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. Pythagoras' Theorem
    2. Four-sided
    3. Some Angles of Regular Polygons
    4. Ptolemy's Theorem
    5. Prism (Volumes)
    6. Pyramids, Volumes
    7. 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 Theorem
    5. Descartes' Rule of Signs
    6. Vieta's Root Theorem
    7. Horner's Method or Synthetic Division
    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. The Gamma Function
    10. Gaussian Integral
    11. Stirling Approximation for Factorials
    12. How to plot the gamma function
    13. Binomial 3
    14. Pascal's Extended Triangle
    15. Binomial Theorem Proof for Nonnegative Powers by Induction
    16. Summing Binomial Coefficients
    17. Binomial Proof Negative Integers
    18. Binomial Theorem Proof Using Algebra
    19. Multinomial Expansion
    20. Multinomial Theorem
    21. Polynomial Equations
    22. Difference Equations Using Algebra
    23. Factorial Polynomials and Differences
    24. Factorial Polynomials Negative n
    25. Factorial Polynomials Negative First Difference
    26. Converting Polynomials to Factorials
    27. Stirling Numbers of the Second Kind and Factorial Polynomials
    28. Stirling Numbers of the First Kind
  6. Trigonometry
    1. Basic Formulae
    2. Compound and DoubleAngles
    3. Pythagoras Theorem
    4. Half Angle Formulae
    5. Compound Angle Proofs
    6. Heron's Formula
    7. Sum and Product of Sine and Cosine
    8. Multiple Angles: De Moivre's Theorem
    9. Sine, Cosine and Tangent of Multiple Angles (Chebyshev's Method)
    10. Cosine Multiple Angle Formulae
    11. Sine Multiple Angle Formulae
    12. Tangent Multiple Angle Formulae
    13. DeMoirve's Theorem Extended Cosine
    14. DeMoirve's Theorem Extended Sine
  7. Probability
    1. What is Probability
    2. Birthday Paradoxes
    3. Monty Hall and Similar Problems
  8. Various
  9. Gregory Series
  10. Machin Formula