Table of Contents
Numbers - Sets - Basic Math - Functions - Geometry - Trigonometry

Chapter 1 - Numbers

The Real Numbers

• 1) Natural Numbers
  The history of numbers started with the set of natural numbers or counting numbers.
• 2) Zero
  Zero as a number came later and there are restrictions using it in mathematics.
• 3) Negative Numbers
  Negative numbers compared with positive numbers and the restrictions in using them.
• 4) Integers
  The set of integers include zero and all the negative and positive whole numbers.
• 5) Rational Numbers
  Rational numbers described as the ratio of two other numbers.
• 6) Common Fractions
  Fractions composed of a numerator over a denominator and the reciprocal reverses them.
• 7) Decimal Fractions
  Conversion to a decimal fraction creates an integer with a decimal point and a decimal part.
• 8) Irrational Numbers Math Mysteries
  Irrational numbers cannot be described as a ratio and they complete the set of real numbers.

More Numbers

• 9) Absolute Value
  The absolute value operation turns a positive or negative number to a positive number.
• 10) Infinity Math Mysteries
  Infinity and negative infinity are used in math to solve problems.
• 11) Special Numbers Math Mysteries
  Properties of special numbers such as pi, e and phi, used in the golden ratio, help understand math phenomena.
• 12) Prime Numbers Math Mysteries
  The prime numbers are not multiples of other numbers and combined they create all the composite numbers.
• 13) Imaginary Numbers Math Mysteries
  Imaginary numbers are used to solve problems and to create complex numbers.
• 14) Systems of Numeration
  Different systems of numeration are used in math and computers, including decimal, octal and binary systems.

Chapter 2 - Sets

Set Properties

• 1) Set Definition
  Sets are defined by their of elements except the empty set that by definition has no elements.
• 2) Universal Set
  The universal set is all the answers to an equation and contains all proper subsets.
• 3) Power Set
  A power set contains all the possible subsets of another set and the empty set.
• 4) Set Union
  The set union is the combining of the set elements of two sets.
• 5) Set Intersection
  The set intersection is the sharing of elements of two sets that are not disjointed.
• 6) Set Complement
  The complement to a set is the difference between the set and the universal set.

Set Identity Laws

• 7) Set Identity Laws
• 8) Set Commutative Law
• 9) Set Associative Law
• 10) Set Distributive Law
• 11) DeMorgan's Set Identity Laws

Chapter 3 - Basic Math

Arithmetic Rules

• 1) Addition
  Addition is the math operation for the summing of numbers and is shown as a plus sign.
• 2) Subtraction
  Subtraction is the math operation taking one number away from another and is shown as a minus sign.
• 3) Multiplication
  Multiplication is the math operation for taking one number times another and is shown as a multiplication sign.
• 4) Division
  Division is finding the ratio of two numbers, the dividend over the divisor and is shown as a division sign.

Arithmetic Laws

• 5) Operators & Identity Laws
• 6) Symmetry & Transitive Laws
• 7) Commutative Laws
• 8) Distributive Law
• 9) Associative Laws

Chapter 4 - Functions

Function Descriptions

• 1) Function Definition
  A function is an equation whose variables can be mapped on coordinates, such as the Cartesian Plane.
• 2) Function Notation
  The notations used in writing math functions with two variables has a general form.
• 3) Function Domain
  The domain set of a math function is established by the equation.
• 4) Function Range
  The range set of a math function is established by the equation.
• 5) Composite Functions
  The composite function is one function that is a combination of two other functions.
• 6) Inverse Functions
  Inverse functions are two opposite functions that produce symmetric results.

Function Examples

• 7) Linear Functions
  The linear function is based on simple linear equations shown in a form using numeric constants.
• 8) Power Functions
  The power functions have a base number with an exponent, such as in square, square root and cube functions.
• 9) Quadratic Functions
  The quadratic functions use the general quadratic equation to solve for the quadratic roots of an equation.
• 10) Logarithmic Functions
  The logarithmic functions is the inverse to the exponential function and is related to the power functions.
• 11) Exponential Functions Math Mysteries
  The exponential function is the inverse to the natural logarithmic function and is related to the power functions.
• 12) Factorial Functions Math Mysteries
  The factorial function uses multiplication of the natural numbers to increase quickly.
• 13) Limit Functions Math Mysteries
  The limit function tests other function as the independent variable approaches a constant number.
• 14) Summation Functions
  The summation function checks the continuity of other functions over a range and can converge or diverge.
• 15) Percentage Functions
  The common percentage function is used to measure the size of the slice.

Chapter 5 - Geometry

• 1) Geometry Basics
  Basic shapes include points, lines, planes and solids shown on number lines or geometric spaces with origins.
• 2) Geometry Rules
  Five geometric rules are the foundation for geometry about straight lines, circles, right angles and parallel lines.
• 3) Euclidean Geometry
  In Euclidean geometry the slope of a straight line and its intercept point can be determined.
• 4) Geometric Polygons
  Polygons all have calculable areas include triangles, rectangles, parallelograms, rhombi and squares.
• 5) Conic Sections Math Mysteries
  The curvilinear conic sections are circles, parabolas and hyperbolas with asymptotes, focal points and radii.
• 6) Geometric Solids
  Geometric solid shapes have a calculable volume and include cubes, pyramids, prisms, and spheres.
• 7) Geometric Polyhedra Math Mysteries
  Polyhedra can be regular or semi-regular, and include the parallelepiped, the tetrahedron and the hexahedron.

Chapter 6 - Trigonometry

• 1) Pythagorean Theorem
  The Pythagorean Theorem looks at the angle, sides, and hypotenuse of a right triangle.
• 2) Pythagorean Proof Math Mysteries
  The proof of the Pythagorean Theorem can be done with specific examples.
• 3) Pi Value Math Mysteries
  The special number pi is used to find the circumference of a circle and to convert degrees to radians.
• 4) Trigonometric Conventions
  The conventions include using the unit circle where x is the adjacent side and y is the opposite side.
• 5) Sine Function
  The trigonometric sine and cosecant functions are used to evaluate angles.
• 6) Cosine Function
  The trigonometric cosine and secant functions are used to evaluate angles.
• 7) Tangent Function
  The trigonometric tangent and cotangent functions are used to evaluate angles.
• 8) Trigonometry Laws
  The trigonometric laws of identify, the law of sines and the law of cosines are used to solve a triangle.