P-adic analysis compared with real (Record no. 55799)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03583nam a22002777a 4500 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20191022143111.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 191022b ||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780821852248 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512.74 KAT |
| 100 ## - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Katok, Svetlana |
| 245 ## - TITLE STATEMENT | |
| Title | P-adic analysis compared with real |
| Statement of responsibility, etc | / Svetlana Katok |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc | Providence, R.I. : American Mathematical Society |
| Name of publisher, distributor, etc | : Mathematics Advanced Study Semesters, |
| Date of publication, distribution, etc | ©2007. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | xiii, 152 pages |
| Other physical details | : illustrations |
| Dimensions | ; 22 cm |
| 490 ## - SERIES STATEMENT | |
| Series statement | Student mathematical library, v. 37. |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Contents note | Foreword : MASS and REU at Penn State University --<br/>Preface --<br/>ch. 1. Arithmetic of the p-adic numbers --<br/>1.1. From Q to R ; the concept of completion --<br/>Exercises 1-8 --<br/>1.2. Normed fields --<br/>Exercises 9-16 --<br/>1.3. Construction of the completion of a normed field --<br/>Exercises 17-19 --<br/>1.4. The field of p-adic numbers Qp --<br/>Exercises 20-25 --<br/>1.5. Arithmetical operations in Qp --<br/>Exercises 26-31 --<br/>1.6. The p-adic expansion of rational numbers --<br/>Exercises 32-34 --<br/>1.7. Hensel's Lemma and congruences --<br/>Exercises 35-44 --<br/>1.8. Algebraic properties of p-adic integers --<br/>1.9. Metrics and norms on the rational numbers. Ostrowski's theorem --<br/>Exercises 45-46 --<br/>1.10. A digression : what about Qg if g is not a prime? --<br/>Exercises 47-50 --<br/>ch. 2. The topology of Qp vs. the topology of R --<br/>2.1. Elementary topological properties --<br/>Exercises 51-53 --<br/>c.2. Cantor sets --<br/>Exercises 54-65 --<br/>2.3. Euclidean models of Zp --<br/>Exercises 66-68. ch. 3. Elementary analysis in Qp --<br/>3.1. Sequences and series --<br/>Exercises 69-73 --<br/>3.2. p-adic power series --<br/>Exercises 74-78 --<br/>3.3. Can a p-adic power series be analytically continued? --<br/>3.4. Some elementary functions --<br/>Exercises 79-81 --<br/>3.5. Further properties of p-adic exponential and logarithm --<br/>3.6. Zeros of p-adic power series --<br/>Exercises 82-83 --<br/>ch. 4. p-adic functions --<br/>4.1. Locally constant functions --<br/>Exercises 84-87 --<br/>4.2. Continuous and uniformly continuous functions --<br/>Exercises 88-90 --<br/>4.3. Points of discontinuity and the Baire Category Theorem --<br/>Exercises 91-96 --<br/>4.4. Differentiability of p-adic functions --<br/>4.5. Isometries of Qp --<br/>Exercises 97-100 --<br/>4.6. Interpolation --<br/>Exercises 101-103 --<br/>Answers, hints, and solutions for selected exercises --<br/>Bibliography --<br/>Index. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | The book gives an introduction to p-adic numbers from the point of view of number theory, topology, and analysis. Compared to other books on the subject, its novelty is both a particularly balanced approach to these three points of view and an emphasis on topics accessible to undergraduates. In addition, several topics from real analysis and elementary topology which are not usually covered in undergraduate courses (totally disconnected spaces and Cantor sets, points of discontinuity of maps and the Baire Category Theorem, surjectivity isometries of compact metric spaces) are also included in the book. They will enhance the reader's understanding of real analysis and intertwine the real and p-adic contexts of the book." "The book includes a large number of exercises. Answers, hints, and solutions for most of them appear at the end of the book. The book can be successfully used in a topic course or for self-study."--Jacket |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Algebra |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | p-adic analysis. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Analyse p-adique. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | p-adische Analysis |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Teoria dos números. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Análise p-ádica. |
| 700 ## - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Katok, Svetlana |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | Mathematics Departmental Library |
No items available.
