Chapter 1 Sets 1.1 Set theory 1.2 Maps 1.3 Equivalence relations and equivalence classes 1.4 Factor sets 1.5 Number theory 1.6 The Chinese Remainder Theorem 拓展閱讀·數(shù)學(xué)家的故事 Chapter 2 Groups 2.1 Definitions and examples 2.2 Subgroups 2.3 Cyclic groups 2.4 Permutation groups 2.5 Dihedral groups 拓展閱讀·數(shù)學(xué)家的故事 Chapter 3 Properties of Groups 3.1 Cosets and Lagrange's Theorem 3.2 Normal subgroups and factor groups 3.3 Homomorphisms of groups 3.4 Isomorphisms of groups 3.5 Fundamental Isomorphism theorem of groups 3.6 Endmorphisms and automorphisms of groups 拓展閱讀·數(shù)學(xué)家的故事 Chapter 4 Rings and Fields 4.1 Rings 4.2 Subrings and Ideals 4.3 Ring homomorphisms 4.4 Maximal ideals and prime ideals 4.5 Extension fields 4.6 Algebraic extensions 拓展閱讀·數(shù)學(xué)家的故事 附錄1 Chapter 1教學(xué)PPT 1.1 Set theory 1.2 Maps 1.3 Equivalence relations and equivalence classes 1.4 Factor sets 1.5 Number theory 1.6 The Chinese Remainder Theorem 附錄2 Chapter 2教學(xué)PPT 2.1 Definitions and examples 2.2 Subgroups 2.3 Cyclic groups 2.4 Permutation groups 2.5 Dihedral groups 附錄3 Chapter 3教學(xué)PPT 3.1 Cosets and Lagrange's Theorem 3.2 Normal subgroups and factor groups 3.3 Homomorphisms of groups 3.4 Isomorphisms of groups 3.5 Fundamental Isomorphism theorem of groups
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