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 LEADER 04335nam 22006614a 450 001 9910962448703321 005 20250609111612.0 010 $a1-280-20546-6 010 $a9786610205462 010 $a0-306-46949-9 024 7 $a10.1007/0-306-46949-9 035 $a(CKB)111056486604440 035 $a(EBL)3035523 035 $a(SSID)ssj0000257973 035 $a(PQKBManifestationID)11218422 035 $a(PQKBTitleCode)TC0000257973 035 $a(PQKBWorkID)10254687 035 $a(PQKB)11496396 035 $a(DE-He213)978-0-306-46949-7 035 $a(Au-PeEL)EBL3035523 035 $a(CaPaEBR)ebr10048253 035 $a(CaONFJC)MIL20546 035 $a(OCoLC)70736479 035 $a(PPN)237928981 035 $a(MiAaPQ)EBC3035523 035 $a(MiAaPQ)EBC196976 035 $a(EXLCZ)99111056486604440 100 $a20000922d2000 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aTheoretical methods in condensed phase chemistry /$fedited by Steven D. Schwartz 205 $a1st ed. 2002. 210 $aDordrecht ;$aBoston $cKluwer Academic Publishers$dc2000 215 $a1 online resource (318 p.) 225 1 $aProgress in theoretical chemistry and physics ;$vv. 5 300 $aDescription based upon print version of record. 311 08$a1-4020-0410-9 311 08$a0-7923-6687-5 320 $aIncludes bibliographical references and index. 327 $aClassical and Quantum Rate Theory for Condensed Phases -- Feynman Path Centroid Dynamics -- Proton Transfer in Condensed Phases: Beyond the Quantum Kramers Paradigm -- Nonstationary Stochastic Dynamics and Applications to Chemical Physics -- Orbital-Free Kinetic-Energy Density Functional Theory -- Semiclassical Surface Hopping Methods for Nonadiabatic Transitions in Condensed Phases -- Mechanistic Studies of Solvation Dynamics in Liquids -- Theoretical Chemistry for Heterogeneous Reactions of Atmospheric Importance. The HC1+CIONO2 Reaction on Ice -- Simulation of Chemical Reactions in Solution Using an AB Initio Molecular Orbital-Valence Bond Model -- Methods for Finding Saddle Points and Minimum Energy Paths. 330 $aThis book is meant to provide a window on the rapidly growing body of theoretical studies of condensed phase chemistry. A brief perusal of physical chemistry journals in the early to mid 1980?s will find a large number of theor- ical papers devoted to 3-body gas phase chemical reaction dynamics. The recent history of theoretical chemistry has seen an explosion of progress in the devel- ment of methods to study similar properties of systems with Avogadro?s number of particles. While the physical properties of condensed phase systems have long been principle targets of statistical mechanics, microscopic dynamic theories that start from detailed interaction potentials and build to first principles predictions of properties are now maturing at an extraordinary rate. The techniques in use range from classical studies of new Generalized Langevin Equations, semicl- sical studies for non-adiabatic chemical reactions in condensed phase, mixed quantum classical studies of biological systems, to fully quantum studies of m- els of condensed phase environments. These techniques have become sufficiently sophisticated, that theoretical prediction of behavior in actual condensed phase environments is now possible. and in some cases, theory is driving development in experiment. The authors and chapters in this book have been chosen to represent a wide variety in the current approaches to the theoretical chemistry of condensed phase systems. I have attempted a number of groupings of the chapters, but the - versity of the work always seems to frustrate entirely consistent grouping. 410 0$aProgress in theoretical chemistry and physics ;$vv. 5. 606 $aChemistry, Physical and theoretical 606 $aCondensed matter 615 0$aChemistry, Physical and theoretical. 615 0$aCondensed matter. 676 $a541/.0421 701 $aSchwartz$b Steven David$01824786 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910962448703321 996 $aTheoretical methods in condensed phase chemistry$94392117 997 $aUNINA