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  • CM 1015 Computational Mathematics
  • Preface
  • How to Prove It
  • 1 Number Bases, Conversion and Operations
    • 1.1 Number Bases
    • 1.2 Why different bases matter? (optional)
      • 1.2.1 Comparison of Typical Use Cases
      • 1.2.2 Why They’re Important
    • 1.3 Number Conversion
      • 1.3.1 Converting from Decimal to Other Number Base
      • 1.3.2 Conversion Shortcuts with Binary Number
      • 1.3.3 Non-integer Number Conversion
    • 1.4 Operations with Binary Number
    • 1.5 Negative Numbers in Binary (optional)
  • 2 Series and Sequence
    • 2.1 Little Gauss (optional)
    • 2.2 Sequence
    • 2.3 Series
    • 2.4 Recursive Sequences
  • 3 Modular Arithmetic
    • 3.1 Congruence
    • 3.2 Operations in Modular Arithmetics
    • 3.3 Fermat’s Little Theorem (optional)
  • 4 Introduction to Trigonometry
    • 4.1 Angles
      • 4.1.1 Units of Measurement
      • 4.1.2 Type of Angles
    • 4.2 Triangles
      • 4.2.1 Special Triangles
      • 4.2.2 Similar Triangles
      • 4.2.3 Pythagoras’ Theorem
    • 4.3 Trigonometric Relations
      • 4.3.1 Basic Ratios (Right Triangles)
      • 4.3.2 Law of Sines
      • 4.3.3 Law of Cosines
      • 4.3.4 Special Angles (Summary Table)
  • 5 Functions and Graphs
    • 5.1 Numbers and Intervals
      • 5.1.1 Number Sets
      • 5.1.2 Intervals on the Real Line
    • 5.2 Functions
      • 5.2.1 Introduction to functions
      • 5.2.2 Type of Functions
      • 5.2.3 Composite Functions
      • 5.2.4 Inverse Functions
      • 5.2.5 Properties of Function
    • 5.3 Graph Sketching
    • 5.4 Application of Functions
  • 6 Kinematics
    • 6.1 Introduction to Kinematics
    • 6.2 Motion as a Function
    • 6.3 Graphical Interpretation
    • 6.4 Worked Examples
  • 7 Trigonometric Functions
    • 7.0.1 Pythagorean Identities
  • 8 Exponential and Logarithmic Functions
  • 9 Limit and Differentiation
  • 10 Linear Algebra, Vector and Matrices
  • 11 Combinatorics and Probability
  • Proudly published with bookdown

CM 1015 Computational Mathematics

CM 1015 Computational Mathematics

Chiuchiyin

2025-09-21