Math Book Table of Contents

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

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 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 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.

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.

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.

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 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.

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.

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 Mysteries
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 Mysteries
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 triangle.
2) Theorem 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) 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.