Euler–Maclaurin formula
zonotopes
Birkhoff polytope
permutohedra
magic squares
number theory
combinatorics
complex analysis
Margaret Bayer
List of books about polyhedra
Zbl
1147.52300

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