Table of Contents
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LEARN ABOUT SETS
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What is a set?
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Why are sets important?
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Examples of sets
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Set representations
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Enumerations
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Venn diagrams
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Special sets
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Operations on sets
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Complement
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Union
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Intersection
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Difference
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Relationships between sets
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Equivalence
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Subset
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Proper subset
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Number of a set
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Sets and computer programming
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Data types
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Object oriented programming
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LEARN ABOUT NUMBERS
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What is a counting number?
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The set to be counted
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Number of the set to be counted
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Operations on counting numbers
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How do I add counting numbers?
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How do I subtract counting numbers?
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What are integers
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Why do we need more than counting numbers?
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Introduction to integers.
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How do I add and subtract integers?
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How do I multiply integers?
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How do I divide integers?
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Learn about fractions
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What is a fraction?
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How are fractions useful?
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How are fractions and integers different?
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How can I picture fractions?
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How do I multiply fractions?
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How do I add fractions?
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What is a mixed number?
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How do I divide fractions?
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Learn about decimal numbers
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What is a decimal number?
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Why are decimal numbers important?
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What are the limitations of decimal numbers?
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How do I do arithmetic with decimal numbers?
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How do I work with fractions and decimal numbers?
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What use is a calculator to do decimal arithmetic?
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Learn some important rules about numbers
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Commutative law
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Associative law
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Distributive law
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Identity elements
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Fun and games with numbers
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SOME GEOMETRIC CONCEPTS
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What is a point?
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A graphic example
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Indicator of position
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What is distance?
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LEARN ABOUT COORDINATE SYSTEMS
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What is a coordinate system?
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Points on a coordinate system
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Distance of a point from the origin
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One dimensional coordinate systems
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Two dimensional coordinate systems
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A look at higher dimensional coordinate systems
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LEARN ABOUT VECTORS
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What is a vector?
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How do I describe a vector?
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Magnitude and direction
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Coordinates
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What is the difference between a point and a vector?
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How are vectors useful?
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Giving directions
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Describing things in nature
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Extends arithmetic into geometry
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The geometry of Euclid
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The geometry of Descartes
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Some things you can do to change a vector
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How do I change a vector’s magnitude?
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How do I change a vector’s direction?
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Working with more than one vector
How do I add two vectors and what does it mean?
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How do I subtract two vectors and what does it mean?
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LEARN ABOUT ANGLES
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What is an angle?
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What is the property we are we changing?
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What is the angle between two line segments that do not intersect?
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How do we associate angles with numbers?
Degree measure of angles
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Radian measure of angles
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LEARN ABOUT FUNCTIONS
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What is a function?
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Some examples of functions
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Linear functions
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Quadratic functions
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General polynomial functions
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LEARN ABOUT CIRCULAR FUNCTIONS
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What is a circular function?
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A graphic example
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Sine
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Cosine
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Tangent
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LEARN ABOUT ABSTRACT NUMBER SYSTEMS
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What does “closure” mean?
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What is an abstract number system?
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The counting number system
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The integers number system
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The rational number system
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The real number system
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The nested property of these number systems
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LEARN ABOUT COMPLEX NUMBERS
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What is a complex number?
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Numbers as we have discussed them
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Why do we need complex numbers?
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An abstract definition of the complex number system
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The axioms of complex numbers
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What are some of the interesting properties of the complex number system?
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All of our previous number systems are describable in terms of complex numbers.
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Every real number has a square root.
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Different representations of complex numbers
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Polar representation of complex numbers
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Arithmetical operations on polar representation of complex numbers
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Notations used for complex numbers
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The real part of a complex number
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The imaginary part of a complex number
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History of the terminology surrounding complex numbers
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Confusion related to the terminology
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Graphical representation of complex numbers
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Representing complex numbers in a coordinate system
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Relationship to two-dimensional vectors
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Some applications of complex numbers in the physical world
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LEARN ABOUT DERIVATIVES OF FUNCTIONS
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What is the slope of a function?
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How can I visualize a derivative?
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Why are derivative so very important?
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Derivatives of some special functions
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LEARN ABOUT FORMULAS
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What is a formula?
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Practical applications of formulas
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What is the practical difference between functions and formulas?
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Evaluating formulas