LEADER 04501nam 2200601 a 450 001 9910133223003321 005 20200520144314.0 010 $a1-283-20343-X 010 $a9786613203434 010 $a0-470-64054-5 010 $a0-470-64053-7 035 $a(CKB)3400000000015945 035 $a(EBL)698853 035 $a(OCoLC)746326253 035 $a(SSID)ssj0000520833 035 $a(PQKBManifestationID)11335848 035 $a(PQKBTitleCode)TC0000520833 035 $a(PQKBWorkID)10517742 035 $a(PQKB)10503580 035 $a(MiAaPQ)EBC698853 035 $a(PPN)250682761 035 $a(EXLCZ)993400000000015945 100 $a20100218d2010 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAlgebra and number theory $ean integrated approach /$fMartyn R. Dixon, Leonid A. Kurdachenko, Igor Ya. Subbotin 210 $aHoboken, N.J. $cWiley$dc2010 215 $a1 online resource (538 p.) 300 $aIncludes index. 311 $a0-470-49636-3 327 $aAlgebra 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 327 $aExercise 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 327 $aExercise 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 8.3 327 $a8.4 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 330 $aExplore 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 606 $aNumber theory 606 $aAlgebra 615 0$aNumber theory. 615 0$aAlgebra. 676 $a512 700 $aDixon$b Martyn R$g(Martyn Russell),$f1955-$062617 701 $aKurdachenko$b L$0522034 701 $aSubbotin$b Igor Ya.$f1950-$0522035 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910133223003321 996 $aAlgebra and number theory$9835197 997 $aUNINA