Ken Ward's Mathematics Pages
Contents
Arithmetic Algebra
Square Roots
Cube Roots
Method of Indeterminate Coefficients
Geometry
Pythagoras' Theorem
Four-sided
Some Angles of Regular Polygons
Ptolemy's Theorem
Prism (Volumes)
Pyramids, Volumes
Proportions, Areas and Similar Patterns
Number Theory
Indeterminate Equations
Euclid's Algorithm
Euclid's Extended Algorithm
Computing gcd and ax+by=d at the same time
Decimal to Fraction Conversion Using Euclid
Continued Fractions
Continued Fractions Using An Algorithm
Modular Arithmetic
Linear Congruence Equations
Chinese Remainder Theorem and the Chinese Problem
Chinese Problem Formula 1
Chinese Remainder Theorem due to Gauss
Number Base Systems
Fermat's Factorisation Method
Fermat's Method Odd and Even a's and b's
Fermat's Method: Sieve
Divisibility Tests Method 1 (All Numbers)
Table of Coefficients
Divisibility: Method 2
Table of Rules for Divisibility using Method 2
Divisibility Trial Division
Polynomials
Roots
Square Roots
Complex Numbers
Rational Root Theorem
Descartes' Rule of Signs
Vieta's Root Theorem
Horner's Method or Synthetic Division
Horner Scheme Rationale
Odd and Even Roots
Solving Cubic Equations - Various Methods
Cubic Equation Solution Cardan's Method
Cardano Method Examples
Identical Polynomials (Polynomial Argument)
Series
Arithmetic and Geometric Series
Sums of the Natural Numbers (Various Methods)
Sums of the Squares of the Natural Numbers
Sum of the Powers of the Natural Numbers (General)
Sums of the Powers of Natural Numbers and Bernoulli Numbers
Bernoulli Numbers (Generating)
Pascal's Triangle
Binomial Theorem
The Gamma Function
Gaussian Integral
Stirling Approximation for Factorials
How to plot the gamma function
Binomial 3
Pascal's Extended Triangle
Binomial Theorem Proof for Nonnegative Powers by Induction
Summing Binomial Coefficients
Binomial Proof Negative Integers
Binomial Theorem Proof Using Algebra
Multinomial Expansion
Multinomial Theorem
Polynomial Equations
Difference Equations Using Algebra
Factorial Polynomials and Differences
Factorial Polynomials Negative n
Factorial Polynomials Negative First Difference
Converting Polynomials to Factorials
Stirling Numbers of the Second Kind and Factorial Polynomials
Stirling Numbers of the First Kind
Trigonometry
Basic Formulae
Compound and DoubleAngles
Pythagoras Theorem
Half Angle Formulae
Compound Angle Proofs
Heron's Formula
Sum and Product of Sine and Cosine
Multiple Angles: De Moivre's Theorem
Sine, Cosine and Tangent of Multiple Angles (Chebyshev's Method)
Cosine Multiple Angle Formulae
Sine Multiple Angle Formulae
Tangent Multiple Angle Formulae
DeMoirve's Theorem Extended Cosine
DeMoirve's Theorem Extended Sine
Probability
What is Probability
Birthday Paradoxes
Monty Hall and Similar Problems
Various
Gregory Series
Machin Formula
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Faster Arithmetic - by Ken Ward
Ken's book is packed with examples and explanations that enable you to discover more than 150 techniques to speed up your arithmetic and increase your understanding of numbers. Paperback and Kindle:
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