Section 1 The princile of Mathematical Induction 1.1 Integers and Natural Numbers
1.2 Introduction to the princile of Mathematical Induction
1.3 Some examples of proof using the princile of Mathematical Inductin
集合と関数、グラフ、写像
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Section 2 Sets and Functions 2.1 Sets
2.2 Unions, Intersections and Complements of Sets
2.3 Subsets and Power Sets
2.4 The specificationof Sets
2.5 Binary Relations
2.6 Congruences
2.7 Partitions and Equivalence Relations
2.8 Partial Oeders and Lattices
2.9 Cartecian Products of Sets
2.10 Functions between Sets
2.11 Composition of Functions
2.12 The Graph of a Function
2.13 The Inverse of a FUnction
2.14 Injective, Surjective and Bijective Functions
2.15 Partial Mapping
グラフ論、ハミルトン経路と回路
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Section 3 Graph Theory 3.1 Undirected Graphs
3.2 Incidence and Adjacency
3.3 Incidence and Adjacency Tables and Matrices
3.4 Complemete Graphs
3.5 Bipartial Graphs
3.6 Isomorphphism of Graphs
3.7 Subgraphs
3.8 Vertex Degrees
3.9 Walks, Trails and Path
3.10 Connected Graphs
3.11 The components of a Graph
3.12 Circuits
3.13 Eulerian Trails and Circuits
3.14 Hamiltonian Paths and Circuit
3.15 Forests and Trees
3.16 Spanning Trees
3.17 Directed Graphs
3.18 Adjacency Matrices and Directed Graphs
3.19 Directed Graphs and Binary Relations
抽象代数、2項関係、モノイド、群
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Section 4 Abstract Algebra 4.1 Binary Operations on Sets
4.2 Commutative Binary Operations
4.3 Associative Binary Operations
4.4 Semigroups
4.5 The General Associative Law
4.6 Identity elements
4.7 Monoide
4.8 Inverses
4.9 Groups
4.10 Homomorphisms and Isomorphisms
4.11 Quaternions
4.12 Quaternions and Vectors
4.13 Quaternions and Rotations
自然数、整数、数学帰納法<2BA1s1.pdf>
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