Logic and Proofs (3/5), 1.1 Proposition Logic, 1.2 Proposition Equivalences, 1.3 Predicates and Quantifiers, 1.4 Nested Quantifiers

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第一週Logic and Proofs (1/5)
1.1 Proposition Logic
1.2 Proposition Equivalences
1.3 Predicates and Quantifiers
1.4 Nested Quantifiers
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第一週Logic and Proofs (2/5)
1.1 Proposition Logic
1.2 Proposition Equivalences
1.3 Predicates and Quantifiers
1.4 Nested Quantifiers
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第二週Logic and Proofs (3/5)
1.1 Proposition Logic
1.2 Proposition Equivalences
1.3 Predicates and Quantifiers
1.4 Nested Quantifiers
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第二週Logic and Proofs (4/5)
1.5 Rules of Inference
1.6 Introduction to Proofs
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第三週Logic and Proofs (5/5)
1.7 Proof Methods and Strategy
Sets, Functions, Sequences, and Sums (1/3)
Preliminary Test #1
2.1 Sets
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第四週Sets, Functions, Sequences, and Sums (2/3)
2.2 Set Operations
2.3 Functions
2.4 Sequences and Summations
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第四週Sets, Functions, Sequences, and Sums (3/3)
2.2 Set Operations
2.3 Functions
2.4 Sequences and Summations
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第五週Algorithms and the Integers (1/4)
3.4 The Integers and Division
3.5 Primes and Greatest Common Divisors
3.6 Integers and Algorithms
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第五週Algorithms and the Integers (2/4)
3.4 The Integers and Division
3.5 Primes and Greatest Common Divisors
3.6 Integers and Algorithms
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第五週Algorithms and the Integers (3/4)
3.4 The Integers and Division
3.5 Primes and Greatest Common Divisors
3.6 Integers and Algorithms
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第七週Algorithms and the Integers (4/4)
3.7 Applications of Number Theory
Induction and Recur (1/4)
4.1 Mathematical Induction
4.2 Strong Induction and Well-Ordering
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第七週Induction and Recur (2/4)
4.1 Mathematical Induction
4.2 Strong Induction and Well-Ordering
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第八週Induction and Recur (3/4)
4.3 Recursive Definitions and Structural Induction
4.4 Recursive Algorithms
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第八週Induction and Recur (4/4)
4.3 Recursive Definitions and Structural Induction
4.4 Recursive Algorithms
Counting (1/2)
5.1 The Basics of Counting
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第九週Counting (2/2)
5.2 The Pigeonhole Principle
5.3 Permutations and Combinations
5.4 Binomial Coefficients
5.5 Generalized Permutations and Combinations
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第十一週Advanced Counting Techniques (1/4)
7.1 Recurrence Relations
7.2 Solving Linear Recurrence Relations
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第十二週Advanced Counting Techniques (2/4)
7.4 Generating Functions
Example 1-3
7.5 Inclusion-Exclusion
7.6 Applications of Inclusion-Exclusion
8.1 Relations and Their Properties
8.2 n-ary Relations and Their Applications
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第十二週Advanced Counting Techniques (3/4)
7.4 Generating Functions
Example 1-3
7.5 Inclusion-Exclusion
7.6 Applications of Inclusion-Exclusion
8.1 Relations and Their Properties
8.2 n-ary Relations and Their Applications
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第十二週Advanced Counting Techniques (4/4)
7.4 Generating Functions
Example 1-3
7.5 Inclusion-Exclusion
7.6 Applications of Inclusion-Exclusion
Relations (1/4)
8.1 Relations and Their Properties
8.2 n-ary Relations and Their Applications
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第十四週Relations (2/4)
8.3 Representing Relations
8.4 Closures of Relations
8.5 Equivalence Relations
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第十四週Relations (3/4)
8.3 Representing Relations
8.4 Closures of Relations
8.5 Equivalence Relations
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第十五週Relations (4/4)
8.6 Partial Orderings
Graphs(1/3)
9.1 Graphs and Graph Models
9.2 Graph Terminology and Special Types of Graphs
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第十六週Graphs (2/3)
9.3 Representing Graphs and Graph Isomorphism
9.4 Connectivity
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第十七週Graphs (3/3)
9.5 Euler and Hamilton Paths
9.6 Shortest-Path Problems
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