Algebra and number theory : an integrated approach / / Martyn R. Dixon, Leonid A. Kurdachenko, Igor Ya. Subbotin

• Autore: Dixon Martyn R (Martyn Russell), <1955->
• Pubblicazione: Hoboken, N.J., : Wiley, c2010
• Descrizione fisica: 1 online resource (538 p.)
• Disciplina: 512
• Soggetto topico: Number theory; Algebra
• Altri autori: KurdachenkoL SubbotinIgor Ya. <1950->
• Note generali: Includes index.
• Nota di contenuto: Algebra and Number Theory: An Integrated Approach; CONTENTS; PREFACE; CHAPTER 1 SETS; 1.1 Operations on Sets; Exercise Set 1.1; 1.2 Set Mappings; Exercise Set 1.2; 1.3 Products of Mappings; Exercise Set 1.3; 1.4 Some Properties of Integers; Exercise Set 1.4; CHAPTER 2 MATRICES AND DETERMINANTS; 2.1 Operations on Matrices; Exercise Set 2.1; 2.2 Permutations of Finite Sets; Exercise Set 2.2; 2.3 Determinants of Matrices; Exercise Set 2.3; 2.4 Computing Determinants; Exercise Set 2.4; 2.5 Properties of the Product of Matrices; Exercise Set 2.5; CHAPTER 3 FIELDS; 3.1 Binary Algebraic Operations ; Exercise Set 3.13.2 Basic Properties of Fields; Exercise Set 3.2; 3.3 The Field of Complex Numbers; Exercise Set 3.3; CHAPTER 4 VECTOR SPACES; 4.1 Vector Spaces; Exercise Set 4.1; 4.2 Dimension; Exercise Set 4.2; 4.3 The Rank of a Matrix; Exercise Set 4.3; 4.4 Quotient Spaces; Exercise Set 4.4; CHAPTER 5 LINEAR MAPPINGS; 5.1 Linear Mappings; Exercise Set 5.1; 5.2 Matrices of Linear Mappings; Exercise Set 5.2; 5.3 Systems of Linear Equations; Exercise Set 5.3; 5.4 Eigenvectors and Eigenvalues; Exercise Set 5.4; CHAPTER 6 BILINEAR FORMS; 6.1 Bilinear Forms; Exercise Set 6.1; 6.2 Classical Forms ; Exercise Set 6.26.3 Symmetric Forms over R; Exercise Set 6.3; 6.4 Euclidean Spaces; Exercise Set 6.4; CHAPTER 7 RINGS; 7.1 Rings, Subrings, and Examples; Exercise Set 7.1; 7.2 Equivalence Relations; Exercise Set 7.2; 7.3 Ideals and Quotient Rings; Exercise Set 7.3; 7.4 Homomorphisms of Rings; Exercise Set 7.4; 7.5 Rings of Polynomials and Formal Power Series; Exercise Set 7.5; 7.6 Rings of Multivariable Polynomials; Exercise Set 7.6; CHAPTER 8 GROUPS; 8.1 Groups and Subgroups; Exercise Set 8.1; 8.2 Examples of Groups and Subgroups; Exercise Set 8.2; 8.3 Cosets; Exercise Set 8.3 ; 8.4 Normal Subgroups and Factor GroupsExercise Set 8.4; 8.5 Homomorphisms of Groups; Exercise Set 8.5; CHAPTER 9 ARITHMETIC PROPERTIES OF RINGS; 9.1 Extending Arithmetic to Commutative Rings; Exercise Set 9.1; 9.2 Euclidean Rings; Exercise Set 9.2; 9.3 Irreducible Polynomials; Exercise Set 9.3; 9.4 Arithmetic Functions; Exercise Set 9.4; 9.5 Congruences; Exercise Set 9.5; CHAPTER 10 THE REAL NUMBER SYSTEM; 10.1 The Natural Numbers; 10.2 The Integers; 10.3 The Rationals; 10.4 The Real Numbers; ANSWERS TO SELECTED EXERCISES; INDEX
• Sommario/riassunto: Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications. Based on the authors' extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines-linear algebra, abstract algebra, and number the
• Titolo autorizzato: Algebra and number theory
• ISBN: 1-283-20343-X; 9786613203434; 0-470-64054-5; 0-470-64053-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910133223003321
• Lo trovi qui: Univ. Federico II