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Knowledge of Mathematics

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  • Mathematics
    • Elementary Calculus
    • Linear Algebra
    • Real Analysis
    • Topology
    • Topological Vector Spaces
    • Set-Valued Analysis
    • Stochastic Analysis
    • Nonlinear Analysis
      • Fuzzy Metric Spaces
      • Probabilistic Metric Spaces
      • Fixed-Point Theory
    • Near Vector Spaces
  • Applied Mathematics
    • Probability and Statistics
      • Probability
      • Statistics
      • Applied Probability
      • Applied Statistics
    • Operations Research
      • Introduction to Operations Research
      • Systems Reliability
      • Scheduling Problems
      • Meta Heuristics
    • Optimization
      • Nonlinear Programming
      • Optimization in Vector Spaces
      • Continuous-Time Optimization
      • Robust Optimization
      • Interval Optimization
      • Fuzzy Optimization
      • Stochastic Optimization
    • Game Theory
    • Mathematical Economics
    • Mathematical Finance
    • Actuarial Mathematics
    • Foundations of Fuzzy Sets
    • Theory of Fuzzy Sets
  • Arithmetics
    • 中學算術
    • 精算數學
    • 期貨與選擇權
  • Academic Achievements
    • Academic Services
    • Published Books
    • Published Papers
    • World’s Top 2% Scientists
    • 全球前 2% 頂尖科學家
  • References
    • Whole Lists
    • Theory of Fuzzy Sets
    • Fuzziness and Randomness
    • Optimization
    • Fuzzy Optimization
    • Nonlinear Analysis
    • Game Theory
    • Mathematical Economics
    • Computational Intelligence
    • Evolutionary Computation
    • Scheduling Problems
    • Systems Reliability
  • Arts
    • Classical Musics
    • Paintings
    • Sculptures
  • Hyperlink
Knowledge of Mathematics

Detailed proofs will be provided as clear as possible

中學算術

數與函數

  • 實數
  • 函數

平面座標系

一元二次方程式

  • 基本概念
  • 根與係數的關係

數列與級數

  • 等差數列與等差級數
  • 等比數列與等比級數
  • 收斂與發散
  • 數學歸納法

多項式

  • 四則運算
  • 餘式定理與因式定理
  • 最高公因式與最低公倍式
  • 多項函數與方程式
  • 根與係數

指數與對數

  • 指數律 
  • 對數的運算
  • 首數與尾數

三角函數

  • 三角函數的關係式
  • 同界角
  • 和差公式
  • 倍角與半角公式
  • 和差化積與積化和差
  • 反三角函數
  • 正餘弦定理

複數

  • 基本概念
  • 複數極式
  • 複數與極式的運算
  • 複數的方根

圓與球

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