Numbers and Functions: Steps Into Analysis

R. P. Burn

Cambridge University Press, Aug 28, 2000 - Mathematics - 356 pages

The transition from studying calculus in high school to studying mathematical analysis in college is notoriously difficult. In this new edition of Numbers and Functions, Dr. Burn invites the student to tackle each of the key concepts, progressing from experience through a structured sequence of several hundred problems to concepts, definitions and proofs of classical real analysis. The problems, with all solutions supplied, draw readers into constructing definitions and theorems. This novel approach to rigorous analysis will enable students to grow in confidence and skill and thus overcome traditional difficulties in learning this subject.

Contents

• V: 3
• VI: 6
• VII: 8
• VIII: 10
• X: 14
• XII: 16
• XIII: 17
• XIV: 18
• XVI: 19
• XVII: 21
• XIX: 22
• XX: 28
• XXI: 29
• XXII: 30
• XXIII: 31
• XXIV: 35
• XXV: 36
• XXVI: 37
• XXVII: 38
• XXVIII: 44
• XXIX: 45
• XXX: 49
• XXXII: 50
• XXXIII: 52
• XXXIV: 53
• XXXV: 56
• XXXVI: 57
• XXXVII: 59
• XXXVIII: 68
• XXXIX: 69
• XL: 70
• XLI: 72
• XLII: 73
• XLIII: 75
• XLIV: 76
• XLV: 78
• XLVI: 79
• XLVII: 80
• XLVIII: 81
• L: 83
• LI: 85
• LII: 86
• LIII: 87
• LIV: 88
• LV: 89
• LVI: 90
• LVII: 91
• LVIII: 92
• LIX: 95
• LX: 104
• LXI: 107
• LXIII: 108
• LXIV: 109
• LXV: 110
• LXVII: 111
• LXVIII: 112
• LXIX: 113
• LXX: 114
• LXXI: 116
• LXXII: 117
• LXXIII: 118
• LXXIV: 119
• LXXV: 120
• LXXVI: 122
• LXXVII: 123
• LXXVIII: 125
• LXXIX: 126
• LXXX: 128
• LXXXI: 129
• LXXXII: 131
• LXXXIII: 141
• LXXXIV: 143
• LXXXVIII: 144
• LXXXIX: 145
• XCI: 146
• XCII: 147
• XCIII: 148
• XCIV: 149
• XCV: 150
• XCVI: 151
• XCVIII: 154
• C: 156
• CI: 159
• CII: 162
• CIII: 163
• CIV: 164
• CV: 166
• CVI: 167
• CVII: 168
• CVIII: 171
• CIX: 182
• CX: 183
• CXI: 185
• CXII: 187
• CXIII: 188
• CXIV: 190
• CXV: 192
• CXVI: 194
• CXVII: 195
• CXVIII: 197
• CXIX: 203
• CXX: 205
• CXXII: 206
• CXXIV: 207
• CXXV: 211
• CXXVI: 212
• CXXVII: 213
• CXXVIII: 215
• CXXX: 216
• CXXXI: 219
• CXXXII: 224
• CXXXIII: 226
• CXXXV: 230
• CXXXVII: 232
• CXXXVIII: 234
• CXXXIX: 235
• CXL: 239
• CXLI: 240
• CXLII: 243
• CXLIII: 251
• CXLIV: 254
• CXLV: 255
• CXLVI: 256
• CXLVII: 258
• CXLVIII: 260
• CXLIX: 261
• CL: 262
• CLI: 265
• CLII: 267
• CLIV: 268
• CLV: 270
• CLVII: 271
• CLIX: 273
• CLXI: 276
• CLXII: 286
• CLXIII: 287
• CLXV: 289
• CLXVI: 290
• CLXVII: 291
• CLXVIII: 292
• CLXIX: 293
• CLXX: 294
• CLXXI: 295
• CLXXII: 296
• CLXXIII: 297
• CLXXIV: 298
• CLXXVI: 299
• CLXXVII: 302
• CLXXVIII: 309
• CLXXIX: 310
• CLXXX: 312
• CLXXXI: 313
• CLXXXII: 315
• CLXXXIII: 317
• CLXXXIV: 318
• CLXXXV: 319
• CLXXXVI: 322
• CLXXXVIII: 326
• CXC: 328
• CXCI: 337
• CXCII: 342
• CXCIII: 346
• CXCIV: 351

Bibliographic information

• Title: Numbers and Functions: Steps Into Analysis
• Author: R. P. Burn
• Edition: illustrated, reprint, revised
• Publisher: Cambridge University Press, 2000
• ISBN: 0521788366, 9780521788366
• Length: 356 pages
• Subjects: Mathematics / Mathematical Analysis; Mathematics / Probability & Statistics / General