MAT1830 思维导图

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MAT1830 思维导图 by Mind Map: MAT1830 思维导图

1. 数论 Number Theory

1.1. 整除 divide and divisible

1.1.1. Euclidean Algorithm

1.1.2. Extended Euclidean Algorithm

1.1.3. 鉴别质数

1.2. 同余 congruence

1.2.1. 判定同余的方法

1.2.2. 同余的性质

1.2.3. Solving Linear Congruence

1.2.4. Modular Inverse

2. 逻辑 Logic

2.1. 命题逻辑Propositional Logic

2.1.1. Proposition的性质

2.1.2. Common Connectives

2.1.3. Tautology

2.1.4. Contradication

2.1.5. Logical Equivalence and Useful Logic Laws

2.1.6. Rules of Inference

2.1.7. Consequence

2.2. 谓词逻辑Predicate Logic

2.2.1. Predicate的性质

2.2.2. Building Sentences from Predicates

2.2.3. Quantifiers and Alternating Quantifiers

2.2.4. Interpretation of Sentences

2.2.5. Consequence

2.2.6. Useful Equivalences

2.3. 归纳Induction

2.3.1. (Normal) Mathematical Induction

2.3.2. Strong Mathematical Induction

2.3.3. Well-ordering

3. 集合 Set

3.1. Set的性质

3.2. Important Set

3.3. Subset and Characteristic Functions

3.4. Set Operations and Venn Diagram

3.5. Ordered Pairs and Cartesian Product

4. 函数 Function

4.1. Domain, Codomain and Image

4.2. Common Functions

4.3. One-to-one Function

4.4. Functions of Several Variables

4.5. Boolean Function

4.6. Composite of Function

4.7. Inverse of Function

5. 关系 Relation

5.1. Binary and Tenary Relation

5.2. Relation v.s. Function

5.3. Subset Relation

5.4. Congruence Relation

5.5. Equivalence Relation and Equivalence Class

5.6. Order Relation

6. 排列与广义排列Selection and Arrangement

6.1. Ordered Selection without Repetition

6.2. Ordered Selection with Repetition

6.3. Unordered Selection without Repetiton

6.4. Unordered Selection with Repetition

6.5. Pigeonhole Principle

6.6. Pascal's Triangle and Binomial Theorem

7. 概率 Probability

7.1. Probaibility Space and Events

7.2. Operation on Events

7.3. Independent Events

7.4. Conditional Probability

7.5. Bayes' Theorem

7.6. Random Variables

7.7. Expectation and Variance of Random Variables

7.8. Common Discrete Probability Distribution

8. 递归 Recursion

8.1. Recursively Defined Function

8.2. Recursive Algorithm

8.3. Sequence and Recurrence Relation

9. 图与树 Graph and Tree

9.1. Common Problems with Graph

9.2. Walk, paths and trails

9.3. Degree of Graph and Euler's Theorem

9.4. Bridges

9.5. Property of Tree

9.6. Spanning Tree

9.7. Breath First Ordering and Queue

9.8. Depth First Ordering and Stack