Mathematics (9820)
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GCE A-Level - Higher 3 (H3) の学習者向けの無料Mathematics (9820)学習ノート。各章のリンクから、要点・例題・練習問題への導線にアクセスできます。
Mathematical Statements
Definition, Proposition and Theorem
Conditionals
Quantifiers
Logical connectives
Converse
Inverse
Contrapositive
Negation
Mathematical Proofs and Reasoning Principles
Direct proof
Disproof by counterexample
Proof by contradiction
Proof of existence and uniqueness
Proof of uniqueness
Proof by construction and proof by cases
Proof by mathematical induction
Proof by cases
Pigeonhole and symmetry principles
Combinatorial arguments and proofs
Symmetry principle
Assumed Knowledge from H2 Mathematics and Additional Content
Functions and Graphs concepts
Sequences and Series concepts
Complex Numbers concepts
Calculus concepts
Improper integrals
Probability (including counting) concepts
Inclusion-Exclusion principle
Cauchy-Schwarz inequality
Triangle inequality
Operations involving limits
Problem Solving Heuristics
Working backwards
Uncovering pattern and structure
Solving a simpler or similar problem
Considering cases
Restating the problem (e.g. contrapositive)
Assumed Knowledge from H2 Mathematics — Additional Content
Summation of series by the method of differences
Reduction formulae and improper integrals
Bijection and inclusion-exclusion principles
Classical inequalities: AM-GM, Cauchy-Schwarz, triangle
Limits and growth-rate comparisons
Congruence and modular arithmetic
Mathematical Investigation and Reading Mathematical Texts
Formulating a conjecture
Extension, generalisation and special cases
Complete or critique a solution
Applying results and definitions beyond the defined content areas
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