- 1) Natural Numbers
The history of numbers started with the set of natural numbers or counting
- 2) Zero
Zero as a number came later and there are restrictions using it in mathematics.
- 3) Negative Numbers
Negative numbers are compared to positive numbers and there are 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 can be described as the ratio of two other numbers.
- 6) Common Fractions
Fractions are composed of a numerator over a denominator and the reciprocal
- 7) Decimal Fractions
Conversion to a decimal fraction creates an integer with a decimal point and
a decimal part.
- 8) Irrational Numbers Math
Irrational numbers cannot be described as a ratio and they complete the set
of real numbers.
- 9) Absolute Value
The absolute value operation turns a positive or negative number to a positive
- 10) Infinity Math
Infinity and negative infinity are used in math to solve problems.
- 11) Special Numbers Math
Properties of special numbers such as pi, e and phi, used in the golden ratio,
help understand math phenomena.
- 12) Prime Numbers Math
The prime numbers are not multiples of other numbers and combined they create
all the composite numbers.
- 13) Imaginary Numbers Math
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
- 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
- 3) Power Set
A power set contains all the possible subsets of another set and the empty
- 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.
- 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.
- 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
- 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
- 6) Inverse Functions
- Inverse functions are two opposite functions that produce
- 7) Linear Functions
The linear function is based on simple linear equations shown in a form using
- 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
The exponential function is the inverse to the natural logarithmic function
and is related to the power functions.
- 12) Factorial Functions Math
The factorial function uses multiplication of the natural numbers to increase
- 13) Limit Functions Math
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.
- 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) Polygons
Polygons all have calculable areas include triangles, rectangles, parallelograms,
rhombi and squares.
- 5) Conic Sections Math
The curvilinear conic sections are circles, parabolas and hyperbolas with
asymptotes, focal points and radii.
- 6) Solids
Geometric solid shapes have a calculable volume and include cubes, pyramids,
prisms, and spheres.
- 7) Polyhedra Math
Polyhedra can be regular or semi-regular, and include the parallelepiped,
the tetrahedron and the hexahedron.
- 1) Pythagorean Theorem
The Pythagorean Theorem looks at the angle, sides, and hypotenuse of a right
- 2) Theorem Proof Math
The proof of the Pythagorean Theorem can be done with specific examples.
- 3) Pi Value Math
The special number pi is used to find the circumference of a circle and to
convert degrees to radians.
- 4) Trigonometry 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.
Go To Book Chapters
- Preface - Tutorials -
Calculator - Bibliography
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