| 000 | 02372cam a2200325 i 4500 | ||
|---|---|---|---|
| 001 | 1617537 | ||
| 003 | EG-ScBUE | ||
| 005 | 20240908093807.0 | ||
| 008 | 951002t1996 nyua f b 001 0 eng d | ||
| 020 | _a0387946179 (hardcover : alk. paper) | ||
| 020 | _a9780387946177 | ||
| 040 |
_aDLC _beng _erda _cDLC _dDLC _dEG-ScBUE |
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| 082 | 0 | 4 |
_a511.3 _bEXN _222 |
| 100 | 1 |
_aExner, George R., _eauthor. |
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| 245 | 1 | 3 |
_aAn accompaniment to higher mathematics / _cGeorge R. Exner. |
| 264 | 1 |
_aNew York : _bSpringer, _c[1996] |
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| 264 | 4 | _cc1996 | |
| 300 |
_axvii, 198 pages : _billustrations ; _c25 cm. |
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| 336 |
_2rdacontent _atext _btxt |
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| 337 |
_aunmediated _2rdamedia _bn |
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| 338 |
_avolume _bnc _2rdacarrier |
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| 490 | 0 | _aUndergraduate texts in mathematics | |
| 504 | _aIncludes bibliographical references and index. | ||
| 520 | _aThis text prepares undergraduate mathematics students to meet two challenges in the study of mathematics, namely, to read mathematics independently and to understand and write proofs. The book begins by teaching how to read mathematics actively, constructing examples, extreme cases, and non-examples to aid in understanding an unfamiliar theorem or definition (a technique familiar to any mathematician, but rarely taught); it provides practice by indicating explicitly where work with pencil and paper must interrupt reading. The book then turns to proofs, showing in detail how to discover the structure of a potential proof from the form of the theorem (especially the conclusion). It shows the logical structure behind proof farms (especially quantifier arguments), and analyzes, thoroughly, the often sketchy coding of these forms in proofs as they are ordinarily written. The common introductory material (such as sets and functions) is used for the numerous exercises, and the book concludes with a set of "Laboratories" on these topics in which the student can practice the skills learned in the earlier chapters. Intended for use as a supplementary text in courses on introductory real analysis, advanced calculus, abstract algebra, or topology, the book may also be used as the main text for a "transitions" course bridging the gap between calculus and higher mathematics. | ||
| 650 | 7 |
_aProof theory. _2BUEsh _96607 |
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| 651 | _2BUEsh | ||
| 653 |
_bENGGEN _cDecember2017 |
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| 655 | _vReading book | ||
| 942 |
_2ddc _cBB |
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| 999 |
_c25712 _d25684 |
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