LEADER 04048nam 22006135 450 001 996418200003316 005 20230322105619.0 010 $a3-030-47295-7 024 7 $a10.1007/978-3-030-47295-5 035 $a(CKB)5310000000016825 035 $a(MiAaPQ)EBC6231720 035 $a(DE-He213)978-3-030-47295-5 035 $a(PPN)248595784 035 $a(EXLCZ)995310000000016825 100 $a20200619d2020 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$ap-adic Numbers$b[electronic resource] $eAn Introduction /$fby Fernando Q. Gouvêa 205 $a3rd ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (xiii, 366 pages) $cillustrations 225 1 $aUniversitext 311 $a3-030-47294-9 327 $a1 Apéritif -- 2 Foundations -- 3 The p-adic Numbers -- 4 Exploring ?p -- 5 Elementary Analysis in ?p -- 6 Vector Spaces and Field Extensions -- 7 Analysis in ?p -- 8 Fun With Your New Head -- A Sage and GP: A (Very) Quick Introduction -- B Hints and Comments on the Problems -- C A Brief Glance at the Literature -- Bibliography -- Index. 330 $aThere are numbers of all kinds: rational, real, complex, p-adic, and more. The p-adic numbers are not as well known as the others, but they play a fundamental role in number theory and in other parts of mathematics, capturing information related to a chosen prime number p. They also allow us to use methods from calculus and analysis to obtain results in algebra and number theory. This book is an elementary introduction to p-adic numbers. Most other books on the subject are written for more advanced students; this book provides an entryway to the subject for students with an undergraduate mathematics education. Readers who want to have an idea of and appreciation for the subject will probably find what they need in this book. Readers on the way to becoming experts can begin here before moving on to more advanced texts. This third edition has been thoroughly revised to correct mistakes, make the exposition clearer, and call attention to significant aspects that are usually reserved for advanced books. The most important addition is the integration of mathematical software for computations with p-adic numbers and functions. A final chapter includes a selection of problems for further exploration. From the reviews of the first and second editions: "Perhaps the most suitable text for beginners" - The Mathematical Gazette "This text perfectly fulfills what it proposes" - Mathematical Reviews "An extraordinarily nice manner to introduce the uninitiated to the subject" - Mededelingen van het wiskundig genootschap "If I had to recommend one book on the subject to a student ? or even to a fully grown mathematician ...? it would still be this book" - MAA Reviews. 410 0$aUniversitext 606 $aNumber theory 606 $aAlgebra 606 $aField theory (Physics) 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aField Theory and Polynomials$3https://scigraph.springernature.com/ontologies/product-market-codes/M11051 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 615 0$aNumber theory. 615 0$aAlgebra. 615 0$aField theory (Physics). 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 14$aNumber Theory. 615 24$aField Theory and Polynomials. 615 24$aAnalysis. 676 $a512.74 700 $aGouvêa$b Fernando Q$4aut$4http://id.loc.gov/vocabulary/relators/aut$0382239 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418200003316 996 $aP-adic numbers$9374898 997 $aUNISA