Ken Ward's Mathematics Pages



Contents

  1. Arithmetic Algebra
    1. Square Roots
    2. Cube Roots
    3. Method of Detached Coefficients
    4. Method of Indeterminate Coefficients
  2. Geometry
    1. Four-sided
    2. Prism (Volumes)
    3. Pyramids
    4. Proportions, Areas and Similar Patterns
  3. Number Theory
    1. Indeterminate Equations
    2. Euclid's Algorithm
    3. Euclid's Extended Algorithm
    4. Computing gcd and ax+by=d at the same time
    5. Decimal to Fraction Conversion Using Euclid
    6. Continued Fractions
    7. Continued Fractions Using An Algorithm
    8. Modular Arithmetic
    9. Linear Congruence Equations
    10. Chinese Remainder Theorem and the Chinese Problem
    11. Chinese Problem Formula 1
    12. Chinese Remainder Theorem due to Gauss
    13. Number Base Systems
    14. Fermat's Factorisation Method
    15. Fermat's Method Odd and Even a's and b's
    16. Fermat's Method: Sieve
    17. Divisibility Tests Method 1 (All Numbers)
      1. Table of Coefficients
    18. Divisibility: Method 2
      1. Table of Rules for Divisibility using Method 2
    19.  Divisibility Trial Division
  4. Polynomials
    1. Roots
    2. Square Roots
    3. Complex Numbers
    4. Rational Root TheoreIdentim
    5. Descartes' Rule of Signs
    6. Vieta's Root Theorem
    7. Horner's Method
    8. Odd and Even Roots
    9. Solving Cubic Equations - Various Methods
    10. Cubic Equation Solution Cardan's Method
    11. Cardano Method Examples
    12. Identical Polynomials (Polynomial Argument)

  5. Series
    1. Arithmetic and Geometric Series
    2. Sums of the Natural Numbers (Various Methods)
    3. Sums of the Squares of the Natural Numbers
    4. Sum of the Powers of the Natural Numbers (General)
    5. Sums of the Powers of Natural Numbers and Bernoulli Numbers
    6. Bernoulli Numbers (Generating)
    7. Pascal's Triangle
    8. Binomial Theorem
    9. Binomial 3
    10. Pascal's Extended Triangle
    11. Binomial Theorem Proof for Nonnegative Powers by Induction
    12. Summing Binomial Coefficients
    13. Binomial Proof Negative Integers
    14. Binomial Theorem Proof Using Algebra
    15. Multinomial Expansion
    16. Multinomial Theorem
    17. Polynomial Equations
  6. Trigonometry
    1. Basic Formulae
    2. Compound and DoubleAngles
    3. Pythagoras Theorem
    4. Half Angle Formulae
    5. Heron's Formula
    6. Sum and Product of Sine and Cosine
    7. Multiple Angles: De Moivre's Theorem
    8. Sine, Cosine and Tangent of Multiple Angles (Chebyshev's Method)
    9. Cosine Multiple Angle Formulae
    10. Sine Multiple Angle Formulae
    11. Tangent Multiple Angle Formulae
    12. DeMoirve's Theorem Extended
  7. Various
    1. Gregory Series
    2. Machin Formula