cs1231s nus notes

Week 1

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• Discrete Math
• Integer (整数)
• Properties of Integer
• Rational Number
• Mathematical Proof
• Direct Proof
• Indirect Proof
• Mathematical Statement
• Propositional Logic

Week 2

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• Conditional Statement
• Mathematical Argument
• Rule of Inference (推理规则)
• Fallacy
• Predicate
• Quantifier
• Universal Statement
• Existential Statement

Week 3

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• Quantified Rule of Inference
• Deductive Reasoning (演繹推理)

Set

• Set
• Set Notation
• Subset
• Empty Set

Number Theory

• Prime Number (质数)
• Divisibility (可除性)

Week 4

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Set

• Ordered Pair
• Cartesian Product
• Set Equality
• Interval
• Mutually Disjoin Set
• Set Partition
• Power Set
• Set Theorem

Relation

• Relation
• Relation Composition
• Relation Property

Number Theory

• Quotient-Remainder Theorem

Week 5

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• Equivalence Relation
• Partial Order
• Kahn’s Algorithm

Good to Have

Geometry

• Discrete Geometry

Number Theory - Divisibility and Primes

• Factor
• GCD
• Modulo

Counting

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• Combinatorics
• Counting
• Combination
• Permutation