gistfile1.txt

Arithmetic
	 Whole Numbers
		 Basic Place Value
			 Recognize Place Values to 10,000,000
			 Greatest and Least Values of Given Digits to 10,000,000
			 Higher Order Place Value and Number Placement Problems
			 Round Large Numbers
		 Additon and Subtraction
			 Add Whole Numbers
			 Subtract Whole Numbers
			 Estimate Whole Number Sums and Differences
		 Multiplication
			 Multiply Multiple Digits by One Digit
			 Higher Order One Digit Multiplication Word Problems
			 Relate One Digit Number Patterns to Multiplication
			 Multiply Numbers with the Associative Property
			 Multiply Two Digits by Two or More Digits
			 Multiply and Compare with Greater/Less Than
			 Relate Number Patterns to Multiplication
			 Higher Order Multiplication Word Problems
			 Multiply Whole Numbers
			 Mental Multiplication
		 Division
			 Divide Two Digits by One or Two Digits Without Remainders
			 Higher Order Division to 1000 by One Digit
			 Divide More than Two Digits by One Digit with Remainders
			 Relate Division to Multiplication
			 Estimate Whole Number Products and Quotients
		 Long Division
			 Long Division Without Remainders
			 Divide up to Four Digits by Two Digits with Remainders
			 Groups and Remainders Word Problems
			 Long Division Word Problems
			 Divide Whole Numbers
		 Order of Operations
			 Introduction to Order of Operations
			 Divide and Subtract with Remainders in Word Problems
			 Division and Subtraction Word Problems
			 Higher Order Division and Subtraction Word Problems
			 Multiply and Add Word Problems
			 Multiply and Add or Subtract Word Problems
			 Place Operators to Make True Statements
			 Place Operators to Make True Statements that Include Parentheses
			 Place Parentheses to Make True Statements
		 Exponents and Roots
			 Exponents
			 Evaluate and Compare Powers
			 Perfect Square Roots
			 Evaluate Square Roots
	 Factors
		 Prime and Composite Numbers
		 Prime Factorization
		 Identify Factor Pairs
		 Divisibility Rules to Find Factors
		 GCF Greatest Common Factor
		 Common Multiples
		 LCM Least Common Multiple
	 Integers
		 Integers in the Real World
		 Integers on a Number Line
		 Absolute Value of Integers
		 Add Integers with the Same Signs
		 Add Integers with Different Signs
		 Integer Addition
		 Subtract Integers with the Same Sign
		 Subtract Integers with Different Signs
		 Integer Subtraction
		 Multiply Integers
		 Divide Integers
	 Fractions
		 Introduction to Fractions
		 Equivalent Fractions
		 Simplify Fractions
		 Simplify Fractions Word Problems
		 Compare Fractions
			 Compare Fractions using Pictures
			 Compare Fractions that have Common Numerators or Denominators
			 Compare Fractions without Common Numerators or Denominators
			 Compare Fractions without Common Numerators or Denominators Word Problems
			 Estimate and Round Fractions and Mixed Numbers
			 Convert and Compare Mixed Numbers and Improper Fractions
		 Add and Subtract Fractions
			 Add Fractions with Common Denominators
			 Subtract Fractions with Common Denominators
			 Add and Subtract with Common Denominators
			 Add and Subtract Fractions with Common Denominators Word Problems
			 Add Fractions with Different Denominators
			 Subtract Fractions with Different Denominators
		 Add and Subtract Mixed Numbers
			 Add Mixed Numbers with Common Denominators
			 Subtract Mixed Numbers with Common Denominators
			 Subtract Mixed Numbers with Different Denominators
			 Add and Subtract Three Mixed Numbers
			 Add and Subtract Mixed Numbers Word Problems
		 Multiply and Divide Fractions
			 Multiply Whole Numbers and Fractions
			 Multiply Two Fractions
			 Multiply Three or More Fractions and Whole Numbers
			 Multiply Mixed Numbers
			 Multiply Mixed Numbers Word Problems
			 Reciprocal Fractions
			 Divide Fractions and Whole Numbers
			 Divide Fractions
			 Divide Whole Numbers by Mixed Numbers
			 Divide Mixed Numbers
			 Multiply and Divide Fractions and Mixed Numbers
			 Estimate Products of Whole Numbers and Fractions
		 Ratios
			 Definition of a Ratio
			 Equivalent Ratios
			 Ratios in Simplest Form
			 Compare Ratios in Decimal Form
			 Unit Rates
	 Decimals
		 Basic Decimals
			 Place Value Charts and Decimals to Thousandths
			 Equivalent Decimals Ending in Zero
			 Decimals in Words
			 Decimal Place Value
			 Decimals in Expanded Form
		 Compare Decimals
			 Compare and Order Decimals
			 Compare and Compose Decimals and Fractions
			 Compare, Order and Identify Decimal Inequalities
		 Round Decimals
			 Round Decimal Numbers
			 Round Decimals with Place Value
		 Add and Subtract Decimals
			 Add and Subtract Decimal Numbers
			 Mental Math to Add and Subtract Decimals
			 Add and Subtract Decimals with Front-End Estimation
			 Round Decimals to Estimate Sums and Differences
		 Multiply and Divide Decimals
			 Decimal Multiplication
			 Decimal Division
			 Multiply Decimals and Whole Numbers
			 Estimate Products and Quotients of Decimals
		 Powers of Ten and Scientific Notation
			 Multiply Decimals by Powers of Ten
			 Multiplication and Powers of Ten
			 Division and Powers of Ten
			 Scientific Notation
	 Rational and Irrational numbers
		 Rational Numbers
		 Add Rational Numbers
		 Subtract Rational Numbers
		 Multiply Rational Numbers
		 Divide Rational Numbers
		 Irrational Numbers
		 Irrational Square Roots
	 Percents
		 Overview of Percents
		 Percent of a Number
		 Simple Interest
		 Percent of Change
		 Percent of Increase
		 Percent of Decrease
		 Prices Involving Discounts
		 Total Bill Including Tip and Tax
	 Conversions Between Fractions, Decimals, and Percents
		 Convert Percents to Fractions and Decimals
			 Percents as Decimals
			 Percents as Fractions
		 Convert Fractions to Percents and Decimals
			 Fraction and Decimal Conversion
			 Convert Mixed Numbers to Decimals
			 Compare Mixed Numbers and Decimals
			 Convert Between Fractions or Mixed Numbers and Decimals
			 Add Fractions and Convert to Decimals
			 Fractions as Percents
		 Convert Decimals to Percents and Fractions
			 Convert Decimals to Fractions
			 Convert Decimals into Simplified Mixed Numbers
			 Decimals as Percents
			 Compare and Order Fractions and Decimals
			 Convert between Decimals, Fractions, and Percents
Algebra
	 Real Numbers Variables, and Expressions
		 The Real Numbers
		 Order Real Numbers
		 Integers
			 Absolute Value of Integers
			 Integer Addition
			 Integer Subtraction
			 Integer Multiplication
			 Integer Division
		 The Order of Operations
			 Order of Operations
			 PEMDAS in Numerical Expressions
			 Algebra Expressions with Exponents
			 Algebra Expressions with Fraction Bars
			 Order of Operations and Variable Substitution
		 Algebra Expressions and Variables
			 Expressions and Variables
			 Evaluate Single Variable Expressions
			 Evaluate Expressions with One or More Variables
			 Words that Describe Mathematical Operations
			 Translate Between English Phrases and Algebraic Expressions
			 Calculator Use with Algebra Expressions
		 Properties and Axioms of Real Numbers
			 Real Number Properties and Axioms
			 Distributive Property
			 Expressions and the Distributive Property
			 When to Use the Distributive Property
			 Distributive Property to Evaluate Formulas with Decimals
			 Additive inverses and Absolute Values
			 Associative and Commutative Property with Decimals
			 Associative and Commutative Property with Fractions
			 Addition and Multiplication Properties with Real Numbers
			 Fraction and Mixed Number Applications
		 Simplifying Expressions
			 Simplify Variable Expressions Involving Addition and Subtraction
			 Simplify Variable Expressions Involving Multiplication and Division
			 Simplify Variable Expressions Involving Multiple Operations
			 Simplify Algebraic Expressions
	 Linear Equations
		 Basic Equations
			 Writing Basic Equations
			 Sentences as Single Variable Equations
			 Addition and Subtraction Phrases as Equations
			 Multiplication and Division Phrases as Equations
			 Input-Output Tables
			 Function Rules for Input-Output Tables
			 Input-Output Tables for Function Rules
		 One-Step Equations and the Properties of Equality
			 One-Step Equations and Properties of Equality
			 Single Variable Equations with Addition and Subtraction
			 Properties of Equality with Fractions
			 Single Variable Equations with Multiplication and Division
			 Properties of Equality with Decimals
			 Checking Solutions to Equations
		 Solve Two-Step Equations
			 Two-Step Equations
			 Two-Step Equations from Verbal Models
			 Two-Step Equations with Addition and Multiplication
			 Two-Step Equations with Addition and Division
			 Two-Step Equations with Subtraction and Multiplication
			 Two-Step Equations with Subtraction and Division
			 Applications of Two-Step Equations
		 Solve Multi-Step Equations
			 Multi-Step Equations
			 Multi-Step Equations with Like Terms and Distribution
			 Multi-Step Equations with Fractions
			 Multi-Step Equations with Decimals
			 Multi-Step Equations with Decimals, Fractions, and Parentheses
			 Applications of Multi-Step Equations
			 Equations with Variables on Both Sides
			 Solving for a Variable
			 Absolute Value Equations
		 Linear Equations in the Real World
			 Applications of Linear Equations
			 Problem-Solving Models
			 Guess and Check, Work Backward
			 Applications Using Linear Models
		 Distance, Rate, and Time
			 D = RT
			 Solving for Elapsed Time Related to Rate
			 Finding the Total Time Given a Distance between Two Objects
			 Applications of Finding Time Using Multiple Steps
			 Finding Total Distance Using Multiple Steps Word Problems
			 Find the Rate, Given Time and Distance
			 Solving Length and Distance Problems Involving Time
	 Linear Inequalities
		 Solve One Step Linear Inequalities
		 Inequalities on a Number Line
		 Inequalities that Describe Patterns
		 Inequality Expressions
		 Inequalities with Addition and Subtraction
		 Inequalities with Multiplication and Division
		 Multi-Step Inequalities
		 Checking Solutions to Inequalities
		 Compound Inequalities
		 Graph and Solve Absolute Value Inequalities
		 Intervals and Interval Notation
		 Applications with Inequalities
	 Graphs and functions
		 Graphing in the Coordinate Plane
			 Graphs in the Coordinate Plane
			 Points in the Coordinate Plane
			 Ordered Pairs in Four Quadrants
			 Coordinate Locations on a Map
			 Graphs on a Coordinate Plane
			 Graphs Based on Rules
			 Rules Based on Graphs
			 Identify Types of Linear and Nonlinear Graphs
			 Function Families
		 Functions and Function Notation
			 Function Notation
			 Domain and Range of a Function
			 Applications of Functions
			 Identify Functions and the Vertical Line Test
			 Even and Odd Functions and Function Symmetry
			 Operations on Functions
			 Composition of Functions
		 Graph Linear Equations in Two Variables
			 Graph of a Linear Equation in Two Variables
			 Graphs of Linear Equations
			 Horizontal and Vertical Line Graphs
			 Graph Using Intercepts
			 Problem Solving with Linear Graphs
			 Graphs of Absolute Value Equations
			 Linear and Absolute Value Function Families
		 Graphing Slope
			 Slope
			 Rates of Change
			 Slope of a Line Using Two Points
			 Graph Using Slope-Intercept Form
		 The Forms of a Linear Equation
			 Standard Form of Linear Equations
			 Slope-Intercept Form of Linear Equations
			 Point-Slope Form of Linear Equations
			 Forms of Linear Equations
		 Parallel and Perpendicular Lines
			 Equations of Parallel and Perpendicular Lines
			 Equations of Parallel Lines
			 Equations of Perpendicular Lines
			 Families of Lines
		 The Equation of a Line
			 Determining the Equation of a Line
			 Write an Equation Given the Slope and a Point
			 Write an Equation Given Two Points
			 Write a Function in Slope-Intercept Form
			 Fitting Lines to Data
			 Linear Interpolation and Extrapolation
			 Applications of Linear Interpolation and Extrapolation
	 Systems of Equations and Inequalities
		 Consistent and Inconsistent Linear Systems
		 Checking a Solution for a Linear System
		 Graphs of Linear Systems
		 Systems of Linear Equations in Two Variables
		 Solving Linear Systems
			 Linear Systems by Elimination
			 Solving Systems by Multiplying One Equation
			 Solving Systems by Multiplying Both Equations
			 Linear Systems by Elimination Using Multiplication
			 Systems Using Substitution
			 Comparing Methods for Solving Linear Systems
			 Applications of Linear Systems
			 Mixture Problems
			 Systems of Linear Equations in Three Variables
			 Linear Programming
		 Solving Systems of Linear Inequalities
			 Graphs of Systems of Linear Inequalities in Two Variables
			 Evaluate Solutions for Linear Inequalities in Two Variables
			 Graphing to Check Solutions to Systems of Linear Inequalities
			 Systems of Inequalities
			 Quadratic Inequalities
			 Polynomial and Rational Inequalities
	 Polynomials and Factoring
		 Monomials, Binomials, and Trinomials
		 Polynomials in Standard Form
		 Addition and Subtraction of Polynomials
		 Polynomial Multiplication
			 Multiply Polynomials by Monomials
			 Multiply Binomials by Binomials
			 Multiply Polynomials by Binomials
			 Multiply Polynomials by Polynomials
		 Polynomial Factoring
			 Factoring Polynomials
			 Monomial Factors of Polynomials
		 Polynomial Special Products
			 Special Products of Polynomials
			 Factor Difference of Squares
			 Factor Perfect Square Trinomials
			 Sum and Difference of Cubes
		 Quadratic Expressions
			 Factor Quadratics with a Leading Coefficient of 1
			 Factor Quadratic Expressions with Negative Coefficients
			 Factor Quadratics
			 Factor by Grouping
			 Zero Product Principle
			 Applications of Factoring
		 Polynomial Division
			 Dividing Polynomials
			 Long Division of Polynomials
			 Synthetic Division of Polynomials
			 Finding Zeros of Polynomials
			 Zeroes and Intercepts of Polynomials
		 Graphing Polynomials
			 Identify Parts of Polynomial Graphs
			 Graphs of Polynomials Using Transformations
			 Graphs of Polynomials Using Zeros
			 Graphing Calculator to Analyze Polynomial Functions
	 Rational Expressions
		 Working with Rational Expressions
		 Simplifying Rational Expressions
		 Excluded Values for Rational Expressions
		 Restricted Domain and Range
		 Multiply and Divide Rational Expressions
			 Products and Quotients of Rational Expressions
			 Multiplication of Rational Expressions
			 Division of Rational Expressions
			 Complex Fractions
		 Add and Subtract Rational Expressions
			 Addition and Subtraction of Rational Expressions
			 Adding and Subtracting Rational Expressions where One Denominator is the LCD
			 Applications of Adding and Subtracting Rational Expressions
		 Percent
			 Percent Problems
			 Simple Interest
			 The Percent Equation
			 Proportions and Percents
		 Proportions
			 Proportions using LCD
			 Proportions using Cross-Multiplication
			 Rational Equations and Proportions
			 Applications of Ratios and Proportions
		 Proportion and Scale
			 Proportions and Scale
			 Dimensional Analysis
			 Applications of Scale and Indirect Measurement
		 Direct Variations
			 Direct Variation
			 Applications Using Direct Variation
			 Graphs of Linear Models of Direct Variation
		 Inverse Variation and Rational Functions
			 Direct and Inverse Variation
			 Inverse Variation Models
			 Estimate Graphs of Rational Functions
			 Horizontal and Vertical Asymptotes
			 Vertical Asymptotes
			 Horizontal Asymptotes
			 Oblique Asymptotes
			 Determining Asymptotes by Division
			 Inverse Variation Problems
			 Joint and Combined Variation
			 Applications Using Rational Equations
	 Roots and Irrational numbers
		 Exponents and Irrational Numbers
			 Negative and Zero Exponents
			 Fractional Exponents
			 Zero, Negative, and Fractional Exponents
			 Operations with Roots and Irrational Numbers
		 The Pythagorean Theorem
			 Pythagorean Theorem and its Converse
			 Pythagorean Triples
			 Converse of the Pythagorean Theorem
			 Solving Equations Using the Pythagorean Theorem
			 Applications Using the Pythagorean Theorem
			 Distance Formula
			 Midpoint Formula
		 Radical Expressions
			 Simplify Expressions with Radicals
			 Multiplication and Division of Radicals
			 Raising a Product or Quotient to a Power
			 Addition and Subtraction of Radicals
			 nth Roots
		 Radical Equations
			 Equations with Radicals
			 Equations with Square Roots
			 Equations with Radicals on Both Sides
			 Equations with Variables Under and not Under a Radical
			 Graphs of Square Root Functions
			 Shifts of Square Root Functions
			 Graphing Cube Root Functions
			 Square and Cube Root Function Families
			 Applications Using Radicals
	 Solving Quadratic and Exponential Equations and Functions
		 Quadratic and Exponential Equations and Functions
		 Solving Quadratic Equations
			 Use Square Roots to Solve Quadratic Equations
			 Square Root Applications
			 Completing the Square
			 Completing the Square when the Leading Coefficient Equals 1
			 Vertex Form of a Quadratic Equation by Completing the Square
			 Use Graphs and Technology to Solve Quadratic Equations
			 The Quadratic Formula
			 The Discriminant
			 Quadratic Equation Applications
		 Graphing Quadratic Functions and Equations
			 Graph Quadratic Functions and Equations
			 Graphing with the Vertex Form of Quadratic Functions
			 Graphs of Quadratic Functions in Intercept Form
			 Roots to Determine a Quadratic Function
			 Quadratic Functions and Equations
	 Exponential Functions and Properties of Exponents
		 Properties of Exponents in Variable Expressions
			 Exponential Properties Involving Products
			 Exponential Properties Involving Quotients
			 Exponential Terms Raised to an Exponent
			 Exponential Properties in Variable Expressions
		 Exponential Growth and Decay Functions
			 Exponential Functions
			 Solving Equations with Exponents
			 Exponential Growth and Decay
			 Exponential Growth
			 Exponential Decay
			 Geometric Sequences and Exponential Functions
			 Graphs of Exponential Functions
			 Applications of Exponential Functions
		 Logarithms
			 Common and Natural Logarithms
			 Analysis of Logarithmic Graphs
			 Logarithm Properties
			 Change of Base
			 Product and Quotient Properties of Logarithms
			 Power Property of Logarithms
			 Inverse Properties of Logarithms
			 Logistic Functions
		 Linear, Exponential and Quadratic Models
			 Identifying Linear, Exponential, and Quadratic Models
			 Linear, Quadratic, and Cubic Models
			 Cubic Models
			 Applications of Function Models
	 Matrices
		 Matrix Algebra
			 Introduction to Matrices
			 Adding and Subtracting Matrices
			 Multiplying Matrices by a Scalar
			 Matrix Multiplication
			 Matrix Operations
			 Determinants
			 Cramer's Rule
		 Matrix Equations
			 Solving Matrix Equations
			 Augmented Matrices
			 Row Operations and Row Echelon Forms
			 Writing and Solving a Matrix Equation for a Linear System
			 Solving Linear Systems Using Matrices and Technology
			 Inverse Matrices
			 Applications of Matrices
			 Partial Fraction Expansions
Geometry
	 Basics of geometry
		 Geometry Terms
		 Shapes
			 2D Shapes
			 Identify Shapes
			 Identify Less Common Shapes
			 Composite Shapes
		 Line Segments
			 Definition of Line Segment
			 Midpoints and Segment Bisectors
			 Midpoint Formula
			 Points that Partition Line Segments
		 Angles
			 Introduction to Angles
			 Identification of Angles by Vertex and Ray
			 Measuring Angles
			 Classifying Angles
			 Congruent Angles and Angle Bisectors
			 Constructions and Bisectors
		 Angle Pairs
			 Angle Properties and Theorems
			 Complementary Angles
			 Supplementary Angles
			 Missing Measures of Complementary and Supplementary Angles
			 Vertical Angles
		 Basic Polygons
			 Classify Polygons
			 Vertices and Sides
			 Polygon Classification in the Coordinate Plane
	 Reasoning and Proof
		 Patterns and Reasoning
			 Basic Visual Patterns
			 Identify Basic Pattern Type
			 Number Patterns
			 Reasoning Types
			 Inductive Reasoning from Patterns
			 Conjectures and Counterexamples
			 Deductive Reasoning
		 Logic Statements
			 Truth Tables
			 And and Or Statements
			 Negative Statements
			 If Then Statements
			 Converse, Inverse, and Contrapositive Statements
		 Properties and Proofs
			 Introduction to Proofs
			 Properties of Equality and Congruence
			 Proofs: Angle Pairs and Segments
			 Proofs involving Parallel and Perpendicular Lines
			 Parallelogram Proofs
			 Proofs Involving Triangles
			 Indirect Proof in Algebra and Geometry
	 Lines
		 Line Types
		 Parallel and Skew Lines
		 Transversals
			 Parallel Lines and Transversals
			 Corresponding Angles
			 Alternate Interior Angles
			 Alternate Exterior Angles
			 Same Side Interior Angles
			 Angles and Perpendicular Lines
		 Lines in the Coordinate Plane
			 Parallel Lines in the Coordinate Plane
			 Perpendicular Lines in the Coordinate Plane
			 Line Construction
	 Triangles
		 Classifying Triangles
			 Classify Triangles
			 Classify Triangles by Angle Measurement
			 Classify Triangles by Side Measurement
			 Isosceles Triangles
			 Equilateral Triangles
		 Triangle Area and Perimeter
			 Area and Perimeter of Triangles
			 Triangle Area
			 Unknown Dimensions of Triangles
		 Triangle Congruency
			 CPCTC
			 Congruence Statements
			 Third Angle Theorem
			 Congruent Triangles
			 SSS
			 SAS
			 ASA and AAS
			 HL
		 Triangle Relationships
			 Triangle Angle Sum Theorem
			 Exterior Angles and Theorems
			 Midsegment Theorem
			 Perpendicular Bisectors
			 Angle Bisectors in Triangles
			 Concurrence and Constructions
			 Medians
			 Altitudes
			 Comparing Angles and Sides in Triangles
			 Triangle Inequality Theorem
		 Right Triangles
			 Pythagorean Theorem
	 The Pythagorean Theorem
	 Basics of Pythagorean Theorem
	 Pythagorean Theorem to Classify Triangles
	 Pythagorean Triples
	 Converse of the Pythagorean Theorem
	 Pythagorean Theorem Applications
			 Right Triangles in Algebra
	 Pythagorean Theorem and its Converse
	 Solving Equations Using the Pythagorean Theorem
	 Applications Using the Pythagorean Theorem
			 Distance Formula
	 Distance and Triangle Classification Using the Pythagorean Theorem
	 Distance Formula and the Pythagorean Theorem
	 Distance Between Parallel Lines
	 The Distance Formula and Algebra
	 Applications of the Distance Formula
			 Special Triangles
	 Special Right Triangles and Ratios
	 45-45-90 Right Triangles
	 30-60-90 Right Triangles
	 Quadrilaterals and Polygons
		 Basic Squares and Rectangles
			 Squares
			 Rectangles
			 Square and Rectangle Area and Perimeter
			 Perimeter of Squares and Rectangles
			 Area of Squares and Rectangles
			 Unknown Dimensions of Squares and Rectangles
		 Quadrilaterals
			 Quadrilateral Classification
			 Parallelogram Classification
			 Parallelograms
			 Area of a Parallelogram
			 Unknown Dimensions of Parallelograms
			 Estimation of Parallelogram Area in Scale Drawings
			 Trapezoids
			 Area and Perimeter of Trapezoids
			 Area of Parallelograms: Squares, Rectangles and Trapezoids
			 Kites
			 Area and Perimeter of Rhombuses and Kites
			 Area and Perimeter of Composite Shapes
			 Quadrilateral Classification in the Coordinate Plane
		 Polygons
			 Regular and Irregular Polygons
			 Area of Regular and Irregular Polygons
			 Area and Perimeter of Similar Polygons
			 Construct Regular Polygons
			 Congruent Polygons
			 Corresponding Parts of Congruent Figures
		 Polygon Angle Measures
			 Determine Missing Angle Measures
			 Interior Angles in Convex Polygons
			 Exterior Angles in Convex Polygons
	 Circles
		 Parts of a Circle
			 Semicircles and Quarter Circles
			 Identify Circle Components
			 Use Diameter, Radius and Pi
			 Circumference
			 Diameter or Radius of a Circle Given Circumference
		 Area of a Circle
			 Circle Area
			 Areas of Combined Figures Involving Semicircles
			 Radius or Diameter of a Circle Given Area
		 Arcs and Chords
			 Arcs in Circles
			 Area of Sectors and Segments
			 Arc Length
			 Chords and Central Angle Arcs
			 Segments from Chords
		 Circles and Angles
			 Inscribed Angles in Circles
			 Inscribed Quadrilaterals in Circles
			 Angles On and Inside a Circle
			 Angles Outside a Circle
		 Tangent Lines and Theorems
			 Tangent Lines
			 Intersecting Secants Theorem
			 Tangent Secant Theorem
			 Circles in the Coordinate Plane
	 Similarity
		 Similar Figures
		 Ratio and Proportion in Similar Figures
		 Similar Polygons and Scale Factors
		 Corresponding Parts of Similar Figures
		 Indirect Measurement
		 Indirect Measurement Applications
		 Triangle Similarity
			 AA Similarity
			 SSS Similarity
			 SAS Similarity
		 Triangle Proportionality
			 Proportional Triangles
			 Inscribed Similar Triangles
			 Parallel Lines, Transversals, and Proportionality
			 Proportions and Angle Bisectors
			 Theorems Involving Similarity
		 Dilation
			 Dilation of a Shape
			 Dilation in the Coordinate Plane
			 Mapping Dilations
			 Self-Similarity and Fractals
	 Rigid Transformations
		 Identify Transformation Types
		 Symmetry
			 Lines of Symmetry
			 Reflection Symmetry
			 Rotation Symmetry
		 Translations
			 Geometric Translation
			 Sliding Figures
			 Translation Notation
			 Translation Applications in Circle Similarity
		 Rotations
			 Defining Rotation
			 Rotation Rules
		 Reflections
			 Defining Reflection
			 Rules for Reflections
			 Reflecting Figures
		 Composition of Transformations
			 Composite Transformations
			 Notation for Composite Transformations
			 Tessellations
	 Solid Figures
		 Polyhedrons
		 Faces, Edges, and Vertices of Solids
		 Cross-Sections and Nets
		 Surface Area
		 Volume
		 Cross Sections and Basic Solids of Revolution
		 Composite Solids
		 Area and Volume of Similar Solids
		 Surface Area and Volume Applications
		 Prisms
			 Surface Area and Volume of Prisms
			 Surface Area of Prisms
			 Volume of Prisms
			 Volume of Prisms Using Unit Cubes
			 Volume of Rectangular Prisms
			 Volume of Triangular Prisms
		 Pyramids
			 Surface Area and Volume of Pyramids
			 Volume of Pyramids
		 Cylinders
			 Surface Area and Volume of Cylinders
			 Surface Area of Cylinders
			 Volume of Cylinders
			 Heights of Cylinders Given Surface Area or Volume
		 Cones
			 Surface Area and Volume of Cones
			 Surface Area of Cones
			 Volume of Cones
		 Spheres
			 Surface Area and Volume of Spheres
			 Surface Area of Spheres
			 Volume of Spheres
Trigonometry
	 Right triangles and the Pythagorean theorem
		 Pythagorean Theorem
		 Converse of the Pythagorean Theorem
		 Pythagorean Triples
		 Applications Using the Pythagorean Theorem
		 The Pythagorean Theorem for Area and Perimeter
		 Distance Formula and the Pythagorean Theorem
		 Pythagorean Theorem to Classify Triangles
		 Special Right Triangles and Ratios
		 45-45-90 Right Triangles
		 30-60-90 Right Triangles
	 Trigonometric Ratios
		 Trig Functions
			 Right Triangle Trigonometry
			 Calculator Trig Functions
			 SIN
			 COS
			 Sine and Cosine of Complementary Angles
			 TAN
			 SEC CSC COT
		 Solving Triangles
			 The Pythagorean Theorem and Trigonometry
			 Trig Function Applications
			 Angles of Elevation and Depression
			 Right Triangles and Bearings
			 Solve Right Triangles
			 Applications of Inverse Trigonometric Functions
			 Inverse Trig Functions using Algebra
		 Trig in the Unit Circle
			 Trigonometry and the Unit Circle
			 Measuring Rotation
			 Angles of Rotation in Standard Positions
			 Coterminal Angles
			 Signs of Trigonometric Functions
			 Trigonometric Functions and Angles of Rotation
			 Reference Angles and Angles in the Unit Circle
			 Trigonometric Functions of Negative Angles
			 Trigonometric Functions of Angles Greater than 360 Degrees
			 Exact Values for Inverse Sine, Cosine, and Tangent
		 Inverse Trigonometric Functions
			 Inverse Trig Functions
			 Inverses by Mapping
			 Composition of Trig Functions and Their Inverses
			 Definition of Inverse Reciprocal Trig Functions
			 Composition of Inverse Reciprocal Trig Functions
			 Trig Functions as Algebra Expressions
	 Graphing Trigonometric Functions
		 Radians
			 Radian Measure
			 Conversion between Degrees and Radians
			 Trig Functions and Radians with Technology
			 Rotations in Radians
			 Angular Velocity
			 Length of an Arc
			 Area of a Sector
			 Length of a Chord
		 Sine and Cosine Graphs
			 Sine Graph and Cosine Graph
			 Translating Sine and Cosine Functions
			 Vertical Translations
			 Horizontal Translations or Phase Shifts
			 Amplitude, Period, and Frequency
			 Amplitude
			 Period and Frequency
			 Trigonometric Identities and Equations
			 General Sinusoidal Graphs
		 Six Trig Function Graphs
			 Graphing Tangent, Cotangent, Secant and Cosecant
			 Tangent Graphs
			 Tangent and Cotangent Graphs
			 Sine and Cosecant Graphs
			 Cosine and Secant Graphs
			 Graph Inverse Trigonometric Functions
	 Trigonometric Identities
		 Trig Identities
			 Fundamental Trigonometric Identities
			 Quotient Identities
			 Reciprocal Identities
			 Pythagorean Identities
			 Even and Odd Identities
			 Cofunction Identities
		 Basic Trig Identity Applications
			 Trig Identities to Find Exact Trigonometric Values
			 Simplifying Trigonometric Expressions
			 Proofs of Trigonometric Identities
			 Simpler Form of Trigonometric Equations
			 Solving Trigonometric Equations
			 Solving Trigonometric Equations Using Basic Algebra
			 Trigonometric Equations Using the Quadratic Formula
			 Trigonometric Equations Using Factoring
		 Sum and Difference Identities
			 Sum and Difference Formulas
			 Simplifying Trigonometric Expressions using Sum and Difference Formulas
			 Sine Sum and Difference Formulas
			 Cosine Sum and Difference Formulas
			 Tangent Sum and Difference Formulas
			 Solving Trigonometric Equations using Sum and Difference Formulas
			 Finding Exact Trigonometric Values Using Sum and Difference Formulas
			 Applications of Sum and Difference Formulas
		 Double and Half Angle Identities
			 Double and Half Angle Formulas
			 Double Angle Identities
			 Simplifying Trigonometric Expressions with Double-Angle Identities
			 Solving Equations with Double-Angle Identities
			 Half Angle Formulas
			 Trigonometric Equations Using Half Angle Formulas
		 Sum to Product and Triple Angle Formulas
			 Sum to Product Formulas for Sine and Cosine
			 Product to Sum Formulas for Sine and Cosine
			 Triple-Angle Formulas and Linear Combinations
	 Non-Right Triangle Trigonometry
		 Law of Sines and Law of Cosines
			 Laws of Sines and Cosines
			 Law of Sines
			 Angle-Angle-Side Triangles
			 Angle-Side-Angle Triangles
			 Side-Side-Angle: The Ambiguous Case
			 Law of Cosines
			 Determination of Unknown Angles Using Law of Cosines
			 Identify Accurate Drawings of Triangles
			 Applications of the Law of Cosines
			 Trigonometry Word Problems
		 Area of Non-Right Triangles
			 Area Formula for Non-Right Triangles
			 Introduction to the Triangle Area Formula
			 Determination of Unknown Triangle Measures Given Area
			 Heron's Formula
			 General Solutions of Triangles
	 Polar System and Complex Numbers
	 The Polar Coordinate System
		 The Polar Coordinate System and Graphing
			 Plots of Polar Coordinates
			 Distance Between Two Polar Coordinates
			 Graph Polar Equations
			 Transformations of Polar Graphs
			 Special Polar Equations and Graphs
		 Polar Curves and Rectangular Conversions
			 Polar and Rectangular Conversions
			 Rectangular to Polar Conversions
			 Rectangular to Polar Form for Equations
			 Intersections of Polar Curves
			 Equivalent Polar Curves
			 Systems of Polar Equations
		 Complex Numbers
			 Imaginary and Complex Numbers
			 Imaginary Numbers
			 The Complex Numbers
			 Quadratic Formula and Complex Sums
			 Products and Quotients of Complex Numbers
			 Product and Quotient Theorems
			 Trigonometric Form of Complex Numbers
			 Polar Form of a Complex Number
			 DeMoivre's Theorem and nth Roots
			 DeMoivre's Theorem
			 Equations Using DeMoivre's Theorem
			 Geometry of Complex Roots
PreCalculus
	 Fundamentals
		 Real numbers
		 Exponents and radicals
		 Algebraic Expressions
		 Rational Expressions
		 Equations
		 Modeling with equations
		 Inequalities
		 Coordinate Geometry
		 Lines
		 Modeling variation
	 Functions
		 What is a function
		 Graphs of functions
		 Increase and decreasing functions
			 Average rate of change
		 Transformations of functions
		 Quadratic functions
			 Maxima and minima
		 Modeling with functions
		 Combining functions
		 One-to-one functions and their inverses
	 Polynomial and Rational functions
		 Polynomial functions and graphing them
		 Dividing polynomials
		 Real zeros of polynomials
		 Complex numbers
		 Complex zeros and fundamental theorem of algebra
		 Rational functions
	 Exponential and logarithmic functions
		 Exponential functions
		 Logarithmic functions
		 Laws of Logarithms
		 Exponential and Logarithmic equations
		 Modeling with exponential and logarithmic equations
	 Trigonometric Functions of Real Numbers
		 Unit Circle
		 Trigonometric Functions of Real Numbers
		 Trigonometric Graphs
		 Modeling Harmonic Motion
	 Trigonometric Functions of Angles
		 Angle measure
		 Trigonometry of right triangles
		 Trigonometric functions of angles
		 Law of sines
		 Law of cosines
	 Analytic Trigonometry
		 Trigonometric identities
		 Addition and subtraction formulas
		 Double-angle, half-angle, and sum-product formulas
		 Inverse trigonometric functions
		 Trigonometric equations
	 Polar Coordinates and Vectors
		 Polar coordinates
		 Graphs of polar equations
		 Polar form of complex numbers
			 Demoivre's theorem
		 Vectors
		 Dot Product
	 Systems of equations and inequalities
		 Systems of equations
		 Systems of linear equations in two variables
			 two variables
			 several variables
			 matrices
		 Algebra of matrices
		 Inverses of matrices and matrix equations
		 Determinants and Cramer's rule
		 Partial fractions
		 Systems of inequalities
	 Analytic Geometry
		 Parabolas
		 Ellipses
		 Hyperbolas
		 Shifted Conics
		 Rotation of axes
		 Polar equations of conics
		 Plane curves and parametric equations
	 Sequences and series
		 Sequences and summation notation
		 Arithmetic sequences
		 Geometric sequences
		 Mathematical induction
		 Binomial theorem
Single Variable Calculus
	 Functions and Models
		 Ways to represent a functions
		 Essential functions
		 New functions from old functions
		 Exponential functions
		 Inverse functions and logarithms
	 Limits and Derivatives
		 Limit of a functions
		 Calculating limits using the limit laws
		 Precise definition of a limit
		 Continuity
		 Limits at infinity: horizontal asymptotes
		 Derivatives and rates of change
		 Derivative as a function
	 Differentiation
		 Derivatives of polynomials and exponential functions
		 Product and quotient rules
		 Derivatives of trigonometric functions
		 Chain rule
		 Implicit differentiation
		 Derivatives of logarithmic functions
		 Exponential growth and decay
		 Linear approximations and differentials
			 Taylor polynomials
		 Hyperbolic functions
	 Applications of Differentiation
		 Max and min values
		 Mean value theorem
		 How derivatives affect the shape of a graph
		 Indeterminate form and l'Hospital's rule
		 Optimization Problems
		 Newton's method
		 Antiderivatives
	 Integrals
		 Areas and distances
		 Definite integrals
		 Fundamental theorem of calculus
		 Indefinite integrals and the Net change theorem
		 Substitution rule
	 Applications of Integration
		 Areas between curves
		 Volumes
		 Volumes by cylindrical shells
		 Average value of a function
	 Techniques of Integration
		 Integration by parts
		 Trigonometric integrals
		 Trigonometric Substitution
		 Integration of rational functions by partial fractions
		 Strategy for integration
		 Approximate integration
		 Improper integrals
	 Further applications of Integration
		 Arc length
		 Area of a surface of revolution
		 Applications to physics,engineering, economics, or biology
		 Probability
	 Differential Equations
		 Modeling with differential equations
		 Direction fields and Euler's method
		 Separable equations
		 Models for population growth
		 Linear equations
	 Parametric Equations
		 Curves defined by parametric equations
		 Calculus with parametric curves
	 Polar Coordinates
		 Areas and lengths in polar coordinates
		 Conic sections in polar coordinates
	 Infinite Sequences and Series
		 Sequences
		 Series
		 Integral test and estimates of sum
		 Comparison tests
		 alternating seres
		 Absolute convergence
		 Ratio test and root test
		 Power series
		 Representing functions as power series
		 Taylor and Maclaurin series
		 Applications of Taylor polynomials
Multivariable Calculus
	 Vectors and the geometry of space
		 3d coordinate system
		 Vectors
		 Dot Product
		 Cross Product
		 Equations of lines and planes
		 Cylinders and quadric surfaces
	 Vector Functions
		 Vectors functions and space curves
		 Derivatives and integrals of vector functions
		 Arc length and curvature
		 Velocity and acceleration
	 Partial derivatives
		 Functions of several variables
		 Limits and continuity
		 Partial derivatives
		 Tangent planes and linear approximations
		 Chain rule
		 Directional derivatives and the gradient vector
		 Maximum and minimum values
		 Lagrange multipliers
	 Multiple Integrals
		 Double integrals over rectangles
		 Iterated integrals
		 Double integrals over general regions
		 Double integrals in polar coordinates
		 Application of double integrals
		 Surface area
		 Triple integrals
		 Triple integrals in cylindrical coordinates
		 Triple integrals in spherical coordinates
		 Change of variables in multiple integrals
	 Vector Calculus
		 Vector Fields
		 Line integrals
		 Fundamental theorem for line integrals
		 Green's theorem
		 Curl and divergence
		 Parametric surfaces and their areas
		 Surface integrals
		 Stoke's Theorem
		 Divergence Theorem
	 Second-Order Differential Equations
		 Second-Order Linear Equations
		 Nonhomogenous linear equations
		 Applications of second-order differential eqatuions
		 Series Solutions
Linear Algebra
	 Systems of linear equations
		 What is linear algebra?
		 Solving systems of linear equations
		 Reduced row-echelon formulas
		 Types of solutions
		 Homogeneous Systems of Equations
		 Nonsingular matrices
	 Vectors
		 Vector Operations
		 Linear combinations
		 Spanning sets
		 Linear independence
		 Linear dependence and spans
		 Orthogonality
	 Matrices
		 Matrix operations
		 Matrix multiplication
		 Matrix inverses and systems of linear equations
		 Matrix inverses and nonsingular matrices
		 Column and row spaces
		 The four subsets
	 Vector spaces
		 Vector spaces
		 Subspaces
		 Linear independence and spanning sets
		 Bases
		 Dimension
		 Properties of Dimension
	 Determinants
		 Determinant of a matrix
		 Properties of determinants of matrices
	 Eigenvalues
		 Eigenvalues and eigenvectors
		 Properties of eigenvalues and eigenvectors
		 Similarity and diagonalization
	 Linear Transformations
		 Linear transformations
		 Injective linear transformations
		 Surjective linear transformations
		 Invertible linear transformations
	 Representations
		 Vector representations
		 Matrix representations
		 Change of basis
		 Orthonormal Diagonalization
Differential Equations
	 Basic Concepts
		 Definitions
		 Direction Fields
	 First Order Differential Equations
		 Linear Equations
		 Separable Equations
		 Exact Equations
		 Bernoulli differential equations
		 Substitutions
		 Intervals of validity
		 Modeling with first order differential equations
		 Equilibrium solutions
		 Euler's method
	 Second order differential equations
		 Basic concepts
		 Real roots
		 Complex roots
		 Repeated roots
		 Reduction of order
		 Fundamental sets of solutions
			 More details about Wronskian
		 Nonhomogenous differential equations
		 Undetermined coefficients
		 Variation of parameters
		 Mechanical Vibrations
	 Laplace Transforms
		 Definition
		 Laplace transform
		 Inverse Laplace transform(IVP)
		 Step functions
		 Solving IVP's with Laplace transforms
		 Nonconstant coefficient IVP's
		 IVP's with step functions
		 Dirac Delta function
		 Convolution Integral
		 Table of Laplace transforms
	 Systems of Differential Equations
		 Systems of differential equations basics
		 Solutions to systems
		 Phase plane
		 Real eigenvalues
		 complex eigenvalues
		 repeated eigenvalues
		 Nonhomogeneous systems
		 Laplace transform to solve a system
	 Series Solutions
		 constructing a series solutions 
		 Euler equations
	 Higher order Differential Equations
		 Basic concepts for nth order linear equations
		 Linear homogenous differential equations
		 Undetermined coefficients
		 variation of parameters
		 laplace transforms
		 systems of differential equations
		 series solutions
	 Boundary Value Problems and Fourier Series
		 Boundary Value Problems
		 Eigenvalues and eigenfunctions
		 Periodic functions and orthogonal functions
		 Fourier sine series
		 Fourier cosine series
		 Fourier series
		 Convergence of fourier series
	 Partial Differential Equations
		 Heat equation
		 Wave equation
		 Separation of variables
			 terminology
			 Solving the heat equation
		 Heat equation with non-zero temperature boundaries
		 Laplace's equation
			 on a rectangle
			 on a disk
		 Vibrating string
			 wave equation solution
Proofs
	 Fundamentals
		 Sets
			 Introduction
			 Cartesian Products
			 Subsets
			 Power Sets
			 Union, Intersection, Difference
			 Complement
			 Venn Diagrams
			 Indexed Sets
			 Sets that are Number Systems
			 Russell's Paradox
		 Logic
			 Statements
			 And, Or, Not
			 Conditional Statements
			 Biconditional statements
			 Truth tables for statements
			 Logical equivalence
			 Quantifiers
			 Translating English to symbolic logic
			 Negating statements
			 Logical Inference
		 Counting
			 Counting lists
			 Factorials
			 Counting subsets
			 Pascal's triangle and the binomial theorem
			 Inclusion-exclusion
	 How to prove conditional statements
		 Direct Proof
			 Theorems
			 Definitions
			 Direct Proof
			 Using Cases
			 Treating similar cases
		 Contrapositive Proof
			 Contrapositive proof
			 Congruence of integers
			 Mathematical writing
		 Proof by Contradiction
			 Proving statements with contradiction
			 Proving conditional statements by contradiction
			 Combining techniques
	 More on Proofs
		 Proving non-conditional statements
			 If-and-only-If proof
			 Equivalent statements
			 Existence Proofs; Existence and Uniqueness Proofs
			 Constructive versus non-constructive proofs
		 Proofs Involving Sets
			 How to prove a∈A
			 How to prove A⊆B
			 How to prove A=B
			 Examples: Perfect Numbers
		 Disproof
			 Counterexamples
			 Disproving existence statements
			 Disproof by contradiction
		 Mathematical Induction
			 Proof by strong induction
			 Proof by smallest counterexample
			 Fibonacci Numbers
	 Relations, Functions, and Cardinality
		 Relations
			 Properties of relations
			 Equivalence of relations
			 Equivalence classes and partitions
			 The integers modulo n
			 Relations between sets
		 Functions
			 Functions
			 Injective and surjective functions
			 The pigeonhole principles
			 Composition
			 Inverse functions
			 Image and preimage
		 Cardinality of sets
			 Sets with equal cardinalities
			 Countable and uncountable sets
			 Comparing cardinalities
			 The Cantor-Bernstein-Schroeder Theorem
Combinatorics
	 Graph Theory
		 Elements of Graph Theory
			 Graph Models
			 Isomorphism
			 Edge Counting
			 Planar graphcs
		 Covering circuits and graph coloring
			 Euler cycles
			 Hamilton circuits
			 Graph coloring
			 Coloring theorems
		 Trees and searching
			 Properties of trees
			 Search trees and spanning trees
			 Traveling salesperson problem
			 Tree analysis of sorting algorithms
		 Network algorithms
			 Shortest paths
			 Minimum spanning trees
			 Network flows
			 Algorithmic matching
			 The Transportation problem
	 Enumeration
		 General counting methods for arrangements and selections
			 Basic counting principles
			 Simple arrangements and selections
			 Arrangements and selections with repetitions
			 Distributions
			 Binomial identities
		 Generating Functions
			 Generating function models
			 Calculating coefficients of generating functions
			 Partitions
			 Exponential generating functions
		 Recurrence Relations
			 Recurrence relation models
			 Divide-and-conquer relations
			 Solution of linear recurrence relations
			 Solution of inhomogeneous recurrence relations
			 Solutions with generating functions
		 Inclusion-Exclusion
			 Counting with Venn Diagrams
			 Inclusion-Exclusion Formula
			 Restricted positions and rook polynomials
	 Additional topics
		 Polya's Enumeration Formula
			 Equivalence and symmetry groups
			 Burnside's theorems
			 Cycle index
			 Polya's formula
		 Games with graphs
			 Progressively finite games
			 Nim-type games
Abstract Algebra
	 Preliminaries
		 Sets and equivalence relations
	 The integers
		 Mathematical induction
		 Division algorithm
	 Groups
		 Integer equivalence classes and symmetries
		 Definitions and examples
		 Subgroups
	 Cyclic groups
		 Cyclic subgroups
		 Multiplicative group of complex numbers
		 Method of repeated squares
	 Permutation groups
		 Definitions and notation
		 Dihedral groups
	 Cosets and Lagrange's Theorem
		 Cosets
		 Lagrange's theorem
		 Fermat's and Euler's Theorems
	 Intro To Cryptography
		 Private Key Cryptography
		 Public key cryptography
	 Algebraic Coding theory
		 Error-detecting and correcting codes
		 Linear codes
		 Parity-check and generator matrices
		 Efficient decoding
	 Isomorphisms
		 Definition and examples
		 Direct products
	 Normal subgroups and factor groups
		 Factor groups and normal subgroups
		 The simplicity of the alternating group
	 Homomorphisms
		 Group homomorphisms
		 The isomorphism theorem
	 Matrix group and symmetry
		 Matrix groups
		 Symmetry
	 Structure of groups
		 Finite Abelian groups
		 Solvable groups
	 Group actions
		 Groups acting on sets
		 The class equation
		 Burnside's Counting Theorem
	 The Sylow Theorems
		 The Sylow Theorem
		 Examples and applications
	 Rings
		 Rings
		 Integral domains and fields
		 Ring homomorphisms and ideals
		 Maximal and prime ideals
	 Polynomials
		 Polynomial rings
		 Division algorithm
		 Irreducible polynomials
	 Integral domains
		 Fields of fractions
		 Factorization in integral domains
	 Lattices and boolean algebras
		 Lattices
		 Boolean algebras
		 Algebra of electrical circuits
	 Fields
		 Extension Fields
		 Splitting Fields
		 Geometric Constructions
	 Finite Fields
		 Structure of a Finite Field
		 Polynomial Codes
	 Galois Theory
		 Field Automorphisms
		 The Fundamental Theorem
		 Applications
Number Theory
	 Basic properties of the integers
		 Divisibility and primality
		 Ideals and greatest common divisors
		 Consequences of unique factorization
	 Congruences
		 Equivalence relations
		 Definitions and basic properties of congruences
		 Solving linear congruences
		 The Chinese Remainder Theorem
		 Residue classes
		 Euler's phi function
		 Euler's theorem and Fermat's little theorem
		 Quadratic Residues
	 Computing with large integers
		 Asymptotic notation
		 Machine models and complexity theory
		 Basic integer arithmetic
		 Computing in Zn 
		 Faster integer arithmetic
	 Euclid's algorithm
		 Basic Euclidean algorithm
		 Extended Euclidean algorithm
		 Computing modular inverses and Chinese remaindering
		 Speeding up algorithms via modular computation
		 An effective version of Fermat's two squares theorem
		 Rational reconstruction and applications
		 RSA cryptosystem
	 Distribution of primes
		 Chebyshev's Theorem on the density of primes
		 Bertrand's postulate
		 Merten's theorem
		 The sieve of Eratosthenes
		 The prime number theorem
	 Abelian groups
		 Definitions, basic properties, examples
		 Subgroups
		 Cosets and quotient groups
		 Group homomorphisms and isomorphisms
		 Cyclic groups
		 Structure of finite abelian groups
	 Rings
		 Definitions, basic properties, examples
		 Polynomial rings
		 Ideals and quotient rings
		 Ring homomorphisms and isomorphisms
		 The structure of Zn*
	 Finite and discrete probability distributions
		 Basic definitions
		 Conditional probability and independence
		 Random variables
		 Expectation and variance
		 Some useful bounds
		 Balls and bins
		 Hash functions
		 Statistical distance
		 Measures of randomness and the leftover hash lemma
		 Discrete probability distributions
	 Probabilistic algorithms
		 Basic definitions
		 Generating a  random number from a given interval
		 Generate and test paradigm
		 Generating a random prime
		 Generating a random non-increasing sequence
		 Generating a random factored number
		 Complexity theory
	 Probabilistic primary testing
		 Trial division
		 Miller-Rabin test
		 Generating random primes using Miller-Rabin test
		 Factoring and computing Euler's phi function
	 Finding generators and discrete logarithms in Zp*
		 Finding a generator for Zp*
		 Computing discrete logarithms in Zp*
		 The Diffie-Hellman key establishment protocol
	 Quadratic reciprocity and computing modular square roots
		 The Legendre symbol
		 The Jacobi symbol
		 Computing the Jacobi symbol
		 Testing quadratic residuosity
		 Computing modular square roots
		 The quadratic residuosity assumption
	 Modules and vector spaces
		 Definitions, basic properties, examples
		 Submodules and quotient modules
		 Module homomorphisms and isomorphisms
		 Linear independence and bases
		 Vector spaces and dimensions
	 Matrices
		 Basic definitions and properties
		 Matrices and linear maps
		 Inverse of a matrix
		 Gaussian elimination
		 Applications of Gaussian elimination
	 Subexponential-time discrete logarithms and factoring
		 Smooth numbers
		 Algorithm for discrete logarithms
		 Algorithm for factoring integers
	 More rings
		 Algebras
		 The field of fractions of an integral domain
		 Unique factorization of polynomials
		 Polynomial congruences
		 Minimal polynomials
		 General properties of extension fields
		 Formal derivatives
		 Formal power series and Laurent series
		 Unique factorization domains
	 Polynomial arithmetic and applications
		 Basic arithmetic
		 Computing minimal polynomials in F[X]/(f)(I)
		 Euclid's algorithm
		 Computing modular inverses and Chinese remaindering
		 Rational function reconstruction and applications
		 Faster polynomial arithmetic
	 Linearly generated sequences and applications
		 Basic definition and properties
		 Computing minimal polynomials: a special case
		 Computing minimal polynomials: a more general case
		 Solving sparse linear systems
		 Computing minimal polynomials in F[X]/(f)(II)
		 The algebra of linear transformations
	 Finite fields
		 Preliminaries
		 Existence of finite fields
		 Subfield structure and uniqueness of finite fields
		 Conjugates, norms and traces
	 Algorithms for finite fields
		 Tests for and constructing irreducible polynomials
		 Computing minimal polynomials in F[X]/(f)(III)
		 Factoring polynomials: square-free decomposition
		 Factoring polynomials: the Cantor-Zassenhaus algorithm
		 Factoring polynomials: Berlekamp's algorithm
		 Deterministic factorization algorithms
	 Deterministic primality testing
		 Basic idea
		 Algorithm and its analysis
Cryptography
	 Classical Cryptography
		 Simple Cryptosystems
			 Shift Cipher
			 Substitution cipher
			 Affine cipher
			 Vigenere cipher
			 Hill cipher
			 Permutation cipher
			 Stream ciphers
		 Cryptanalysis
			 Cryptanalysis of affine cipher
			 Cryptanalysis of substitution cipher
			 Cryptanalysis of Vigenere cipher
			 Cryptanalysis of Hill cipher
			 Cryptanalysis of LFSR stream cipher
	 Shannons Theory
		 Introduction
		 Elementary Probability theory
		 Perfect secrecy
		 Entropy
			 Huffman Encodings
		 Properties of entropy
		 Spurious keys and unicity distance
		 Product cryptosystems
	 Block ciphers and advanced encryption standard(AES)
		 Introduction
		 Substitution-Permutation networks
		 Linear cryptanalysis
			 Piling-up lemma
			 Linear approximations of S-boxes
			 Linear attack on an SPN
		 Differential Cryptanalysis
		 Data Encryption standard(DES)
			 Description of DES
			 Analysis of DES
		 Advanced encryption standard
			 Description of AES
			 Analysis of AES
		 Modes of operations
	 Cryptographic Hash functions
		 Hash functions and data integrity
		 Security of hash functions
			 Random Oracle model
			 Algorithms in the random oracle model
			 Comparison of security criteria
		 Iterated hash functions
			 Merkle-Damgard Construction
			 Secure hash algorithm
		 Message authentication codes(MAC)
			 Nested MACs and HMAC
			 CBC-MAC and authenticated encryption
		 Unconditionally secure MACs
			 Strongly universal hash families
			 Optimality of deception probabilities
	 RSA cryptosystem and Factoring integers
		 Introduction to public-key cryptography
		 More number theory
			 Euclidean algorithm
			 Chinese remainder theorem
		 RSA cryptosystem
			 Implementing RSA
		 Primality testing
			 Legendre and Jacobi symbols
			 Solovay-Strassen algorithm
			 Miller-Rabin algorithm
		 Square roots modulo n
		 Factoring algorithms
			 Pollard p – 1 algorithm
			 Pollard Rho algorithm
			 Dixon's Random squares algorithm
			 Factoring algorithms in practice
		 Other attacks on RSA
			 Computing φ(n)
			 The decryption exponent
			 Wiener's low decryption exponent attack
		 Rabin cryptosystem
			 Security of Rabin cryptosystem
		 Semantic security of RSA
			 Partial information concerning plaintext bits
			 Optimal asymmetric encryption padding
	 Public-key Cryptography and Discrete Logarithms
		 ElGamal cryptosystem
		 Algorithms for the discrete logarithm problem
			 Shank's algorithm
			 Pollard Rho discrete logarithm algorithm
			 Pohlig-Hellman algorithm
			 Index Calculus method
		 Lower bounds on the complexity of genetic algorithms
		 Finite fields
		 Elliptic curves
			 Elliptic curves over the reals
			 Elliptic curves modulo a prime
			 Properties of elliptic curves
			 Point compression and ECIES
			 Computing point multiples on elliptic curves
		 Discrete logarithm algorithms in practice
		 Security of ElGamal systems
			 Bit security of discrete logarithms
			 Semantic security of ElGamal systems
			 Diffie-Hellman problems
	 Signature Schemes
		 Introduction
		 Security requirements for signature schemes
			 Signatures and hash functions
		 ElGamal signature scheme
			 Security of ElGamal signature scheme
		 Variants of ElGamal signature scheme
			 Schnorr signature scheme
			 Digital signature algorithm
			 Elliptic Curve DSA
		 Provably secure signature schemes
			 One-time signatures
			 Full domain hash
		 Undeniable signatures
		 Fail-stop signatures
	 Pseudo-random number generation
		 Introduction
			 Examples
		 Indistinguishably of probability distributions
			 Next bit predictors
		 Blum-Blum-Shub generator
			 Security of BBS generator
		 Probabilistic Encryption
	 Identification schemes and entity authentication
		 Introduction
		 Challenge-and-response in the secret-key setting
			 Attack model and adversarial goals
			 Mutual authentication
		 Challenge-and-response in the public-key setting
			 Certificates
			 Public-key identification schemes
		 Schnorr identification scheme
			 Security of the Schnorr identification scheme
		 Okamoto identification scheme
		 Guillou-Quisquater identification scheme
			 Identity-based identification schemes
	 Key distribution
		 Introduction
		 Diffie-Hellman Key Predistribution
		 Unconditionally secure key predistribution
			 The Blom Key Predistribution scheme
		 Key distribution patterns
			 Fiat-Naor key distribution patterns
			 Mitchell-Piper key distribution patterns
		 Session key distribution schemes
			 The Needham-Schroeder(NS) Scheme
			 The Denning-Sacco Attack on the NS scheme
			 Kerberos
			 The Bellare-Rogaway scheme
	 Key agreement schemes
		 Introduction
		 Diffie-Hellman key agreement
			 Station-to-station(STS) key agreement scheme
			 Security of STS
			 Known session key attacks
		 MTI key agreement schemes
			 Known session key attacks on MTI/A0
		 Key agreement using self-certifying keys
		 Encrypted key exchange
		 Conference key agreement schemes
	 Public-key infrastructure
		 Introduction
			 A practical protocol: Secure socket layer
		 Certificates
			 Certificate life-cycle management
		 Trust models
			 Strict hierarchy model
			 Networked PKIs
			 Web Browser model
			 Pretty good privacy
		 Future of PKI
			 Alternatives
		 Identity-based Cryptography
			 The Cocks identity-based encryption scheme
	 Secret sharing schemes
		 Introduction: Shamir Threshold Scheme
			 A simplified (t,t)-threshold scheme
		 Access structures and general secret sharing
			 Monotone circuit construction
			 Formal definitions
		 Information rate and construction of efficient schemes
			 Vector space construction
			 An upper bound on the information rate
			 The decomposition construction
	 Multicast security and copyright protection
		 Introduction
		 Broadcast encryption
			 Improvement using Ramp Schemes
		 Multicast re-keying
			 Blacklisting scheme
			 The Naor-Pinkas Re-keying scheme
			 Logical key hierarchy
		 Copyright protection
			 Fingerprinting
			 Identifiable parent property
			 2-IPP Codes
		 Tracing illegally redistributed keys
Probability
	 Discrete Probability Distributions
		 Simulation of discrete probabilities
		 Discrete probability distributions
	 Continuous probability densities
		 Simulation of continuous probabilities
		 Continuous density functions
	 Combinatorics
		 Permutations
		 Combinations
		 Card Shuffling
	 Conditional Probability
		 Discrete conditional probability
		 Continuous conditional probability
		 Paradoxes
	 Distributions and densities
		 Important distributions
		 Important densities
	 Expected Value and Variance
		 Expected value
		 Variance of discrete random variables
		 Continuous random variables
	 Sums of random variables
		 Sums of discrete random variables
		 Sums of continuous random variables
	 Law of large numbers
		 Discrete random variables
		 Continuous random variables
	 Central limit theorem
		 Bernoulli trials
		 Discrete independent trials
		 Continuous independent trials
	 Generating functions
		 Discrete distributions
		 Branching Process
		 Continuous Densities
	 Markov chains
		 Introduction
		 Absorbing Markov Chains
		 Ergodic Markov Chains
		 Fundamental Limit theorem
		 Mean First Passage Time
	 Random Walks
		 Random walks in Euclidean space
		 Gambler's Ruin
		 Arc Sine laws

The course is pretty extensive, but I think you should add Modular Arithmetic at the end of the Arithmetic section. It is a fundamental topic that will be used many times in the other sections such as Lagrange's theorem, Euler's theorem, etc.