1-Dimensional Cohen-Macaulay Rings / Eben Matlis / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (1973)

Public ISBD Faire une suggestion d'achat Titre : 1-Dimensional Cohen-Macaulay Rings Type de document : document électronique Auteurs : Eben Matlis ; SpringerLink (Online service) Editeur : Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer Année de publication : 1973 Collection : Lecture Notes in Mathematics - LNM, ISSN 0075-8434 num. 327 Importance : 157 p. Format : digital ISBN/ISSN/EAN : 978-3-540-46923-0 Langues : Anglais (eng) Tags : Mathematics  Algebra Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=106598 1-Dimensional Cohen-Macaulay Rings [document électronique] / Eben Matlis ; SpringerLink (Online service)  . - Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer, 1973 . - 157 p. ; digital. - (Lecture Notes in Mathematics - LNM, ISSN 0075-8434; 327) . ISBN : 978-3-540-46923-0 Langues : Anglais (eng) Tags : Mathematics  Algebra Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=106598

100+1 Problems in Advanced Calculus / Paolo Toni / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2022)

Public ISBD Faire une suggestion d'achat Titre : 100+1 Problems in Advanced Calculus : A Creative Journey through the Fjords of Mathematical Analysis for Beginners Type de document : document électronique Auteurs : Paolo Toni, ; Pier Domenico Lamberti, ; SpringerLink (Online service) ; Giacomo Drago, Editeur : Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer Année de publication : 2022 Collection : Problem Books in Mathematics, ISSN 0941-3502 Importance : XVII, 220 p. 171 illus Présentation : online resource ISBN/ISSN/EAN : 978-3-030-91863-7 Langues : Anglais (eng) Tags : Functions of real variables  Mathematical analysis  Real Functions  Analysis Résumé : This book convenes a collection of carefully selected problems in mathematical analysis, crafted to achieve maximum synergy between analytic geometry and algebra and favoring mathematical creativity in contrast to mere repetitive techniques. With eight chapters, this work guides the student through the basic principles of the subject, with a level of complexity that requires good use of imagination. In this work, all the fundamental concepts seen in a first-year Calculus course are covered. Problems touch on topics like inequalities, elementary point-set topology, limits of real-valued functions, differentiation, classical theorems of differential calculus (Rolle, Lagrange, Cauchy, and l’Hospital), graphs of functions, and Riemann integrals and antiderivatives. Every chapter starts with a theoretical background, in which relevant definitions and theorems are provided; then, related problems are presented. Formalism is kept at a minimum, and solutions can be found at the end of each chapter. Instructors and students of Mathematical Analysis, Calculus and Advanced Calculus aimed at first-year undergraduates in Mathematics, Physics and Engineering courses can greatly benefit from this book, which can also serve as a rich supplement to any traditional textbook on these subjects as well Note de contenu : Summary of basic theory of inequalities -- Sets, sequences, functions -- Limits of functions, continuity -- Differentiation -- Classical theorems of differential calculus -- Monotonicity, concavity, minima, maxima, inflection points -- Graphs of functions -- Integrals Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=172326 100+1 Problems in Advanced Calculus : A Creative Journey through the Fjords of Mathematical Analysis for Beginners [document électronique] / Paolo Toni, ; Pier Domenico Lamberti, ; SpringerLink (Online service) ; Giacomo Drago,  . - Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer, 2022 . - XVII, 220 p. 171 illus : online resource. - (Problem Books in Mathematics, ISSN 0941-3502) . ISBN : 978-3-030-91863-7 Langues : Anglais (eng) Tags : Functions of real variables  Mathematical analysis  Real Functions  Analysis Résumé : This book convenes a collection of carefully selected problems in mathematical analysis, crafted to achieve maximum synergy between analytic geometry and algebra and favoring mathematical creativity in contrast to mere repetitive techniques. With eight chapters, this work guides the student through the basic principles of the subject, with a level of complexity that requires good use of imagination. In this work, all the fundamental concepts seen in a first-year Calculus course are covered. Problems touch on topics like inequalities, elementary point-set topology, limits of real-valued functions, differentiation, classical theorems of differential calculus (Rolle, Lagrange, Cauchy, and l’Hospital), graphs of functions, and Riemann integrals and antiderivatives. Every chapter starts with a theoretical background, in which relevant definitions and theorems are provided; then, related problems are presented. Formalism is kept at a minimum, and solutions can be found at the end of each chapter. Instructors and students of Mathematical Analysis, Calculus and Advanced Calculus aimed at first-year undergraduates in Mathematics, Physics and Engineering courses can greatly benefit from this book, which can also serve as a rich supplement to any traditional textbook on these subjects as well Note de contenu : Summary of basic theory of inequalities -- Sets, sequences, functions -- Limits of functions, continuity -- Differentiation -- Classical theorems of differential calculus -- Monotonicity, concavity, minima, maxima, inflection points -- Graphs of functions -- Integrals Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=172326

10th International Conference on Automated Deduction / Mark E. Stickel / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (1990)

Public ISBD Faire une suggestion d'achat Titre : 10th International Conference on Automated Deduction : Kaiserslautern, FRG, July 24-27, 1990 Proceedings Type de document : document électronique Auteurs : Mark E. Stickel ; SpringerLink (Online service) Editeur : Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer Année de publication : 1990 Collection : Lecture Notes in Computer Science - LNCS, ISSN 0302-9743 num. 449 Importance : XVIII, 690 p Présentation : digital ISBN/ISSN/EAN : 978-3-540-47171-4 Langues : Anglais (eng) Descripteurs : Intelligence artificielle Tags : Computer science  Computer Science  Artificial Intelligence  Mathematical Logic and Formal Languages Résumé : This volume contains the papers presented at the 10th International Conference on Automated Deduction (CADE-10). CADE is the major forum at which research on all aspects of automated deduction is presented. Although automated deduction research is also presented at more general artificial intelligence conferences, the CADE conferences have no peer in the concentration and quality of their contributions to this topic. The papers included range from theory to implementation and experimentation, from propositional to higher-order calculi and nonclassical logics; they refine and use a wealth of methods including resolution, paramodulation, rewriting, completion, unification and induction; and they work with a variety of applications including program verification, logic programming, deductive databases, and theorem proving in many domains. The volume also contains abstracts of 20 implementations of automated deduction systems. The authors of about half the papers are from the United States, many are from Western Europe, and many too are from the rest of the world. The proceedings of the 5th, 6th, 7th, 8th and 9th CADE conferences are published as Volumes 87, 138, 170, 230, 310 in the series Lecture Notes in Computer Science Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=104006 10th International Conference on Automated Deduction : Kaiserslautern, FRG, July 24-27, 1990 Proceedings [document électronique] / Mark E. Stickel ; SpringerLink (Online service)  . - Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer, 1990 . - XVIII, 690 p : digital. - (Lecture Notes in Computer Science - LNCS, ISSN 0302-9743; 449) . ISBN : 978-3-540-47171-4 Langues : Anglais (eng) Descripteurs : Intelligence artificielle Tags : Computer science  Computer Science  Artificial Intelligence  Mathematical Logic and Formal Languages Résumé : This volume contains the papers presented at the 10th International Conference on Automated Deduction (CADE-10). CADE is the major forum at which research on all aspects of automated deduction is presented. Although automated deduction research is also presented at more general artificial intelligence conferences, the CADE conferences have no peer in the concentration and quality of their contributions to this topic. The papers included range from theory to implementation and experimentation, from propositional to higher-order calculi and nonclassical logics; they refine and use a wealth of methods including resolution, paramodulation, rewriting, completion, unification and induction; and they work with a variety of applications including program verification, logic programming, deductive databases, and theorem proving in many domains. The volume also contains abstracts of 20 implementations of automated deduction systems. The authors of about half the papers are from the United States, many are from Western Europe, and many too are from the rest of the world. The proceedings of the 5th, 6th, 7th, 8th and 9th CADE conferences are published as Volumes 87, 138, 170, 230, 310 in the series Lecture Notes in Computer Science Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=104006

11th International Conference on Analysis and Optimization of Systems Discrete Event Systems / Guy Cohen ; SpringerLink (Online service) ; Jean-Pierre Quadrat / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (1994)

Public ISBD Faire une suggestion d'achat Titre : 11th International Conference on Analysis and Optimization of Systems Discrete Event Systems : Sophia-Antipolis, June 15?16?17, 1994 Type de document : document électronique Auteurs : Guy Cohen ; SpringerLink (Online service) ; Jean-Pierre Quadrat Editeur : Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer Année de publication : 1994 Collection : Lecture Notes in Control and Information Sciences, ISSN 0170-8643 num. 199 Importance : XIX, 626 p Présentation : online resource ISBN/ISSN/EAN : 978-3-540-39345-0 Langues : Anglais (eng) Tags : Engineering  Computer hardware  Software engineering  Applied mathematics  Engineering mathematics engineering  Robotics  Mechatronics  Applied Mathematics  Computational Methods of Engineering  Computer Hardware  Software Engineering  Programming and Operating Systems Résumé : The conference, coorganized by INRIA and Ecole des Mines de Paris, focuses on Discrete Event Systems (DES) and is aimed at engineers, scientists and mathematicians working in the fields of Automatic Control, Operations Research and Statistics who are interested in the modelling, analysis and optimization of DES. Various methods such as Automata theory, Petri nets, etc. are proposed to describe and analyze such systems. Comparison of these different mathematical approaches and the global confrontation of theoretical approaches with applications in manufacturing, telecommunications, parallel computing, transportation, etc. are the goals of the conference Note de contenu : Logical aspects of control of discrete-event systems: A survey of tools and techniques -- Automata-theoretic verification of coordinating processes -- Hierarchical COCOLOG for finite machines -- Nondeterministic supervision under partial observations -- Avoiding blocking in prioritized synchronization based control of nondeterministic systems -- Supervisory control for nondeterministic systems -- Effective control of logical discrete event systems in a trace theory setting using the reflection operator -- Diagnosability of discrete event systems -- On the supremal L m -closed and the supremal L m -closed and L-controllable sublanguages of a given language -- Continuous-time supervisory synthesis for distributed-clock discrete-event processes -- Conditions for optimization of discrete event systems using temporal logic models -- Partial difference equation extensions to automata regulator theory -- An algebraic temporal logic approach to the forbidden state problem in discrete event control -- Automata timing specification -- Synthesis of static controllers for forbidden states problems in Boolean C/E systems using the Boolean differential calculus -- Analysis of autonomous Petri nets with bulk services and arrivals -- Dependability and performability analysis using stochastic Petri nets -- Controlled Petri nets: A tutorial survey -- Functional and performance analysis of cooperating sequential processes -- Hierarchically combined queueing Petri nets -- Optimizing structural analysis of extended Petri nets models -- Reduced state space generation of concurrent systems using weak persistency -- A new approach to discrete time stochastic Petri nets -- Analysis of timed place/transition nets using minimal state graphs -- An algebraic description of processes of timed Petri nets -- Dioids and discrete event systems -- On structural properties of min-max systems -- Rational series over dioids and discrete event systems -- Stochastic linear systems in the (max, +) algebra -- Cycle times and fixed points of min-max functions -- The characteristic equation and minimal state space realization of SISO systems in the max algebra -- A max-algebra solution to the supervisory control problem for real-time discrete event systems -- Stable earliest starting schedules for periodic job shops: A linear system approach -- Time discrete and continuous control problems convergence of value functions -- Bellman processes -- Maslov optimisation theory: Stochastic interpretation, particle resolution -- Networks methods for endomorphisms of semimodules over min-plus algebras -- Subdirect sum decomposition of finite dimensional pseudomodules -- The algorithmic analysis of hybrid systems -- A unified framework for hybrid control -- Reasoning about hybrid systems with symbolic simulation -- Simple hybrid control systems ? continuous FDLTI plants with quantized control inputs and symbolic measurements -- Controllability and control-law synthesis of linear hybrid systems -- Sample-path-based continuous and discrete optimization of discrete event systems: From gradient estimation to ?rapid learning? -- Infinitesimal perturbation analysis of Generalized Semi-Markov Processes: A tutorial -- A tutorial overview of optimization via discrete-event simulation -- Parallel simulation of discrete event systems -- On the existence and estimation of performance measure derivatives for stochastic recursions -- Perturbation analysis for the GI/G/1 queue with two priority classes -- Supply management in assembly systems: The case of random lead times -- Simulation trees for functional estimation via the phantom method -- Infinitestimal Perturbation Analysis for discrete event systems with discrete lifetime distributions -- Loss networks in thermodynamic limit -- A survey of Markovian methods for stability of networks -- Stationary regime and stability of free-choice Petri nets -- Allocation sequences of two processes sharing a resource -- Stability criteria for yet another class of multidimensional distributed systems -- Flow control of a virtual circuit -- Stochastic scheduling of precedence graphs -- Management of manufacturing systems based on Petri nets -- Approximate closed queueing network model of a manufacturing cell with a batch material transporter -- Optimizing the transient behavior of hedging control policies in manufacturing systems -- Finding optimal number of Kanbans in a manufacturing system via stochastic approximation and perturbation analysis -- Performance evaluation of a generalized kanban system with a general arrival process of demands -- Hoist scheduling problem in a real time context -- On controlling a class of assembly system with alternative production routeing -- Planification Hiérarchisée de la Production: Agrégation du Temps et Cohérence -- Multi-site planning: A centralized or a distributed approach? -- Algorithms for simultaneous scheduling of machines and vehicles in a FMS Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=124655 11th International Conference on Analysis and Optimization of Systems Discrete Event Systems : Sophia-Antipolis, June 15?16?17, 1994 [document électronique] / Guy Cohen ; SpringerLink (Online service) ; Jean-Pierre Quadrat . - Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer, 1994 . - XIX, 626 p : online resource. - (Lecture Notes in Control and Information Sciences, ISSN 0170-8643; 199) . ISBN : 978-3-540-39345-0 Langues : Anglais (eng) Tags : Engineering  Computer hardware  Software engineering  Applied mathematics  Engineering mathematics engineering  Robotics  Mechatronics  Applied Mathematics  Computational Methods of Engineering  Computer Hardware  Software Engineering  Programming and Operating Systems Résumé : The conference, coorganized by INRIA and Ecole des Mines de Paris, focuses on Discrete Event Systems (DES) and is aimed at engineers, scientists and mathematicians working in the fields of Automatic Control, Operations Research and Statistics who are interested in the modelling, analysis and optimization of DES. Various methods such as Automata theory, Petri nets, etc. are proposed to describe and analyze such systems. Comparison of these different mathematical approaches and the global confrontation of theoretical approaches with applications in manufacturing, telecommunications, parallel computing, transportation, etc. are the goals of the conference Note de contenu : Logical aspects of control of discrete-event systems: A survey of tools and techniques -- Automata-theoretic verification of coordinating processes -- Hierarchical COCOLOG for finite machines -- Nondeterministic supervision under partial observations -- Avoiding blocking in prioritized synchronization based control of nondeterministic systems -- Supervisory control for nondeterministic systems -- Effective control of logical discrete event systems in a trace theory setting using the reflection operator -- Diagnosability of discrete event systems -- On the supremal L m -closed and the supremal L m -closed and L-controllable sublanguages of a given language -- Continuous-time supervisory synthesis for distributed-clock discrete-event processes -- Conditions for optimization of discrete event systems using temporal logic models -- Partial difference equation extensions to automata regulator theory -- An algebraic temporal logic approach to the forbidden state problem in discrete event control -- Automata timing specification -- Synthesis of static controllers for forbidden states problems in Boolean C/E systems using the Boolean differential calculus -- Analysis of autonomous Petri nets with bulk services and arrivals -- Dependability and performability analysis using stochastic Petri nets -- Controlled Petri nets: A tutorial survey -- Functional and performance analysis of cooperating sequential processes -- Hierarchically combined queueing Petri nets -- Optimizing structural analysis of extended Petri nets models -- Reduced state space generation of concurrent systems using weak persistency -- A new approach to discrete time stochastic Petri nets -- Analysis of timed place/transition nets using minimal state graphs -- An algebraic description of processes of timed Petri nets -- Dioids and discrete event systems -- On structural properties of min-max systems -- Rational series over dioids and discrete event systems -- Stochastic linear systems in the (max, +) algebra -- Cycle times and fixed points of min-max functions -- The characteristic equation and minimal state space realization of SISO systems in the max algebra -- A max-algebra solution to the supervisory control problem for real-time discrete event systems -- Stable earliest starting schedules for periodic job shops: A linear system approach -- Time discrete and continuous control problems convergence of value functions -- Bellman processes -- Maslov optimisation theory: Stochastic interpretation, particle resolution -- Networks methods for endomorphisms of semimodules over min-plus algebras -- Subdirect sum decomposition of finite dimensional pseudomodules -- The algorithmic analysis of hybrid systems -- A unified framework for hybrid control -- Reasoning about hybrid systems with symbolic simulation -- Simple hybrid control systems ? continuous FDLTI plants with quantized control inputs and symbolic measurements -- Controllability and control-law synthesis of linear hybrid systems -- Sample-path-based continuous and discrete optimization of discrete event systems: From gradient estimation to ?rapid learning? -- Infinitesimal perturbation analysis of Generalized Semi-Markov Processes: A tutorial -- A tutorial overview of optimization via discrete-event simulation -- Parallel simulation of discrete event systems -- On the existence and estimation of performance measure derivatives for stochastic recursions -- Perturbation analysis for the GI/G/1 queue with two priority classes -- Supply management in assembly systems: The case of random lead times -- Simulation trees for functional estimation via the phantom method -- Infinitestimal Perturbation Analysis for discrete event systems with discrete lifetime distributions -- Loss networks in thermodynamic limit -- A survey of Markovian methods for stability of networks -- Stationary regime and stability of free-choice Petri nets -- Allocation sequences of two processes sharing a resource -- Stability criteria for yet another class of multidimensional distributed systems -- Flow control of a virtual circuit -- Stochastic scheduling of precedence graphs -- Management of manufacturing systems based on Petri nets -- Approximate closed queueing network model of a manufacturing cell with a batch material transporter -- Optimizing the transient behavior of hedging control policies in manufacturing systems -- Finding optimal number of Kanbans in a manufacturing system via stochastic approximation and perturbation analysis -- Performance evaluation of a generalized kanban system with a general arrival process of demands -- Hoist scheduling problem in a real time context -- On controlling a class of assembly system with alternative production routeing -- Planification Hiérarchisée de la Production: Agrégation du Temps et Cohérence -- Multi-site planning: A centralized or a distributed approach? -- Algorithms for simultaneous scheduling of machines and vehicles in a FMS Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=124655

13 Lectures on Fermat?s Last Theorem / Paulo Ribenboim / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (1979)

Public ISBD Faire une suggestion d'achat Titre : 13 Lectures on Fermat?s Last Theorem Type de document : document électronique Auteurs : Paulo Ribenboim ; SpringerLink (Online service) Editeur : Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer Année de publication : 1979 Importance : XVI, 302 p Présentation : online resource ISBN/ISSN/EAN : 978-1-4684-9342-9 Langues : Anglais (eng) Tags : Mathematics  Computer science  Number theory  Number Theory  Computer Science Note de contenu : Lecture I The Early History of Fermat?s Last Theorem -- 1 The Problem -- 2 Early Attempts -- 3 Kummer?s Monumental Theorem -- 4 Regular Primes -- 5 Kummer?s Work on Irregular Prime Exponents -- 6 Other Relevant Results -- 7 The Golden Medal and the Wolfskehl Prize -- Lecture II Recent Results -- 1 Stating the Results -- 2 Explanations -- Lecture III B.K. = Before Kummer -- 1 The Pythagorean Equation -- 2 The Biquadratic Equation -- 3 The Cubic Equation -- 4 The Quintic Equation -- 5 Fermat?s Equation of Degree Seven -- Lecture IV The Naïve Approach -- 1 The Relations of Barlow and Abel -- 2 Sophie Germain -- 3 Congruences -- 4 Wendt?s Theorem -- 5 Abel?s Conjecture -- 6 Fermat?s Equation with Even Exponent -- 7 Odds and Ends -- Lecture V Kummer?s Monument -- 1 A Justification of Kummer?s Method -- 2 Basic Facts about the Arithmetic of Cyclotomic Fields -- 3 Kummer?s Main Theorem -- Lecture VI Regular Primes -- 1 The Class Number of Cyclotomic Fields -- 2 Bernoulli Numbers and Kummer?s Regularity Criterion -- 3 Various Arithmetic Properties of Bernoulli Numbers -- 4 The Abundance of Irregular Primes -- 5 Computation of Irregular Primes -- Lecture VII Kummer Exits -- 1 The Periods of the Cyclotomic Equation -- 2 The Jacobi Cyclotomic Function -- 3 On the Generation of the Class Group of the Cyclotomic Field -- 4 Kummer?s Congruences -- 5 Kummer?s Theorem for a Class of Irregular Primes -- 6 Computations of the Class Number -- Lecture VIII After Kummer, a New Light -- 1 The Congruences of Mirimanoff -- 2 The Theorem of Krasner -- 3 The Theorems of Wieferich and Mirimanoff -- 4 Fermat?s Theorem and the Mersenne Primes -- 5 Summation Criteria -- 6 Fermat Quotient Criteria -- Lecture IX The Power of Class Field Theory -- 1 The Power Residue Symbol -- 2 Kummer Extensions -- 3 The Main Theorems of Furtwängler -- 4 The Method of Singular Integers -- 5 Hasse -- 6 The p-Rank of the Class Group of the Cyclotomic Field -- 7 Criteria of p-Divisibility of the Class Number -- 8 Properly and Improperly Irregular Cyclotomic Fields -- Lecture X Fresh Efforts -- 1 Fermat?s Last Theorem Is True for Every Prime Exponent Less Than 125000 -- 2 Euler Numbers and Fermat?s Theorem -- 3 The First Case Is True for Infinitely Many Pairwise Relatively Prime Exponents -- 4 Connections between Elliptic Curves and Fermat?s Theorem -- 5 Iwasawa?s Theory -- 6 The Fermat Function Field -- 7 Mordell?s Conjecture -- 8 The Logicians -- Lecture XI Estimates -- 1 Elementary (and Not So Elementary) Estimates -- 2 Estimates Based on the Criteria Involving Fermat Quotients -- 3 Thue, Roth, Siegel and Baker -- 4 Applications of the New Methods -- Lecture XII Fermat?s Congruence -- 1 Fermat?s Theorem over Prime Fields -- 2 The Local Fermat?s Theorem -- 3 The Problem Modulo a Prime-Power -- Lecture XIII Variations and Fugue on a Theme -- 1 Variation I (In the Tone of Polynomial Functions) -- 2 Variation II (In the Tone of Entire Functions) -- 3 Variation III (In the Theta Tone) -- 4 Variation IV (In the Tone of Differential Equations) -- 5 Variation V (Giocoso) -- 6 Variation VI (In the Negative Tone) -- 7 Variation VII (In the Ordinal Tone) -- 8 Variation VIII (In a Nonassociative Tone) -- 9 Variation IX (In the Matrix Tone) -- 10 Fugue (In the Quadratic Tone) -- Epilogue -- Index of Names Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=127641 13 Lectures on Fermat?s Last Theorem [document électronique] / Paulo Ribenboim ; SpringerLink (Online service)  . - Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer, 1979 . - XVI, 302 p : online resource. ISBN : 978-1-4684-9342-9 Langues : Anglais (eng) Tags : Mathematics  Computer science  Number theory  Number Theory  Computer Science Note de contenu : Lecture I The Early History of Fermat?s Last Theorem -- 1 The Problem -- 2 Early Attempts -- 3 Kummer?s Monumental Theorem -- 4 Regular Primes -- 5 Kummer?s Work on Irregular Prime Exponents -- 6 Other Relevant Results -- 7 The Golden Medal and the Wolfskehl Prize -- Lecture II Recent Results -- 1 Stating the Results -- 2 Explanations -- Lecture III B.K. = Before Kummer -- 1 The Pythagorean Equation -- 2 The Biquadratic Equation -- 3 The Cubic Equation -- 4 The Quintic Equation -- 5 Fermat?s Equation of Degree Seven -- Lecture IV The Naïve Approach -- 1 The Relations of Barlow and Abel -- 2 Sophie Germain -- 3 Congruences -- 4 Wendt?s Theorem -- 5 Abel?s Conjecture -- 6 Fermat?s Equation with Even Exponent -- 7 Odds and Ends -- Lecture V Kummer?s Monument -- 1 A Justification of Kummer?s Method -- 2 Basic Facts about the Arithmetic of Cyclotomic Fields -- 3 Kummer?s Main Theorem -- Lecture VI Regular Primes -- 1 The Class Number of Cyclotomic Fields -- 2 Bernoulli Numbers and Kummer?s Regularity Criterion -- 3 Various Arithmetic Properties of Bernoulli Numbers -- 4 The Abundance of Irregular Primes -- 5 Computation of Irregular Primes -- Lecture VII Kummer Exits -- 1 The Periods of the Cyclotomic Equation -- 2 The Jacobi Cyclotomic Function -- 3 On the Generation of the Class Group of the Cyclotomic Field -- 4 Kummer?s Congruences -- 5 Kummer?s Theorem for a Class of Irregular Primes -- 6 Computations of the Class Number -- Lecture VIII After Kummer, a New Light -- 1 The Congruences of Mirimanoff -- 2 The Theorem of Krasner -- 3 The Theorems of Wieferich and Mirimanoff -- 4 Fermat?s Theorem and the Mersenne Primes -- 5 Summation Criteria -- 6 Fermat Quotient Criteria -- Lecture IX The Power of Class Field Theory -- 1 The Power Residue Symbol -- 2 Kummer Extensions -- 3 The Main Theorems of Furtwängler -- 4 The Method of Singular Integers -- 5 Hasse -- 6 The p-Rank of the Class Group of the Cyclotomic Field -- 7 Criteria of p-Divisibility of the Class Number -- 8 Properly and Improperly Irregular Cyclotomic Fields -- Lecture X Fresh Efforts -- 1 Fermat?s Last Theorem Is True for Every Prime Exponent Less Than 125000 -- 2 Euler Numbers and Fermat?s Theorem -- 3 The First Case Is True for Infinitely Many Pairwise Relatively Prime Exponents -- 4 Connections between Elliptic Curves and Fermat?s Theorem -- 5 Iwasawa?s Theory -- 6 The Fermat Function Field -- 7 Mordell?s Conjecture -- 8 The Logicians -- Lecture XI Estimates -- 1 Elementary (and Not So Elementary) Estimates -- 2 Estimates Based on the Criteria Involving Fermat Quotients -- 3 Thue, Roth, Siegel and Baker -- 4 Applications of the New Methods -- Lecture XII Fermat?s Congruence -- 1 Fermat?s Theorem over Prime Fields -- 2 The Local Fermat?s Theorem -- 3 The Problem Modulo a Prime-Power -- Lecture XIII Variations and Fugue on a Theme -- 1 Variation I (In the Tone of Polynomial Functions) -- 2 Variation II (In the Tone of Entire Functions) -- 3 Variation III (In the Theta Tone) -- 4 Variation IV (In the Tone of Differential Equations) -- 5 Variation V (Giocoso) -- 6 Variation VI (In the Negative Tone) -- 7 Variation VII (In the Ordinal Tone) -- 8 Variation VIII (In a Nonassociative Tone) -- 9 Variation IX (In the Matrix Tone) -- 10 Fugue (In the Quadratic Tone) -- Epilogue -- Index of Names Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=127641

17 Lectures on Fermat Numbers / Michal Křížek / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2001)

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18 Unconventional Essays on the Nature of Mathematics / Reuben Hersh / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2006)

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20 Years of G20 / Rajat Kathuria ; SpringerLink (Online service) ; Prateek Kukreja / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2019)

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200 Years of Ricardian Trade Theory / Ronald Winthrop Jones ; SpringerLink (Online service) ; Rolf Weder / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2017)

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2016 MATRIX Annals / Jan de Gier ; SpringerLink (Online service) ; Cheryl E. Praeger ; Terence Tao / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2018)

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2017 MATRIX Annals / Jan de Gier ; SpringerLink (Online service) ; Cheryl E. Praeger ; Terence Tao / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2019)

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2018 MATRIX Annals / Jan de Gier ; SpringerLink (Online service) ; Cheryl E. Praeger ; Terence Tao / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2020)

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2019-20 MATRIX Annals / Jan de Gier ; SpringerLink (Online service) ; Cheryl E. Praeger ; Terence Tao / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2021)

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2030 Agenda and India: Moving from Quantity to Quality / Sachin Chaturvedi ; SpringerLink (Online service) ; T. C. James ; Sabyasachi Saha ; Prativa Shaw / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2019)

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21st Century Economics / Bruno S. Frey ; SpringerLink (Online service) ; Christoph A. Schaltegger / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2019)

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21st Century Learning for 21st Century Skills / Andrew Ravenscroft / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2012)

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21st Century Sports / Sascha L. Schmidt ; SpringerLink (Online service) / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2020)

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