| Joseph J．Rotman 美国伊利诺伊大学厄巴纳—尚佩恩分校数学系教授。他著有多部数学方面的书，其中包括《Advanced Modern Algebra》 (高等近世代数，本书中文版由机械工业出版社引进出版)、《Galois Theory》等。... .. << 查看详细 |
| preface to the third edition . suggested syllabi to the reader chapter 1 number theory section 1.1 induction section 1.2 binomial theorem and complex numbers section 1.3 greatest common divisors section 1.4 the fundamental theorem of arithmetic section 1.5 congruences section 1.6 dates and days chapter 2 groups i section 2.1 some set theory functions equivalence relations section 2.2 permutations section 2.3 groups symmetry section 2.4 subgroups and lagrange's theorem section 2.5 homomorphisms section 2.6 quotient groups section 2.7 group actions .section 2.8 counting with groups chapter 3 commutative rings i section 3.1 first properties section 3.2 fields section 3.3 polynomials section 3.4 homomorphisms section 3.5 from numbers to polynomials euclidean rings section 3.6 unique factorization section 3.7 irreducibility section 3.8 quotient rings and finite fields section 3.9 a mathematical odyssey latin squares magic squares design of experiments projective planes chapter 4 linear algebra section 4.1 vector spaces gaussian elimination.. section 4.2 euclidean constructions section 4.3 linear transformations section 4.4 eigenvalues section 4.5 codes block codes linear codes decoding chapter 5 fields section 5.1 classical formulas viete's cubic formula section 5.2 insolvability of the general quintic formulas and solvability by radicals quadratics cubics quartics translation into group theory section 5.3 epilog chapter 6 groups ii section 6.1 finite abelian groups section 6.2 the sylow theorems section 6.3 ornamental symmetry chapter 7 commutative rings ii section 7.1 prime ideals and maximal ideals section 7.2 unique factorization section 7.3 noetherian rings section 7.4 varieties section 7.5 generalized divison algorithm monomial orders division algorithm section 7.6 grobner bases appendix a inequalities appendix b pseudocodes hints for selected exercises bibliography index ... |
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