Elementary Number Theory [[electronic resource] /] / by Gareth A. Jones, Josephine M. Jones

• Record Nr.: UNINA9910479869403321
• Autore: Jones Gareth A
• Pubbl/distr/stampa: London : , : Springer London : , : Imprint : Springer, , 1998
• ISBN: 1-4471-0613-X
• Edizione: [1st ed. 1998.]
• Descrizione fisica: 1 online resource (XIV, 302 p.)
• Collana: Springer Undergraduate Mathematics Series, , 1615-2085
• Disciplina: 512/.7
• Soggetti: Number theory; Number Theory
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and indexes.
• Nota di contenuto: 1. Divisibility -- 1.1 Divisors -- 1.2 Bezout’s identity -- 1.3 Least common multiples -- 1.4 Linear Diophantine equations -- 1.5 Supplementary exercises -- 2. Prime Numbers -- 2.1 Prime numbers and prime-power factorisations -- 2.2 Distribution of primes -- 2.3 Fermat and Mersenne primes -- 2.4 Primality-testing and factorisation -- 2.5 Supplementary exercises -- 3. Congruences -- 3.1 Modular arithmetic -- 3.2 Linear congruences -- 3.3 Simultaneous linear congruences -- 3.4 Simultaneous non-linear congruences -- 3.5 An extension of the Chinese Remainder Theorem -- 3.6 Supplementary exercises -- 4. Congruences with a Prime-power Modulus -- 4.1 The arithmetic of ?p -- 4.2 Pseudoprimes and Carmichael numbers -- 4.3 Solving congruences mod (pe) -- 4.4 Supplementary exercises -- 5. Euler’s Function -- 5.1 Units -- 5.2 Euler’s function -- 5.3 Applications of Euler’s function -- 5.4 Supplementary exercises -- 6. The Group of Units -- 6.1 The group Un -- 6.2 Primitive roots -- 6.3 The group Une, where p is an odd prime -- 6.4 The group U2e -- 6.5 The existence of primitive roots -- 6.6 Applications of primitive roots -- 6.7 The algebraic structure of Un -- 6.8 The universal exponent -- 6.9 Supplementary exercises -- 7. Quadratic Residues -- 7.1 Quadratic congruences -- 7.2 The group of quadratic residues -- 7.3 The Legendre symbol -- 7.4 Quadratic reciprocity -- 7.5 Quadratic residues for prime-power moduli -- 7.6 Quadratic residues for arbitrary moduli -- 7.7 Supplementary exercises -- 8. Arithmetic Functions -- 8.1 ; Definition and examples -- 8.2 Perfect numbers -- 8.3 The Mobius Inversion Formula -- 8.4 An application of the Mobius Inversion Formula -- 8.5 Properties of the Mobius function -- 8.6 The Dirichlet product -- 8.7 Supplementary exercises -- 9. The Riemann Zeta Function -- 9.1 Historical background -- 9.2 Convergence -- 9.3 Applications to prime numbers -- 9.4 Random integers -- 9.5 Evaluating ?(2) -- 9.6 Evaluating ?(2k) -- 9.7 Dirichlet series -- 9.8 Euler products -- 9.9 Complex variables -- 9.10 Supplementary exercises -- 10. Sums of Squares -- 10.1 Sums of two squares -- 10.2 The Gaussian integers -- 10.3 Sums of three squares -- 10.4 Sums of four squares -- 10.5 Digression on quaternions -- 10.6 Minkowski’s Theorem -- 10.7 Supplementary exercises -- 11. Fermat’s Last Theorem -- 11.1 The problem -- 11.2 Pythagoras’s Theorem -- 11.3 Pythagorean triples -- 11.4 Isosceles triangles and irrationality -- 11.5 The classification of Pythagorean triples -- 11.6 Fermat -- 11.7 The case n = 4 -- 11.8 Odd prime exponents -- 11.9 Lame and Kummer -- 11.10 Modern developments -- 11.11 Further reading -- Solutions to Exercises -- Index of symbols -- Index of names.
• Sommario/riassunto: Our intention in writing this book is to give an elementary introduction to number theory which does not demand a great deal of mathematical back­ ground or maturity from the reader, and which can be read and understood with no extra assistance. Our first three chapters are based almost entirely on A-level mathematics, while the next five require little else beyond some el­ ementary group theory. It is only in the last three chapters, where we treat more advanced topics, including recent developments, that we require greater mathematical background; here we use some basic ideas which students would expect to meet in the first year or so of a typical undergraduate course in math­ ematics. Throughout the book, we have attempted to explain our arguments as fully and as clearly as possible, with plenty of worked examples and with outline solutions for all the exercises. There are several good reasons for choosing number theory as a subject. It has a long and interesting history, ranging from the earliest recorded times to the present day (see Chapter 11, for instance, on Fermat's Last Theorem), and its problems have attracted many of the greatest mathematicians; consequently the study of number theory is an excellent introduction to the development and achievements of mathematics (and, indeed, some of its failures). In particular, the explicit nature of many of its problems, concerning basic properties of inte­ gers, makes number theory a particularly suitable subject in which to present modern mathematics in elementary terms.

Dielectric phenomena in solids [[electronic resource] ] : with emphasis on physical concepts of electronic processes / / Kwan Chi Kao

• Record Nr.: UNINA9910458075603321
• Autore: Kao Kwan-Chi
• Pubbl/distr/stampa: Amsterdam ; ; Boston, : Academic Press, c2004
• ISBN: 1-280-96139-2; 9786610961399; 1-4294-6491-7; 0-08-047016-5
• Descrizione fisica: 1 online resource (601 p.)
• Disciplina: 537/.24
• Soggetti: Dielectrics; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover; Front matter; Half Title Page; Title Page; Copyright; Dedication Page; Contents; Preface; 1. Introduction; 1.1 Maxwell's Equations; 1.2 Magnetization; 1.3 Electromagnetic Waves and Fields; 1.4 Dimensions and Units; References; 2. Electric Polarization and Relaxation; 2.1 Fundamental Concepts; 2.2 Electric Polarization and Relaxation in Static Electric Fields; 2.3 The Mechanisms of Electric Polarization; 2.4 Classification of Dielectric Materials; 2.5 Internal Fields; 2.6 Electric Polarization and Relaxation in Time-Varying Electric Fields; 2.7 Dielectric Relaxation Phenomena; References; 3. Optical and Electro-Optic Processes 3.1 Nature of Light; 3.2 Modulation of Light; 3.3 Interaction between Radiation and Matter; 3.4 Luminescence; 3.5 Photoemission; 3.6 Photovoltaic Effects; References; 4. Ferroelectrics, Piezoelectrics, and Pyroelectrics; 4.1 Introductory Remarks; 4.2 Ferroelectric Phenomena; 4.3 Piezoelectric Phenomena; 4.4 Pyroelectric Phenomena; References; 5. Electrets; 5.1 Introductory Remarks; 5.2 Formation of Electrets; 5.3 Charges, Electric Fields, and Currents in Electrets; 5.4 Measurements of Total Surface Charge Density and Total Charges; 5.5 Charge Storage Involving Dipolar Charges 5.6 Charge Storage ; Involving Real Charges; 5.7 Basic Effects of Electrets; 5.8 Materials for Electrets; 5.9 Applications of Electrets; References; 6. Charge Carrier Injection from Electrical Contacts; 6.1 Concepts of Electrical Contacts and Potential Barriers; 6.2 Charge Carrier Injection through Potential Barriers from Contacts; 6.3 Tunneling through Thin Dielectric Films between Electrical Contacts; 6.4 Charge Transfer at the Metal-Polymer Interface; References; 7. Electrical Conduction and Photoconduction; PART I: ELECTRICAL CONDUCTION; 7.1 Introductory Remarks 7.2 Ionic Conduction; 7.3 Electronic Conduction; 7.4 Bulk-Limited Electrical Conduction; 7.5 Bulk-Limited Electrical Conduction Involving Two Types of Carriers; 7.6 High-Field Effects; 7.7 Transitions between Electrical Conduction Processes; 7.8 Current Transient Phenomena; 7.9 Experimental Methodology and Characterization; PART II: PHOTOCONDUCTION; 7.10 Quantum Yield and Quantum Efficiency for Photoconduction; 7.11 Generation of Nonequilibrium Charge Carriers; 7.12 Photoconduction Processes; 7.13 Photosensitization; 7.14 Transient Photoconduction; References; 8. Electrical Aging, Discharge, and Breakdown Phenomena8.1 Electrical Aging; 8.2 Electrical Discharges; 8.3 Electrical Breakdown; References; Index
• Sommario/riassunto: In general, a dielectric is considered as a non-conducting or insulating material (such as a ceramic or polymer used to manufacture a microelectronic device). This book describes the laws governing all dielectric phenomena.·A unified approach is used in describing each of the dielectric phenomena, with the aim of answering ""what?"", ""how?"" and ""why"" for the occurrence of each phenomenon;·Coverage unavailable in other books on ferroelectrics, piezoelectrics, pyroelectrics, electro-optic processes, and electrets;·Theoretical analyses are general and broadly applicable;·