You: “It’s been a while since your last post.”
Me: “I apologise.”

You: “What have you been doing these last couple months?”
Me: “I’ve been busy.”

You: “Busy doing what?”
Me: “Learning stuff.”

You: “You mean you’ve been going to school?”
Me: “No.”

You: “So what then? Have you been doing one of those distance learning things?”
Me: “Not exactly. It’s this thing called Khan Academy. It’s a website where you can learn stuff, for free.”

You: “What kind of ‘stuff’ can you learn.”
Me: “Well… stuff like…

Algebra

Conceptual videos and worked examples from basic algebra through algebra 2. Includes videos from the former algebra worked examples playlists.
Algebra: Introduction to Algebra

Videos exploring why algebra was developed and how it helps us explain our world.

The Beauty of Algebra
Origins of Algebra
Abstract-ness
Descartes and Cartesian Coordinates

Algebra: Solving linear equations

Solving one-step and multi-step equations in one variable.

Variables Expressions and Equations
Variables and Expressions 1
Evaluating Expressions with Two Variables
Order of Operations Example
Simple Equations
Solving One-Step Equations
Solving One-Step Equations 2
Algebra: Linear Equations 1
One Step Equations
Evaluate a formula using substitution
Example of Solving for a Variable
Solving for a Variable
Solving for a Variable 2
Algebra: Linear Equations 2
Equations 2
Solving Equations 1
Two-Step Equations
New Operator Definitions
Solving Equations 2
Equations 3
Equations with Variables on Both Sides
Multi-Step Equations
Multi-step equations 1
Multi-step equations 2
Solving Equations with the Distributive Property
Solving equations with the distributive property 2
Algebra: Linear Equations 3
Algebra: Linear Equations 4
Equation Special Cases
Sum of Consecutive Odd Integers
Integer sums
Rearrange formulas to isolate specific variables
Algebraic Word Problem
Basic Rate Problem
Averages
Application problems with equation in one variable
Percent Problems
Word Problem Solving 3
Taking percentages
Growing by a percentage
Another Percent Word Problem
More percent problems
Direct Variation 1
Proportionality Constant for Direct Variation
Direct Variation Application
Early Train Word Problem
Age word problems 1
Age word problems 2
Age word problems 3
Writing Proportions
Converting Repeating Decimals to Fractions 1
Converting Repeating Decimals to Fractions 2
Patterns in Sequences 1
Patterns in Sequences 2
Equations of Sequence Patterns
Finding the 100th Term in a Sequence
Basic Linear Function
Absolute Value Equations
Absolute Value Equations 1
Absolute Value Equations Example 1
Absolute Value Equation Example 2

Algebra: Solving linear inequalities

Solving and writing one-step, multi-step, and compound inequalities in one variable.

Interpreting Inequalities
Inequalities on a number line
Equations and Inequalities
Solving Inequalities
Writing and using inequalities
Writing and using inequalities 2
Writing and using inequalities 3
One-Step Inequalities
One-Step Inequalities 2
Inequalities Using Multiplication and Division
Multi-Step Inequalities
Multi-Step Inequalities 2
Inequalities
Compund Inequalities
Compund Inequalities 2
Compound Inequalities
Compound Inequalities 3
Compound Inequalities 4
Absolute Value Inequalities
Absolute value inequalities Example 1
Absolute Value Inequalities Example 2
Absolute value inequalities example 3

Algebra: Graphing linear equations and inequalities

Understanding the coordinate plane, slope, and intercept. Writing, solving, and graphing linear equations and inequalities.

The Coordinate Plane
Exploring linear relationships
Plotting (x,y) relationships
Plot ordered pairs
Ordered pair solutions of equations
Application problem with graph
Interpreting Linear Graphs
X and Y intercepts
X and Y intercepts 2
Slope of a line
Slope Example
Slope and Rate of Change
Slope and Y-intercept Intuition
Algebra: Slope
Algebra: Slope 2
Algebra: Slope 3
Graphical Slope of a Line
Slope of a Line 2
Slope of a Line 3
Hairier Slope of Line
Graphing a line in slope intercept form
Algebra: Slope and Y-intercept intuition
Algebra: Equation of a line
CA Algebra I: Slope and Y-intercept
Graphing Using Intercepts
Graphing using X and Y intercepts
Algebra: graphing lines 1
Graphs Using Slope-Intercept Form
Linear Equations in Slope Intercept Form
Linear Equations in Point Slope Form
Equation of a line 1
Equation of a line 2
Equation of a Line hairier example
Equation of a line 3
Linear Equations in Standard Form
Graphs of Linear Equations
Direct Variation Models
Recognizing Linear Functions
Converting to slope-intercept form
Point-slope and standard form
Parallel Lines
Parallel Lines 2
Parallel lines 3
Perpendicular Lines
Perpendicular lines 2
Parallel Line Equation
Word Problem Solving 4
Equations of Parallel and Perpendicular Lines
Fitting a Line to Data
Distance Formula
Midpoint Formula
Solving and graphing linear inequalities in two variables 1
Graphing linear inequalities in two variables 2
Graphing Linear Inequalities in Two Variables Example 2
Graphing linear inequalities in two variables 3
CA Algebra I: Graphing Inequalities
Graphing Inequalities
Graphing Inequalities 1
Graphing Inequalities 2

Algebra: Systems of equations and inequalities

Solving a system of equations or inequalities in two variables by elimination, substitution, and graphing.

systems of equations
Officer on Horseback
Patterns and Equations
Two Passing Bicycles Word Problem
Passed Bike Word Problem
Passing Trains
Overtaking Word Problem
Problem Solving Word Problems 2
Solving systems by graphing
Solving systems by graphing 2
Solving systems by graphing 3
U06_L1_T1_we1 Solving Systems by Graphing
Solving systems by substitution 1
Solving systems by substitution 2
Solving systems by substitution 3
Solving systems by elimination
Solving systems by elimination 2
Solving systems by elimination 3
Solving Systems of Equations by Elimination
Solving Systems of Equations by Multiplication
Systems and rate problems
Systems and rate problems 2
Systems and rate problems 3
Mixture problems 1
Mixture problems 2
Mixture problems 3
Graphings Systems of Equations
Testing a solution for a system of equations
Consistent and Inconsistent Systems
Independent and Dependent Systems
Graphical Systems Application Problem
The Substitution Method
Substitution Method 2
Substitution Method 3
Systems of Three Variables
Systems of Three Variables 2
Solutions to Three Variable System
Three Equation Application Problem
Solving Linear Systems by Graphing
Solving Linear Systems by Substitution
Special Types of Linear Systems
Graphing systems of inequalities
U06_L3_T1_we3 Graphing Systems of Inequalities
Graphing systems of inequalities 2
Graphing systems of inequalities 3
CA Algebra I: Systems of Inequalities
Graphical System of Inequalities
Testing Solutions for a System of Inequalities
System of Inequalities Application

Algebra: Ratios &amp; proportions

Solving and writing algebraic ratios and proportions. Solving rational equations.

Introduction to Ratios (new HD version)
Understanding Proportions
Ratios as Fractions in Simplest Form
Simplifying Rates and Ratios
Find an Unknown in a Proportion
Ratio and Proportion
Find an Unknown in a Proportion 2
Another Take on the Rate Problem
Finding Unit Rates
Finding Unit Prices
Writing Proportions
Ratio problem with basic algebra (new HD)
More advanced ratio problem–with Algebra (HD version)
Alternate Solution to Ratio Problem (HD Version)
Unit conversion
Conversion between metric units
Converting within the metric system
Converting pounds to ounces
Converting Gallons to quarts pints and cups
Converting Farenheit to Celsius
Comparing Celsius and Farenheit temperature scales
Applying the Metric System
U.S. Customary and Metric units
Converting Yards into Inches
Unit Conversion with Fractions
Performing arithmetic calculations on units of volume
Application problems involving units of weight
Solving application problems involving units of volume
Unit Conversion Example: Drug Dosage
Perimeter and Unit Conversion
Rational Equations
Solving Rational Equations 1
Solving Rational Equations 2
Solving Rational Equations 3
Applying Rational Equations 1
Applying Rational Equations 2
Applying Rational Equations 3
Extraneous Solutions to Rational Equations
Rational Inequalities 2

Algebra: Absolute value

Understanding absolute value and solving absolute value equations and inequalities.

Absolute Value and Number Lines
Absolute Value 1
Absolute Value of Integers
Comparing Absolute Values
CA Algebra I: Number Properties and Absolute Value
Absolute Value Equations
Absolute Value Equations Example 1
Absolute Value Equation Example 2
U02_L2_T2_we1 Absolute Value Equations.avi
Absolute Value Inequalities
Absolute value inequalities Example 1
Absolute Inequalities 2
Absolute value inequalities example 3

Solving exponential and radical expressions and equations. Using scientific notation and significant figures.

Understanding Exponents
Understanding Exponents 2
Exponent Rules 1
Exponent Rules 2
Level 1 Exponents
Level 2 Exponents
Negative Exponent Intuition
Zero, Negative, and Fractional Exponents
Level 3 exponents
Exponent Rules Part 1
Exponent Rules Part 2
Exponent Properties 1
Exponent Properties 2
Exponent Properties 3
Exponent Properties 4
Exponent Properties 5
Exponent Properties 6
Exponent Properties 7
Exponent Properties Involving Products
Negative and Positive Exponents
Exponent Properties Involving Quotients
Rational Exponents and Exponent Laws
More Rational Exponents and Exponent Laws
Simplifying Expressions with Exponents
Multiplying and Dividing Rational Expressions 1
Multiplying and Dividing Rational Expressions 2
Multiplying and Dividing Rational Expressions 3
Simplifying Expressions with Exponents 2
Simplifying Expressions with Exponents 3
Fractional Exponent Expressions 1
Fractional Exponent Expressions 2
Fractional Exponent Expressions 3
Pythagorean Theorem 1
Pythagorean Theorem 2
Pythagorean Theorem 3
Evaluating exponential expressions
Evaluating exponential expressions 2
Evaluating exponential expressions 3
Scientific notation 1
Scientific notation 2
Scientific notation 3
Scientific Notation I
Scientific Notation Example 2
Scientific Notation 3 (new)
Scientific Notation Examples
Multiplying in Scientific Notation
Significant Figures
More on Significant Figures
Addition and Subtraction with Significant Figures
Multiplying and Dividing with Significant Figures
Understanding Square Roots
Approximating Square Roots
Square Roots and Real Numbers
Simplifying Square Roots
Simplifying Square Roots Comment Response
Finding Cube Roots
Simplifying Cube Roots
Radical Equivalent to Rational Exponents 2
Multiply and Simplify a Radical Expression 1
Multiply and Simplify a Radical Expression 2
How to Rationalize a Denominator

Algebra: Logarithms

Understanding and solving logarithms, including natural logs.

Introduction to Logarithms
Logarithm of a Power
Sum of Logarithms with Same Base
Introduction to logarithm properties
Introduction to logarithm properties (part 2)
Using Multiple Logarithm Properties to Simplify
Change of Base Formula
Logarithmic Scale
Richter Scale
Logarithmic Equations
Solving Logarithmic Equations
Proof: log a + log b = log ab
Proof: log_a (B) = (log_x (B))/(log_x (A))
Proof: A(log B) = log (B^A), log A – log B = log (A/B)
Natural Logarithm with a Calculator
Calculator for Natural Logarithms
Graphing Natural Logarithm Function

Algebra: Polynomials

Using polynomial expressions and factoring polynomials.

Terms coefficients and exponents in a polynomial
Simply a polynomial
Opposite of a Polynomial
Evaluating a polynomial at a given value
Partial Fraction Expansion 1
Partial Fraction Expansion 2
Partial Fraction Expansion 3
Polynomials 2
Simplifying First for Subtracting Rational Expressions
Subtracting Rational Expressions
Subtracting Polynomials
Polynomials1
Subtracting polynomials with multiple variables
Multiplying Monomials
Level 1 multiplying expressions
Dividing Monomials
Multiplying and Dividing Monomials 1
Multiplying and Dividing Monomials 2
Multiplying and Dividing Monomials 3
Multiplying Binomials
Square a Binomial
Special Products of Binomials
Multiplying and Simplifying Rational Expressions
Multiplying Monomials by Polynomials
Multiplying Polynomials
Multiplying Polynomials1
Multiplying Polynomials 1
Multiplying Polynomials 2
Multiplying Polynomials 3
Special Polynomials Products 1
Multiplication of Polynomials
More multiplying polynomials
Special Products of Polynomials 1
Special Products of Polynomials 2
U08_L2_T4_we3 Special Products of Polynomials 3
Polynomial divided by monomial
Dividing multivariable polynomial with monomial
Polynomial Division
Dividing polynomials 1
Algebraic Long Division
Dividing polynomials with remainders
Rationalizing Denominators of Expressions
Interesting Polynomial Coefficient Problem
Algebra II: Simplifying Polynomials
Monomial Greatest Common Factor
Factor polynomials using the GCF
Factoring and the Distributive Property
Factoring and the Distributive Property 2
Factoring and the Distributive Property 3
Factoring Trinomials by Grouping 1
Factoring Trinomials by Grouping 2
U09_L1_T2_we3 Factoring Trinomials by Grouping 3
Factoring Trinomials by Grouping 4
Factoring Trinomials by Grouping 5
Factoring Trinomials by Grouping 6
Factor by Grouping and Factoring Completely
Factoring trinomials with a leading 1 coefficient
Factoring trinomials with a common factor
Factoring trinomials with a non-1 leading coefficient by grouping
Factoring Special Products
U09_L2_T1_we1 Factoring Special Products 1
Factoring Special Products 2
U09_L2_T1_we3 Factoring Special Products 3
Factoring perfect square trinomials
Factoring Sum of Cubes
Factoring difference of squares
Factoring the Difference of Cubes

Solving quadratics through factoring, completing the square, graphing, and the quadratic equation.

Solving Quadratic Equations by Factoring 2.avi
Solving Quadratic Equations by Factoring 3.avi
Completing the square
Completing the Square 1
Completing the Square 3
Completing the Square 2
Completing the Square 4
Completing the Square to Solve Quadratic Equations
CA Algebra I: Completing the Square
Solving Quadratic Equations by Completing the Square
Completing Perfect Square Trinomials
Discriminant for Types of Solutions for a Quadratic
Complex Roots from the Quadratic Formula

Algebra: Functions

Identifying, solving, and graphing various types of functions.

Introduction to functions
Functional Relationships 1
Testing if a relationship is a function
Functions Part 2
Graphing a Basic Function
Functions (Part III)
Functions (part 4)
Domain of a function
Relations and Functions
Graphical Relations and Functions
Domain and Range of a Function
Domain and Range 1
Domain and Range 2
Domain and Range of a Relation
Domain and Range of a Function Given a Formula
Introduction to Function Inverses
Function Inverse Example 1
Function Inverses Example 2
Function Inverses Example 3
Direct Variation 1
Direct Variation Models
Direct and Inverse Variation
Recognizing Direct and Inverse Variation
Direct Inverse and Joint Variation
Inverse Variation Application
Recognizing Odd and Even Functions
Connection between even and odd numbers and functions
Algebra II: Functions, Combinatorics
Algebra II: Functions and Probability
Evaluating Functions
Sum of Functions
Difference of Functions
Product of Functions
Quotient of Functions
A more formal understanding of functions
Proof by Induction
Linear Algebra: Introduction to the inverse of a function
Basic Linear Function
Recognizing Linear Functions
Linear Function Graphs
Graphing Exponential Functions
Graphs of Square Root Functions

Algebra: Conic sections

Identifying and graphing circles, ellipses, parabolas, and hyperbolas.

Introduction to Conic Sections
Identifying Conics 1
Algebra ||: Conic Sections
Identifying Conics 2
Conic Identification 3
Parabola Focus and Directrix 1
Focus and Directrix of a Parabola 2
Non-Linear Systems of Equations 1
Non-Linear Systems of Equations 2
Non-Linear Systems of Equations 3
Conic Sections: Intro to Circles
Algebra II: Circles and Logarithms
Three Points Defining a Circle
Conic Sections: Intro to Ellipses
Foci of an Ellipse
Conic Sections: Intro to Hyperbolas
Conic Sections: Hyperbolas 2
Conic Sections: Hyperbolas 3
Foci of a Hyperbola
Proof: Hyperbola Foci
IIT JEE Circle Hyperbola Intersection
IIT JEE Circle Hyperbola Common Tangent Part 1
IIT JEE Circle Hyperbola Common Tangent Part 2
IIT JEE Circle Hyperbola Common Tangent Part 3
IIT JEE Circle Hyperbola Common Tangent Part 4
IIT JEE Circle Hyperbola Common Tangent Part 5
Tangent Line Hyperbola Relationship (very optional)

Algebra: Complex numbers

Understanding and solving equations with imaginary numbers.

Number Sets
Number Sets 1
Number Sets 2
Number Sets 3
Introduction to i and Imaginary Numbers
Calculating i Raised to Arbitrary Exponents
Complex Numbers
Complex Numbers (part 1)
Complex Numbers (part 2)
i as the Principal Root of -1 (a little technical)
IIT JEE Complex Numbers (part 1)
IIT JEE Complex Numbers (part 2)
IIT JEE Complex Numbers (part 3)
Algebra II: Imaginary and Complex Numbers
Imaginary Roots of Negative Numbers
Complex Conjugates Example
Subtracting Complex Numbers
Multiplying Complex Numbers
Dividing Complex Numbers
Complex Roots from the Quadratic Formula

Algebra: Matrices

Understanding and solving matrices.

Introduction to matrices
Matrix multiplication (part 1)
Matrix multiplication (part 2)
Inverse Matrix (part 1)
Inverting matrices (part 2)
Inverting Matrices (part 3)
Matrices to solve a system of equations
Matrices to solve a vector combination problem
Singular Matrices
Matrices: Reduced Row Echelon Form 1
Matrices: Reduced Row Echelon Form 2
Matrices: Reduced Row Echelon Form 3
Matrix Vector Products
Matrix Vector Products as Linear Transformations
Introduction to the Null Space of a Matrix
Null Space 2: Calculating the null space of a matrix
Null Space 3: Relation to Linear Independence
Column Space of a Matrix
Null Space and Column Space Basis
Visualizing a Column Space as a Plane in R3
Proof: Any subspace basis has same number of elements
Dimension of the Null Space or Nullity
Dimension of the Column Space or Rank
Showing relation between basis cols and pivot cols
Showing that the candidate basis does span C(A)
Expressing a Projection on to a line as a Matrix Vector prod
Linear Algebra: Matrix Product Examples
Matrix Product Associativity
Distributive Property of Matrix Products
Sums and Scalar Multiples of Linear Transformations
More on Matrix Addition and Scalar Multiplication
Linear Algebra: Matrix condition for one-to-one trans
Linear Algebra: Simplifying conditions for invertibility

Algebra: ck12.org Algebra 1 Examples

Select problems from ck12.org’s Algebra 1 FlexBook (Open Source Textbook). This is a good playlist to review if you want to make sure you have a good understanding of all of the major topics in Algebra I.

Variable Expressions
Order of Operations Example
Patterns and Equations
Equations and Inequalities
Domain and Range of a Function
Functions as Graphs
Word Problem Solving Plan 1
Word Problem Solving Strategies
Integers and Rational Numbers
Subraction of Rational Numbers
Multiplication of Rational Numbers
Distributive Property Example 1
Division of Rational Numbers
Square Roots and Real Numbers
Problem Solving Word Problems 2
One Step Equations
Two-Step Equations
Multi-Step Equations
Equations with Variables on Both Sides
Ratio and Proportion
Scale and Indirect Measurement
Percent Problems
Word Problem Solving 3
The Coordinate Plane
Graphing Using Intercepts
Graphs of Linear Equations
Slope and Rate of Change
Graphs Using Slope-Intercept Form
Direct Variation Models
Linear Function Graphs
Word Problem Solving 4
Linear Equations in Slope Intercept Form
Linear Equations in Point Slope Form
Linear Equations in Standard Form
Equations of Parallel and Perpendicular Lines
Fitting a Line to Data
Predicting with Linear Models
Using a Linear Model
Inequalities Using Multiplication and Division
Compound Inequalities
Absolute Value Equations
Absolute Value Inequalities
Graphing Inequalities
Solving Linear Systems by Graphing
Solving Linear Systems by Substitution
Solving Systems of Equations by Elimination
Solving Systems of Equations by Multiplication
Special Types of Linear Systems
Systems of Linear Inequalities
Exponent Properties Involving Products
Exponent Properties Involving Quotients
Zero, Negative, and Fractional Exponents
Scientific Notation
Exponential Growth Functions
Exponential Decay Functions
Geometric Sequences (Introduction)
Word Problem Solving- Exponential Growth and Decay
Multiplication of Polynomials
Special Products of Binomials
Polynomial Equations in Factored Form
Factoring Special Products
Factor by Grouping and Factoring Completely
Solving Quadratic Equations by Square Roots
Solving Quadratic Equations by Completing the Square
Identifying Exponential Models
Graphs of Square Root Functions
How to Rationalize a Denominator
Pythagorean Theorem
Distance Formula
Midpoint Formula
Visual Pythagorean Theorem Proof
Average or Central Tendency: Arithmetic Mean, Median, and Mode
Range, Variance and Standard Deviation as Measures of Dispersion
Stem and Leaf Plots
Histograms
Box-and-whisker Plot
Proportionality
Asymptotes of Rational Functions
Another Rational Function Graph Example
A Third Example of Graphing a Rational Function
Polynomial Division
Simplifying Rational Expressions Introduction
Multiplying and Dividing Rational Expressions
Solving Rational Equations
Two more examples of solving rational equations
Surveys and Samples

American Civics

Videos about how government works in the United States.

Electoral College
Primaries and Caucuses
Deficit and Debt Ceiling
Government’s Financial Condition
Social Security Intro
FICA Tax
Medicare Sustainability
SOPA and PIPA

Arithmetic and Pre-Algebra

The first math topic. Start here if you want to learn the basics (or just want to make sure you know these topics). After this, you should be ready for algebra. This topic includes videos from the former developmental math playlists.
Arithmetic and Pre-Algebra: Addition and subtraction

Adding and subtracting positive and negative whole numbers. Starts with 1+1=2 and covers carrying, borrowing, and word problems.

Basic Subtraction
Subtraction 2
Subtracting Whole Numbers
Subtraction 3: Introduction to Borrowing or Regrouping
Why borrowing works
Level 4 Subtraction
Subtraction Word Problem
Alternate mental subtraction method
Negative Numbers Introduction
Adding Whole Numbers and Applications 1
u09 l1 t2 we4 Adding Real Numbers Application

Arithmetic and Pre-Algebra: Multiplication and division

Multiplying and dividing positive and negative whole numbers, understanding place value, and rounding numbers.

Basic Multiplication
Multiplication 2: The Multiplication Tables
Multiplication 3: 10,11,12 times tables
Division 1
Division 2
Dividing Whole Numbers and Applications 1
Multiplication 4: 2-digit times 1-digit number
Multiplication 5: 2-digit times a 2-digit number
Multiplying Whole Numbers and Applications 2
Lattice Multiplication
Why Lattice Multiplication Works
Multiplying Whole Numbers and Applications 4
Multiplication 6: Multiple Digit Numbers
Multiplication 7: Old video giving more examples
Multiplying Whole Numbers and Applications 6
Division 3: More long division and remainder examples
Partial Quotient Division
Level 4 division
Partial Quotient Method of Division 2
Multiplying Whole Numbers and Applications 1
Place Value 1
Place Value 2
Place Value 3
Rounding Whole Numbers 1
Rounding Whole Numbers 2
Rounding Whole Numbers 3

Arithmetic and Pre-Algebra: Negative numbers

Understanding and using negative numbers.

Negative Numbers Introduction
Ordering Negative Numbers
Multiplying Positive and Negative Numbers
Dividing Positive and Negative Numbers
Why a Negative Times a Negative is a Positive

Arithmetic and Pre-Algebra: Number properties

Defining and using the commutative, associative, distributive, identity, and inverse properties.

Commutative Law of Multiplication
Associative Law of Multiplication
The Distributive Property
The Distributive Property 2
Distributive Property Example 1
CA Algebra I: Number Properties and Absolute Value
Identity Property of 1
Identity property of 1 (second example)
Identity property of 0
Inverse Property of Multiplication
Why Dividing by Zero is Undefined
Why Zero Divided by Zero is Undefined/Indeterminate
Undefined and Indeterminate

Arithmetic and Pre-Algebra: Order of operations

Defining the order in which operations are done in expressions.

Introduction to Order of Operations
More Complicated Order of Operations Example
Order of Operations
Order of Operations 1

Arithmetic and Pre-Algebra: Factors and multiples

Understanding and finding factors and multiples. After these videos, you’ll be ready for fractions.

Prime Numbers
Recognizing Prime Numbers
Recognizing Divisibility
Common Divisibility Examples
Finding Factors of a Number
Prime Factorization
Least Common Multiple
Least Common Multiple (LCM)
Greatest Common Divisor
Algebraic Expression Least Common Multiple

Arithmetic and Pre-Algebra: Fractions

Understanding fractions conceptually, using operations with fractions, and converting fractions.

Numerator and Denominator of a Fraction
Identifying Fraction Parts
Equivalent fractions
Equivalent Fractions Example
Comparing Fractions
Fractions in lowest terms
Comparing Fractions 2
Ordering Fractions
Proper and Improper Fractions
Mixed numbers and improper fractions
Converting Mixed Numbers to Improper Fractions
Changing a Mixed Number to an Improper Fraction
Changing an Improper Fraction to a Mixed Number
Subtracting Fractions
Finding Common Denominators
Adding Mixed Numbers with Unlike Denominators
Subtracting Mixed Numbers
Subtracting Mixed Numbers 2
Subtracting Mixed Numbers Word Problem
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying Fractions and Mixed Numbers
Multiplying Fractions Word Problem
Dividing fractions
Dividing Fractions Example
Dividing Fractions Word Problem
Reciprocal of a Mixed Number
Dividing Mixed Numbers
Dividing Mixed Numbers and Fractions
Converting Fractions to Decimals Example
Converting fractions to decimals
Decimals and Fractions
Converting Repeating Decimals to Fractions 1
Converting Repeating Decimals to Fractions 2
Representing a number as a decimal, percent, and fraction 2
Representing a number as a decimal, percent, and fraction
Points on a number line
Ordering numeric expressions

Arithmetic and Pre-Algebra: Decimals

Understanding decimals conceptually, using operations with decimals, rounding and estimating with decimals, and converting decimals.

Subtracting decimals (old)
Decimal Place Value
Decimal Place Value 2
Decimals on a Number Line
Rounding Decimals
Estimation with Decimals
Comparing Decimals
Subtracting Decimals
Subtracting Decimals Word Problem
Multiplying a Decimal by a Power of 10
Mulitplication 8: Multiplying decimals (Old video)
Multiplying Decimals
Dividing a Decimal by a Power of 10
Dividing Decimals 2.1
Dividing decimal
Dividing Decimals
Mulitplyling Decimals 3
Decimals and Fractions
Converting Fractions to Decimals Example
Converting fractions to decimals
Converting Repeating Decimals to Fractions 1
Converting Repeating Decimals to Fractions 2
Percent and decimals
Representing a number as a decimal, percent, and fraction 2
Representing a number as a decimal, percent, and fraction
Points on a number line
Ordering numeric expressions

Arithmetic and Pre-Algebra: Percents

Understanding, solving, and converting percents.

Describing the Meaning of Percent
Describing the Meaning of Percent 2
Identifying Percent Amount and Base
Representing a number as a decimal, percent, and fraction
Solving Percent Problems
Solving Percent Problems 2
Solving Percent Problems 3
Growing by a percentage
Representing a number as a decimal, percent, and fraction 2
Ordering numeric expressions

Arithmetic and Pre-Algebra: Ratios and proportions (basic)

Solving and writing ratios and proportions without algebra.

Introduction to Ratios (new HD version)
Understanding Proportions
Ratios as Fractions in Simplest Form
Simplifying Rates and Ratios
Find an Unknown in a Proportion 2
Finding Unit Rates
Finding Unit Prices
Unit conversion
Converting units of length
Conversion between metric units
U.S. Customary and Metric units
Converting within the metric system
Converting Gallons to quarts pints and cups
Converting pounds to ounces
Comparing Celsius and Farenheit temperature scales
Converting Farenheit to Celsius
Speed translation

Arithmetic and Pre-Algebra: Exponents (basic)

Understanding and solving exponents without algebra.

Understanding Exponents
Understanding Exponents 2
Level 1 Exponents
Level 2 Exponents
Level 3 exponents
Exponent Rules Part 1
Exponent Rules Part 2

Art History

Spontaneous conversations about works of art where the speakers are not afraid to disagree with each other or art history orthodoxy. Videos are made by Dr. Beth Harris and Dr. Steven Zucker along with other contributors and maintained at smarthistory.khanacademy.org.
Art History: – 400 C.E. Ancient Cultures

Sculpture from the Parthenon’s East Pediment
Victory Stele of Naram-Sin
The Standard of Ur
Colosseum
Law Code Stele of King Hammurabi
The Pergamon Altar
Arch of Titus
Great Lyre from the “King’s Grave” at Ur
After Praxiteles, Venus (Roman Copy)
Mixing Vessel with Odysseus Escaping from the Cyclops’ Cave
Parthenon Frieze
New York Kouros
The Parthenon: Metopes
Neo-Assyrian Art: Human Headed Winged Lion and Bull (Lamassu)
Pair of Centaurs Fighting Cats of Prey from Hadrian’s Villa
Column of Trajan
Erechtheion: Caryatid and Column
Medea Sarcophagus, 140 – 150 C.E.
Ishtar Gate and Processional Way
Nike of Samothrace
Equestrian Sculpture of Marcus Aurelius
Nude Woman (Venus of Willendorf)
Seated Scribe
Hellenistic Art at the Metropolitan: Eros Sleeping and An Old Market Woman
Arch of Constantine
Ramesses II
Rosetta Stone
Bodhisattva from China
Geometric Greek Krater
Buddha of Medicine Bhaishajyaguru (Yaoshi fo)
Dying Gaul
Japan, Muromachi to Momoyama period Negoro ware ewer
Ancient Rome
Temple of Portunus
The Pantheon, Rome

Art History: 400-1300 Medieval Era

Birth of the Gothic: Abbot Suger and the Ambulatory at St. Denis
Two Royal Figures (Saljuq Period)
Last Judgment Tympanum, Cathedral of St. Lazare, Autun
Sutton Hoo Ship Burial
Virgin from Ger
Wise and Foolish Virgins, Sant Quirze de Pedret
Coronation Mantle
Sarcophagus of Junius Bassus
Byzantine Art: Justinian and His Attendants
Santa Sabina
Basilica of Santa Prassede (Praxedes)
Historiated Capitals, Church of Sant Miquel, Camarasa (Noguera)
Ivory panel with Archangel
Santa Maria Maggiore
Berlinghieri’s St. Francis Altarpiece
Cathedral of Notre Dame de Chartres
Hebrew Astrolabe
Pre-Columbian Cup

Art History: 1300-1400 Proto-Renaissance

Sienese Art: Duccio, Martini, and Lorenzetti
Giotto’s Lamentation
Nicola and Giovanni Pisano
Lorenzetti’s Presentation of Jesus in the Temple
Giotto, St. Francis Receiving the Stigmata
Duccio’s The Virgin and Child with Saints Dominic and Aurea
Simone Martini’s Annunciation
Andrea Pisano’s Reliefs on the Campanile in Florence
Sluter’s Well of Moses
Giotto’s The Entombment of Mary
Holy Thorn Reliquary
Icon of Saint George (the “Black George”)
Follower of Bernardo Daddi, The Aldobrandini Triptych

Art History: 1400-1500 Renaissance in Italy and the North

Orsanmichele
Campin’s Merode Altarpiece
Fra Filippo Lippi’s Madonna and Child
Representations of David in the Florentine Renaissance
Linear Perspective: Brunelleschi’s Experiment
Hubert (?) and Jan van Eyck’s Ghent Altarpiece (closed) or The Adoration of the Mystic Lamb
Donatello’s David
Bellini’s St. Francis
Lippi’s Portrait of a Man and Woman at a Casement
Hubert (?) and Jan van Eyck’s Ghent Altarpiece (open) or The Adoration of the Mystic Lamb
Van Eyck’s Portrait of Giovanni Arnolfini and his Wife
Masaccio’s The Tribute Money in the Brancacci Chapel
Christus’s Portrait of a Young Girl
Fra Angelico’s The Annunciation
Christus’s Portrait of a Carthusian
van der Goes’ The Adoration of the Kings
Fra Filippo Lippi
Mantegna’s Saint Sebastian
van der Weyden’s Crucifixion Triptych
Van der Weyden’s Deposition
Van Eyck’s The Madonna in the Church
Masaccio’s Holy Trinity
Piero della Francesca’s The Baptism of Christ
Botticelli’s Birth of Venus
Andrea Mantegna, Camera degli Sposi
Piero della Francesca’s Portraits of the Duke and Duchess of Urbino
Icon of the Triumph of Orthodoxy
The Unicorn in Captivity
Donatello, Saint Mark
Wise and Foolish Virgins, Sant Quirze de Pedret
Masaccio, Virgin and Child Enthroned
Veneziano’s St. Lucy Altarpiece
Donatello’s Feast of Herod
Campin’s Christ and the Virgin
Van der Weyden’s The Last Judgment Polyptych
Brunelleschi’s Dome
Van der Weyden’s Crucifixion, with the Virgin and Saint John
Brunelleschi &amp; Ghiberti The Sacrifice of Isaac
Botticelli’s Primavera
Martini’s Architectural Veduta

Art History: 1500-1600 End of the Renaissance and the Reformation

Parmigianino’s Madonna of the Long Neck
Michelangelo’s Piet�
Pontormo’s Entombment
Raphael’s La belle jardinière
Dürer’s Four Apostles
Bruegel’s The Dutch Proverbs
Toward The High Renaissance
Leonardo’s Virgin of the Rocks
Leonardo da Vinci
Michelangelo’s David
Leonardo’s Last Supper
Rosso Fiorentino’s The Dead Christ with Angels
Parmigianino’s Self-Portrait
Titian’s Noli me Tangere
Dürer’s Prints
Bellini’s and Titian’s The Feast of the Gods
Michelangelo’s Moses
Bronzino and The Mannerist Portrait
Michelangelo’s Slaves
Dürer’s Self-portrait
Cellini’s Perseus
Holbein’s The Merchant Georg Gisze
Raphael’s School of Athens
Holbein’s Christina of Denmark
Raphael’s Portrait of Pope Julius II
Michelangelo’s Last Judgment (Sistine Chapel)
Titian, Portrait of a Man
Michelangelo’s Ceiling of the Sistine Chapel
Leonardo’s Virgin and Child with St Anne and St John the Baptist (Burlington House Cartoon)
Saint Peter’s Basilica
Hans Holbein the Younger’s Henry VIII
Gerard David’s Virgin and Child with Angels
David’s The Virgin and Child with Saints and Donor
Lucas Cranach the Elder’s Cupid complaining to Venus
Bronzino’s Portrait of Eleonora di Toledo with her son Giovanni
Veronese’s The Family of Darius Before Alexander
Lucas Cranach’s Judith with the Head of Holofernes
Titian’s Venus of Urbino
Veronese’s The Dream of Saint Helena
Dürer’s The Large Piece of Turf
Michelangelo, Laurentian Library
El Greco’s Adoration of the Shepherds
Bruegel’s Tower of Babel
Tintoretto’s The Origin of the Milky Way

Art History: 1600-1700 The Baroque

Bernini’s David
Caravaggio’s Narcissus at the Source
Borromini, San Carlo alle Quattro Fontane
Vermeer’s The Glass of Wine
Bernini’s Pluto and Proserpina
Caravaggio’s paintings in the Contarelli Chapel, San Luigi dei Francesi
Rembrandt’s Bathsheba at her Bath
Pierre Le Gros the Younger’s Stanislas Kostka on his Deathbed
Caravaggio’s Calling of Saint Matthew
Baroque Art in Holland Vermeer’s Young Woman with a Water Pitcher
Poussin’s Landscape with St. John and Rape of the Sabines
Guercino’s Saint Luke Displaying a Painting of the Virgin
Hals’s Malle Babbe
Velázquez’s Las Meninas
Caravaggio’s Crucifixion of Saint Peter
Rembrandt’s Girl at a Window
Il Gesù, Rome
Rembrandt’s The Three Crosses
Bernini’s Saint Peter’s Square
Bernini’s Apollo and Daphne
Pozzo’s Saint Ignatius Chapel in the church Il Gesù, 1965 (Rome)
Hals’ Singing Boy with Flute
Rubens’s Arrival (or Disembarkation) of Marie de Medici at Marseilles, Medici Cycle
Velázquez’s Los Borrachos or The Triumph of Bacchus
Bernini’s Bust of Medusa
Claude Lorraine’s The Judgment of Paris
Rubens, The Consequences of War
Velázquez’s Vulcan’s Forge
van Huysum, Vase with Flowers
Bernini’s Ecstasy of Saint Theresa
Rembrandt’s Self-Portraits
Antoine or Louis Le Nain, Peasant Family in an Interior
Gentileschi’s Self-portrait as the Allegory of Painting
Bernini’s Cathedra Petri (Chair of St. Peter)
Caravaggio’s Supper at Emmaus
Carracci’s Crucifixion &amp; Lamentation
Carracci’s Ceiling of the Farnese Palace
Caravaggio’s Death of the Virgin
Bernini’s Sant’Andrea al Quirinale
Ribera’s Martyrdom of Saint Philip

Art History: 1700-1800 Age of Enlightenment

David’s Death of Socrates
David’s Oath of the Horatii
Fragonard’s The Swing
Fragonard’s The Meeting
Girodet’s The Sleep of Endymion
Boy with a Squirrel
Boucher’s Venus Consoling Love
David’s The Lictors Returning to Brutus the Bodies of His Sons
David’s The Intervention of the Sabine Women
Reynolds’s Lady Cockburn and Her Three Eldest Sons
David’s The Emperor Napoleon In His Study at the Tuileries
Peale’s Staircase Group (Portrait of Raphaelle Peale and Titian Ramsay Peale)

Art History: 1800-1848 Industrial Revolution I

Delacroix’s Scene of the massacre at Chios
Romanticism in France Delacroix’s Liberty Leading the People
Romanticism in Spain Goya’s Third of May, 1808
Friedrich’s Abbey among Oak Trees
Turner’s Rain, Steam, and Speed – The Great Western Railway
Delacroix’s The Death of Sardanapalus
Constable’s The Hay Wain
Friedrich’s The Lone Tree
Goya, The Family of Charles IV
Friedrich’s Monk by the Sea
Gros’s Napoleon Bonaparte Visiting the Plague-Stricken in Jaffa
Ingres’ La Grand Odalisque
Géricault’s Raft of the Medusa
Ingres’ Raphael and the Fornarina
Cole’s Expulsion from the Garden of Eden
Cole’s The Oxbow
Goya’s Saturn Devouring One of His Sons
Friedrich’s Woman at a Window
Redgrave’s The Sempstress
Ingres’ Princesse de Broglie
Allston’s Elijah in the Desert
Lane’s Owl’s Head, Penobscot Bay, Maine
Friedrich’s A Walk at Dusk
Erastus Salisbury Field’s Portrait of a Young Woman
Fuseli’s Titania and Bottom

Art History: 1848-1907 Industrial Revolution II

Courbet’s Burial at Ornans
Hunt’s Claudio and Isabella
Bonheur’s Plowing in the Nivernais
Seurat’s Bathers at Asnières
Manet’s Émile Zola
Édouard Manet’s Olympia
Bonheur’s Sheep in the Highlands
Böcklin’s Self-Portrait with Death Playing the Fiddle
Millet’s L’Angelus
Manet’s The Balcony
Van Gogh’s Portrait of the Joseph Roulin
Sir John Everett Millais’s Ophelia
Cézanne’s Still-Life with Plaster Cupid
Cézanne’s Still Life with Apples
Édouard Manet’s The Railway
Courbet’s The Artist’s Studio, A real allegory summing up seven years of my artistic and moral life
Caillebotte’s The Floor Scrapers
Gustave Caillebotte’s Paris Street; Rainy Day
Renoir’s La Loge
Degas’ The Bellelli Family
Cassatt’s The Loge
Manet’s Le déjeuner sur l’herbe
Degas’ The Dance Class
Sargent’s Carnation, Lily, Lily, Rose
Burne Jones’s The Golden Stairs
Cezanne’s The Red Rock
Khnopff’s Jeanne Kéfer
Hunt’s Our English Coasts (“Strayed Sheep”)
Cassatt’s In the Loge
Gauguin’s The Red Cow
Édouard Manet’s Plum Brandy
Garnier’s Paris Opéra
Monet’s The Argenteuil Bridge
Monet’s Gare St. Lazare
Young Woman Powdering Herself
Gauguin’s Nevermore
Morisot’s The Mother and Sister of the Artist
Manet’s In the Conservatory
Cassatt’s Woman with a Pearl Necklace in a Loge
Carpeaux’s Dance
Millet’s The Gleaners
Renoir’s Moulin de la Galette
Manet’s Corner of a Café-Concert
Caillebotte’s Man at his Bath
Vincent van Gogh, Self-Portrait Dedicated to Paul Gauguin
Édouard Manet’s A Bar at the Folies-Bergère
Hunt’s The Awakening Conscience
Burne-Jones’s Hope
Monet’s Rouen Cathedral Series
Sir John Everett Millais’s Christ in the House of His Parents
Degas’s At the Races in the Countryside
Leighton’s An Athlete Wrestling with a Python
Cézanne’s Bathers
Monet’s Cliff Walk at Pourville
Monet’s Poplars
Renoir’s The Grands Boulevards
Post-Impressionism Seurat’s A Sunday on La Grande Jatte – 1884
Monet’s Water Lilies
Dyce’s Pegwell Bay, Kent – a Recollection of October 5th 1858
Toulouse-Lautrec’s At the Moulin Rouge
Cassatt’s Breakfast in Bed
Degas’s Visit to a Museum
Gustav Klimt’s Beethoven Frieze
Gustav Klimt’s The Kiss
John Roddam Spencer Stanhope’s Thoughts of the Past
Symbolism: Munch’s The Storm
Klimt’s Death and Life
Rodin’s The Gates of Hell
van Gogh’s The Bedroom
Renoir’s The Large Bathers
Burne-Jones’ King Cophetua and the Beggar Maid
Cezanne’s The Large Bathers
Millais’s Mariana
Millais’ The Vale of Rest
Cassatt’s The Child’s Bath
Wallis’s Chatterton
Homer’s The Life Line
Homer’s The Fog Warning (Halibut Fishing)

Art History: 1907-1960 Age of Global Conflict

Duchamp’s Boite-en-valise (the red box), series F
Expressionism &amp; Kirchner’s Street, Dresden
Matisse’s Luxe, calme et volupté
Giacometti’s The Palace at 4am
Umbo’s The Roving Reporter
Bellows’ Pennsylvania Station Excavation
Matisse’s The Red Studio
Kandinsky’s Composition VII
Cubism &amp; Picasso’s Still Life with Chair Caning
Arp’s Untitled (Collage with Squares Arranged According to the Laws of Chance)
Giacometti’s City Square
Mark Rothko’s No. 3/No. 13
de Kooning’s Woman I
Picasso’s Les Demoiselles d’Avignon
Matisse’s Piano Lesson
Newman’s Onement I
Italian Futurism
Schwitters’s Merzbild 32A, The Cherry Picture
Magritte’s The Treachery of Images (Ceci n’est pas une pipe)
Three Futurists Balla, Severini and Boccioni
Jawlensky’s Young Girl in a Flowered Hat
Gordon Bunshaft’s Lever House
Höch’s Cut with the Kitchen Knife Dada Through the Last Weimar Beer-Belly Cultural Epoch of Germany
Newman’s Vir Heroicus Sublimis
August Sander’s Portraits
Schiele’s Seated Male Nude (Self-Portrait)
Picasso’s The Reservoir, Horta de Ebro
Feininger’s Cathedral for the Bauhaus
De Stijl: Mondrian’s Composition No. II, with Red and Blue
Cartier-Bresson’s Behind the Gare St. Lazare
Dali’s Metamorphosis of Narcissus
Frank Lloyd Wright, Solomon R. Guggenheim Museum
Picasso’s Guernica
Modigliani’s Young Woman in a Shirt
Neue Sachlichkeit: Otto Dix’s Portrait of the Journalist Sylvia von Harden
Schiele’s Hermits
László Moholy-Nagy’s Composition A.XX
Raymond Duchamp-Villon’s Horse
Grant Wood’s American Gothic
O’Keeffe’s The Lawrence Tree
Hopper’s Nighthawks
Frida Kahlo’s Frieda and Diego Rivera
Abstract Expressionism Pollock’s One: Number 31, 1950
Jasper Johns’ Flag
Brancusi’s Bird in Space
Ludwig Mies van der Rohe’s Seagram Building

Art History: 1960- Age of Post-Colonialism

Photography post 1960: Diane Arbus’ Boy with a Toy Hand Grenade
Bacon’s Triptych – August 1972
Claes Oldenburg’s Floor Cake
Lucian Freud, Standing by the Rags, 1988-89
Dan Flavin, Untitled (To Donna) II
Warhol’s Gold Marilyn Monroe
Sherman’s Untitled Film Still #21
Hesse, Untitled (Rope Piece), 1970
Joseph Beuys, Table with Accumulator
William Eggleston’s Red Ceiling, or Greenwood, Mississippi, 1973
Ed Kienholz and Nancy Reddin Kienholz Useful Art #5: The Western Hotel, 1992
Donald Judd’s Untitled
Gerhard Richter, The Cage Paintings (1-6)
Lichtenstein’s Rouen Cathedral Set V
Eva Hesse’s Untitled
Smithson, Spiral Jetty, 1970
Jackie Winsor’s #1 Rope
Judy Chicago’s Pasadena Lifesaver, Blue Series, No. 4 &amp; Lynda Benglis’s Omega
Gerhard Richter, September
Robert Colescott’s Beauty is in the Eye of the Beholder
Ai Weiwei’s “Remembering” and the Politics of Dissent

Banking and Money

Videos on how banks work and how money is created.

Banking 1
Banking 2: A bank’s income statement
Banking 3: Fractional Reserve Banking
Banking 4: Multiplier effect and the money supply
Banking 5: Introduction to Bank Notes
Banking 6: Bank Notes and Checks
Banking 7: Giving out loans without giving out gold
Banking 8: Reserve Ratios
Banking 9: More on Reserve Ratios (Bad sound)
Banking 10: Introduction to leverage (bad sound)
Banking 11: A reserve bank
Banking 12: Treasuries (government debt)
Banking 13: Open Market Operations
Banking 14: Fed Funds Rate
Banking 15: More on the Fed Funds Rate
Banking 16: Why target rates vs. money supply
Banking 17: What happened to the gold?
Banking 18: Big Picture Discussion
The Discount Rate
Repurchase Agreements (Repo transactions)
Federal Reserve Balance Sheet
Fractional Reserve Banking Commentary 1
FRB Commentary 2: Deposit Insurance
FRB Commentary 3: Big Picture
LIBOR

Biology

Covers topics seen in a first year college or high school biology course.

Introduction to Evolution and Natural Selection
Ape Clarification
Intelligent Design and Evolution
Evolution Clarification
Natural Selection and the Owl Butterfly
DNA
Variation in a Species
Chromosomes, Chromatids, Chromatin, etc.
Mitosis, Meiosis and Sexual Reproduction
Phases of Mitosis
Phases of Meiosis
Embryonic Stem Cells
Cancer
Introduction to Heredity
Punnett Square Fun
Hardy-Weinberg Principle
Bacteria
Viruses
Introduction to Cellular Respiration
Oxidation and Reduction Review From Biological Point-of-View
Oxidation and Reduction in Cellular Respiration
Glycolysis
Krebs / Citric Acid Cycle
Electron Transport Chain
Oxidative Phosphorylation and Chemiosmosis
Photosynthesis
Photosynthesis: Light Reactions 1
Photosynthesis: Light Reactions and Photophosphorylation
Photosynthesis: Calvin Cycle
Photorespiration
C-4 Photosynthesis
CAM Plants
Parts of a cell
Diffusion and Osmosis
The Lungs and Pulmonary System
Red blood cells
Circulatory System and the Heart
Hemoglobin
Anatomy of a Neuron
Sodium Potassium Pump
Correction to Sodium and Potassium Pump Video
Electrotonic and Action Potentials
Saltatory Conduction in Neurons
Neuronal Synapses (Chemical)
Myosin and Actin
Tropomyosin and troponin and their role in regulating muscle contraction
Role of the Sarcoplasmic Reticulum in Muscle Cells
Anatomy of a muscle cell
Role of Phagocytes in Innate or Nonspecific Immunity
Types of immune responses: Innate and Adaptive. Humoral vs. Cell-Mediated
B Lymphocytes (B cells)
Professional Antigen Presenting Cells (APC) and MHC II complexes
Helper T Cells
Cytotoxic T Cells
Review of B cells, CD4+ T cells and CD8+ T cells
Inflammatory Response
The Kidney and Nephron
Secondary Active Transport in the Nephron
Species
Taxonomy and the Tree of Life
Human Prehistory 101: Prologue
Human Prehistory 101 Part 1: Out of (Eastern) Africa
Human Prehistory 101 Part 2: Weathering The Storm
Human Prehistory 101 Part 3: Agriculture Rocks Our World
Human Prehistory 101: Epilogue
Genetics 101 Part 1: What are genes?
Genetics 101 Part 2: What are SNPs?
Genetics 101 Part 3: Where do your genes come from?
Genetics 101 Part 4: What are Phenotypes?

Brain Teasers

Random logic puzzles and brain teasers. Fun to do and useful for many job interviews!

Liar Truthteller Brain Teaser
Toggler Brain Teaser
Alien Abduction Brain Teaser
Light Bulb Switching Brain Teaser
Path Counting Brain Teaser
3-D Path Counting Brain Teaser

Brit Cruise

Video series which explores how modern fields of study are based on ancient ideas. Written &amp; Directed by Brit Cruise, Music by Cameron Murray, Illustration by Mark Phillips.
Journey into Cryptography

Part 1: Intro to Cryptography
Part 2: The Fundamental Theorem of Arithmetic
Part 3: Probability Space
Part 4: Frequency Stability
Part 5: Caesar Cipher
Part 6: Polyalphabetic Cipher
Part 8: Case Study: WW2 Encryption Machines
Part 9: Perfect Secrecy
Part 10: Pseudorandom Number Generators
Part 11: Diffie-Hellman key exchange

CAHSEE Example Problems

Sal working through the 53 problems from the practice test available at http://www.cde.ca.gov/ta/tg/hs/documents/mathpractest.pdf for the CAHSEE (California High School Exit Examination). Clearly useful if you’re looking to take that exam. Probably still useful if you want to make sure you have a solid understanding of basic high school math.

CAHSEE Practice: Problems 1-3
CAHSEE Practice: Problems 4-9
CAHSEE Practice: Problems 10-12
CAHSEE Practice: Problems 13-14
CAHSEE Practice: Problems 15-16
CAHSEE Practice: Problems 17-19
CAHSEE Practice: Problems 20-22
CAHSEE Practice: Problems 23-27
CAHSEE Practice: Problems 28-31
CAHSEE Practice: Problems 32-34
CAHSEE Practice: Problems 35-37
CAHSEE Practice: Problems 38-42
CAHSEE Practice: Problems 43-46
CAHSEE Practice: Problems 47-51
CAHSEE Practice: Problems 52-53

Calculus

Topics covered in the first two or three semesters of college calculus. Everything from limits to derivatives to integrals to vector calculus. Should understand the topics in the pre-calculus playlist first (the limit videos are in both playlists)

Newton Leibniz and Usain Bolt
Introduction to Limits (HD)
Introduction to Limits
Limit Examples (part 1)
Limit Examples (part 2)
Limit Examples (part3)
Limit Examples w/ brain malfunction on first prob (part 4)
Squeeze Theorem
Proof: lim (sin x)/x
More Limits
Epsilon Delta Limit Definition 1
Epsilon Delta Limit Definition 2
Calculus: Derivatives 1 (new HD version)
Calculus: Derivatives 2 (new HD version)
Calculus: Derivatives 2.5 (new HD version)
Derivative Intuition Module
Calculus: Derivatives 1
Calculus: Derivatives 2
Calculus: Derivatives 3
The Chain Rule
Chain Rule Examples
Even More Chain Rule
Product Rule
Quotient Rule
Derivatives (part 9)
Proof: d/dx(x^n)
Proof: d/dx(sqrt(x))
Proof: d/dx(ln x) = 1/x
Proof: d/dx(e^x) = e^x
Proofs of Derivatives of Ln(x) and e^x
Implicit Differentiation
Implicit Differentiation (part 2)
More implicit differentiation
More chain rule and implicit differentiation intuition
Trig Implicit Differentiation Example
Calculus: Derivative of x^(x^x)
Introduction to L’Hopital’s Rule
L’Hopital’s Rule Example 1
L’Hopital’s Rule Example 2
L’Hopital’s Rule Example 3
Maxima Minima Slope Intuition
Inflection Points and Concavity Intuition
Monotonicity Theorem
Calculus: Maximum and minimum values on an interval
Calculus: Graphing Using Derivatives
Calculus Graphing with Derivatives Example
Graphing with Calculus
Optimization with Calculus 1
Optimization with Calculus 2
Optimization with Calculus 3
Optimization Example 4
Introduction to rate-of-change problems
Equation of a tangent line
Rates-of-change (part 2)
Mean Value Theorem
The Indefinite Integral or Anti-derivative
Indefinite integrals (part II)
Indefinite Integration (part III)
Indefinite Integration (part IV)
Indefinite Integration (part V)
Integration by Parts (part 6 of Indefinite Integration)
Indefinite Integration (part 7)
Another u-subsitution example
Introduction to definite integrals
Definite integrals (part II)
Definite Integrals (area under a curve) (part III)
Definite Integrals (part 4)
Definite Integrals (part 5)
Definite integral with substitution
Integrals: Trig Substitution 1
Integrals: Trig Substitution 2
Integrals: Trig Substitution 3 (long problem)
Periodic Definite Integral
Simple Differential Equations
Solid of Revolution (part 1)
Solid of Revolution (part 2)
Solid of Revolution (part 3)
Solid of Revolution (part 4)
Solid of Revolution (part 5)
Solid of Revolution (part 6)
Solid of Revolution (part 7)
Solid of Revolution (part 8 )
Sequences and Series (part 1)
Sequences and series (part 2)
Maclauren and Taylor Series Intuition
Cosine Taylor Series at 0 (Maclaurin)
Sine Taylor Series at 0 (Maclaurin)
Taylor Series at 0 (Maclaurin) for e to the x
Euler’s Formula and Euler’s Identity
Visualizing Taylor Series Approximations
Generalized Taylor Series Approximation
Visualizing Taylor Series for e^x
Polynomial approximation of functions (part 1)
Polynomial approximation of functions (part 2)
Approximating functions with polynomials (part 3)
Polynomial approximation of functions (part 4)
Polynomial approximations of functions (part 5)
Polynomial approximation of functions (part 6)
Polynomial approximation of functions (part 7)
Taylor Polynomials
Exponential Growth
AP Calculus BC Exams: 2008 1 a
AP Calculus BC Exams: 2008 1 b&amp;c
AP Calculus BC Exams: 2008 1 c&amp;d
AP Calculus BC Exams: 2008 1 d
Calculus BC 2008 2 a
Calculus BC 2008 2 b &amp;c
Calculus BC 2008 2d
Partial Derivatives
Partial Derivatives 2
Divergence 1
Divergence 2
Divergence 3
Curl 1
Curl 2
Curl 3
Double Integral 1
Double Integrals 2
Double Integrals 3
Double Integrals 4
Double Integrals 5
Double Integrals 6
Triple Integrals 1
Triple Integrals 2
Triple Integrals 3
(2^ln x)/x Antiderivative Example
Introduction to the Line Integral
Line Integral Example 1
Line Integral Example 2 (part 1)
Line Integral Example 2 (part 2)
Position Vector Valued Functions
Derivative of a position vector valued function
Differential of a vector valued function
Vector valued function derivative example
Line Integrals and Vector Fields
Using a line integral to find the work done by a vector field example
Parametrization of a Reverse Path
Scalar Field Line Integral Independent of Path Direction
Vector Field Line Integrals Dependent on Path Direction
Path Independence for Line Integrals
Closed Curve Line Integrals of Conservative Vector Fields
Example of Closed Line Integral of Conservative Field
Second Example of Line Integral of Conservative Vector Field
Green’s Theorem Proof Part 1
Green’s Theorem Proof (part 2)
Green’s Theorem Example 1
Green’s Theorem Example 2
Introduction to Parametrizing a Surface with Two Parameters
Determining a Position Vector-Valued Function for a Parametrization of Two Parameters
Partial Derivatives of Vector-Valued Functions
Introduction to the Surface Integral
Example of calculating a surface integral part 1
Example of calculating a surface integral part 2
Example of calculating a surface integral part 3
2011 Calculus AB Free Response #1a
2011 Calculus AB Free Response #1 parts b c d
2011 Calculus AB Free Response #2 (a &amp; b)
2011 Calculus AB Free Response #2 (c &amp; d)
2011 Calculus AB Free Response #3 (a &amp; b)
2011 Calculus AB Free Response #3 (c)
2011 Calculus AB Free Response #4a
2011 Calculus AB Free Response #4b
2011 Calculus AB Free Response #4c
2011 Calculus AB Free Response #4d
2011 Calculus AB Free Response #5a
2011 Calculus AB Free Response #5b
2011 Calculus AB Free Response #5c.
2011 Calculus AB Free Response #6a
2011 Calculus AB Free Response #6b
2011 Calculus AB Free Response #6c
2011 Calculus BC Free Response #1a
2011 Calculus BC Free Response #1 (b &amp; c)
2011 Calculus BC Free Response #1d
2011 Calculus BC Free Response #3a
2011 Calculus BC Free Response #3 (b &amp; c)
2011 Calculus BC Free Response #6a
2011 Calculus BC Free Response #6b
2011 Calculus BC Free Response #6c
Error or Remainder of a Taylor Polynomial Approximation
Proof: Bounding the Error or Remainder of a Taylor Polynomial Approximation
2011 Calculus BC Free Response #6d
Constructing a unit normal vector to a curve
2 D Divergence Theorem
Conceptual clarification for 2-D Divergence Theorem
Surface Integral Example Part 1 – Parameterizing the Unit Sphere
Surface Integral Example Part 2 – Calculating the Surface Differential
Surface Integral Example Part 3 – The Home Stretch
Surface Integral Ex2 part 1 – Parameterizing the Surface
Surface Integral Ex2 part 2 – Evaluating Integral
Surface Integral Ex3 part 1 – Parameterizing the Outside Surface
Surface Integral Ex3 part 2 – Evaluating the Outside Surface
Surface Integral Ex3 part 3 – Top surface
Surface Integral Ex3 part 4 – Home Stretch
Conceputal Understanding of Flux in Three Dimensions
Constructing a unit normal vector to a surface
Vector representation of a Surface Integral
Conditions for Stokes Theorem
Stokes Example Part 1
Part 2 Parameterizing the Surface
Stokes Example Part 3 – Surface to Double Integral
Stokes Example Part 4 – Curl and Final Answer

California Standards Test

Sal works through California Standards Test problems. Whether you are in California and studying for that test or just want additional practice, this is a good place to review the major math concepts.
California Standards Test: Algebra I

Sal works through the problems from the CA Standards released questions. It is best first to go through the algebra topic first as it is more comprehensive.

CA Algebra I: Number Properties and Absolute Value
CA Algebra I: Simplifying Expressions
CA Algebra I: Simple Logical Arguments
CA Algebra I: Graphing Inequalities
CA Algebra I: Slope and Y-intercept
CA Algebra I: Systems of Inequalities
CA Algebra I: Simplying Expressions
CA Algebra I: Completing the Square
CA Algebra I: Rational Expressions 1
CA Algebra I: Rational Expressions 2
CA Algebra I: Word Problems
CA Algebra I: More Word Problems
CA Algebra I: Functions

California Standards Test: Algebra II

Sal works through 80 questions taken from the California Standards Test for Algebra II. If you struggle with these you can get more help by viewing the algebra topic and completing its exercises.

California Standards Test: Algebra II
California Standards Test: Algebra II (Graphing Inequalities
CA Standards: Algebra II (Algebraic Division/Multiplication)
CA Standards: Algebra II
Algebra II: Simplifying Polynomials
Algebra II: Imaginary and Complex Numbers
Algebra II: Complex numbers and conjugates
Algebra ||: Conic Sections
Algebra II: Circles and Logarithms
Algebra II: Logarithms Exponential Growth
Algebra II: Logarithms and more
Algebra II: Functions, Combinatorics
Algebra II: binomial Expansion and Combinatorics
Algebra II: Binomial Expansions, Geometric Series Sum
Algebra II: Functions and Probability
Algebra II: Probability and Statistics
Algebra II: Mean and Standard Deviation

California Standards Test: Geometry

Sal does the 80 problems from the released questions from the California Standards Test for Geometry. Basic understanding of algebra is necessary. Go to the geometry topic for a comprehensive treatment of the subject.

CA Geometry: deductive reasoning
CA Geometry: More Proofs
CA Geometry: Similar Triangles 1
CA Geometry: Similar Triangles 2
CA Geometry: More on congruent and similar triangles
CA Geometry: Triangles and Parallelograms
CA Geometry: Area, Pythagorean Theorem
CA Geometry: Area, Circumference, Volume
CA Geometry: Pythagorean Theorem, Area
CA Geometry: Exterior Angles
CA Geometry: Deducing Angle Measures
CA Geometry: Pythagorean Theorem, Compass Constructions
CA Geometry: Compass Construction
CA Geometry: Basic Trigonometry
CA Geometry: More Trig
CA Geometry: Circle Area Chords Tangent
CA Geometry: Secants and Translations

Chemistry

Videos on chemistry (roughly covering a first-year high school or college course).

Elements and Atoms
Introduction to the atom
Orbitals
More on orbitals and electron configuration
Electron Configurations
Electron Configurations 2
Valence Electrons
Groups of the Periodic Table
Periodic Table Trends: Ionization Energy
Other Periodic Table Trends
Ionic, Covalent, and Metallic Bonds
Molecular and Empirical Formulas
Formula from Mass Composition
Another mass composition problem
Balancing Chemical Equations
Stoichiometry
Stoichiometry: Limiting Reagent
Ideal Gas Equation: PV=nRT
Ideal Gas Equation Example 1
Ideal Gas Equation Example 2
Ideal Gas Equation Example 3
Ideal Gas Example 4
Partial Pressure
States of Matter
States of Matter Follow-Up
Specific Heat, Heat of Fusion and Vaporization
Chilling Water Problem
Phase Diagrams
Van Der Waals Forces
Covalent Networks, Metallic, and Ionic Crystals
Vapor Pressure
Suspensions, Colloids and Solutions
Solubility
Boiling Point Elevation and Freezing Point Supression
Introduction to Kinetics
Reactions in Equilibrium
Mini-Video on Ion Size
Keq Intuition (mathy and not necessary to progress)
Keq derivation intuition (can skip; bit mathy)
Heterogenous Equilibrium
Le Chatelier’s Principle
Introduction to pH, pOH, and pKw
Acid Base Introduction
pH, pOH of Strong Acids and Bases
pH of a Weak Acid
pH of a Weak Base
Conjugate Acids and Bases
pKa and pKb Relationship
Buffers and Hendersen-Hasselbalch
Strong Acid Titration
Weak Acid Titration
Half Equivalence Point
Titration Roundup
Introduction to Oxidation States
More on Oxidation States
Hydrogen Peroxide Correction
Redox Reactions
Galvanic Cells
Types of Decay
Half-Life
Exponential Decay Formula Proof (can skip, involves Calculus)
Introduction to Exponential Decay
More Exponential Decay Examples
Macrostates and Microstates
Quasistatic and Reversible Processes
First Law of Thermodynamics/ Internal Energy
More on Internal Energy
Work from Expansion
PV-diagrams and Expansion Work
Proof: U=(3/2)PV or U=(3/2)nRT
Work Done by Isothermic Process
Carnot Cycle and Carnot Engine
Proof: Volume Ratios in a Carnot Cycle
Proof: S (or Entropy) is a valid state variable
Thermodynamic Entropy Definition Clarification
Reconciling Thermodynamic and State Definitions of Entropy
Entropy Intuition
Maxwell’s Demon
More on Entropy
Efficiency of a Carnot Engine
Carnot Efficiency 2: Reversing the Cycle
Carnot Efficiency 3: Proving that it is the most efficient
Enthalpy
Heat of Formation
Hess’s Law and Reaction Enthalpy Change
Gibbs Free Energy and Spontaneity
Gibbs Free Energy Example
More rigorous Gibbs Free Energy/ Spontaneity Relationship
A look at a seductive but wrong Gibbs/Spontaneity Proof
Stoichiometry Example Problem 1
Stoichiometry Example Problem 2
Limiting Reactant Example Problem 1
Empirical and Molecular Formulas from Stoichiometry
Example of Finding Reactant Empirical Formula
Stoichiometry of a Reaction in Solution
Another Stoichiometry Example in a Solution
Molecular and Empirical Forumlas from Percent Composition
Acid Base Titration
Spectrophotometry Introduction
Spectrophotometry Example
Hess’s Law Example
Vapor Pressure Example
Change of State Example

Competition Math

Example problems from random math competitions

2003 AIME II Problem 1
2003 AIME II Problem 3
2003 AIME II Problem 4 (part 1)
Sum of factors of 27000
Sum of factors 2
2003 AIME II Problem 5
2003 AIME II Problem 5 Minor Correction
2003 AIME II Problem 6
2003 AIME II Problem 8
Sum of Polynomial Roots (Proof)
Sum of Squares of Polynomial Roots
2003 AIME II Problem 9
2003 AIME II Problem 12
2003 AIME II Problem 13
2003 AIME II Problem 10
2003 AIME II Problem 11.avi
2003 AIME II Problem 14
2003 AIME II Problem 15 (part 1)
2003 AIME II Problem 15 (part 2)
2003 AIME II Problem 15 (part 3)

Computer Science

Introduction to programming and computer science

Introduction to Programs Data Types and Variables
Binary Numbers
Python Lists
For Loops in Python
While Loops in Python
Fun with Strings
Writing a Simple Factorial Program. (Python 2)
Stepping Through the Factorial Program
Flowchart for the Factorial Program
Python 3 Not Backwards Compatible with Python 2
Defining a Factorial Function
Diagramming What Happens with a Function Call
Recursive Factorial Function
Comparing Iterative and Recursive Factorial Functions
Exercise – Write a Fibonacci Function
Iterative Fibonacci Function Example
Stepping Through Iterative Fibonacci Function
Recursive Fibonacci Example
Stepping Through Recursive Fibonacci Function
Exercise – Write a Sorting Function
Insertion Sort Algorithm
Insertion Sort in Python
Stepping Through Insertion Sort Function
Simpler Insertion Sort Function

Cosmology and Astronomy

Videos attempting to grasp a little bit about our Universe (many of the topics associated with “Big History”)

Scale of Earth and Sun
Scale of Solar System
Scale of Distance to Closest Stars
Scale of the Galaxy
Intergalactic Scale
Hubble Image of Galaxies
Big Bang Introduction
Red Shift
Cosmological Time Scale 1
Cosmological Time Scale 2
Four Fundamental Forces
Birth of Stars
Becoming a Red Giant
White and Black Dwarfs
A Universe Smaller than the Observable
Star Field and Nebula Images
Parallax in Observing Stars
Stellar Parallax
Stellar Distance Using Parallax
Stellar Parallax Clarification
Parsec Definition
Hubble’s Law
Lifecycle of Massive Stars
Supernova (Supernovae)
Supernova clarification
Black Holes
Cepheid Variables 1
Why Cepheids Pulsate
Why Gravity Gets So Strong Near Dense Objects
Supermassive Black Holes
Quasars
Quasar Correction
Galactic Collisions
Earth Formation
Beginnings of Life
Ozone Layer and Eukaryotes Show Up in the Proterozoic Eon
Biodiversity Flourishes in Phanerozoic Eon
First living things on land clarification
Plate Tectonics– Difference between crust and lithosphere
Structure of the Earth
Plate Tectonics — Evidence of plate movement
Plate Tectonics — Geological Features of Divergent Plate Boundaries
Plate Tectonics– Geological features of Convergent Plate Boundaries
Plates Moving Due to Convection in Mantle
Hawaiian Islands Formation
Compositional and Mechanical Layers of the Earth
Seismic Waves
Why S-Waves Only Travel in Solids
Refraction of Seismic Waves
The Mohorovicic Seismic Discontinuity
How we know about the Earth’s core
Pangaea
Scale of the Large
Scale of the Small
Detectable Civilizations in our Galaxy 1
Detectable Civilizations in our Galaxy 2
Detectable Civilizations in our Galaxy 3
Detectable Civilizations in our Galaxy 4
Detectable Civilizations in our Galaxy 5
Human Evolution Overview
Understanding Calendar Notation
Correction Calendar Notation
Development of Agriculture and Writing
Introduction to Light
Seasons Aren’t Dictated by Closeness to Sun
How Earth’s Tilt Causes Seasons
Milankovitch Cycles Precession and Obliquity
Are Southern Hemisphere Seasons More Severe?
Precession Causing Perihelion to Happen Later
What Causes Precession and Other Orbital Changes
Apsidal Precession (Perihelion Precession) and Milankovitch Cycles
Firestick Farming
Carbon 14 Dating 1
Carbon 14 Dating 2
Potassium-Argon (K-Ar) Dating
K-Ar Dating Calculation
Chronometric Revolution
Collective Learning
Land Productivity Limiting Human Population
Energy Inputs for Tilling a Hectare of Land
Random Predictions for 2060

Credit Crisis

Videos on the causes and effects of the credit crisis/crunch.

The housing price conundrum
Housing price conundrum (part 2)
Housing Price Conundrum (part 3)
Housing Conundrum (part 4)
Mortgage-Backed Securities I
Mortgage-backed securities II
Mortgage-backed securities III
Collateralized Debt Obligation (CDO)
Bailout 13: Does the bailout have a chance of working?
Credit Default Swaps
Credit Default Swaps 2
Wealth Destruction 1
Wealth Destruction 2

Currency

Currency Exchange Introduction
Pegging the Yuan
American-Chinese Debt Loop
Debt Loops Rationale and Effects
China keeps peg but diversifies holdings

Current Economics

Discussions of economic topics and how they relate to current events.

Economics of a Cupcake Factory
Cupcake Economics 2
Cupcake Economics 3
Inflation, Deflation &amp; Capacity Utilization
Inflation, Deflation &amp; Capacity Utilization 2
Inflation &amp; Deflation 3: Obama Stimulus Plan
Unemployment
CPI Index
Simple Analysis of Cost per Job Saved from Stimulus
Unemployment Rate Primer
China Pegs to Dollar to Keep Trade Imbalance
Review of China US currency situation
Data on Chinese M1 Increase in 2010
Data on Chinese Foreign Assets Increase in 2010
Data on Chinese US Balance of Payments
Chinese inflation
Floating Exchange Effect on China
Floating Exchange Effect on US

Differential Equations

Topics covered in a first year course in differential equations. Need to understand basic differentiation and integration from Calculus playlist before starting here.

What is a differential equation
Separable Differential Equations
Separable differential equations 2
Exact Equations Intuition 1 (proofy)
Exact Equations Intuition 2 (proofy)
Exact Equations Example 1
Exact Equations Example 2
Exact Equations Example 3
Integrating factors 1
Integrating factors 2
First order homegenous equations
First order homogenous equations 2
2nd Order Linear Homogeneous Differential Equations 1
2nd Order Linear Homogeneous Differential Equations 2
2nd Order Linear Homogeneous Differential Equations 3
2nd Order Linear Homogeneous Differential Equations 4
Complex roots of the characteristic equations 1
Complex roots of the characteristic equations 2
Complex roots of the characteristic equations 3
Repeated roots of the characteristic equation
Repeated roots of the characterisitic equations part 2
Undetermined Coefficients 1
Undetermined Coefficients 2
Undetermined Coefficients 3
Undetermined Coefficients 4
Laplace Transform 1
Laplace Transform 2
Laplace Transform 3 (L{sin(at)})
Laplace Transform 4
Laplace Transform 5
Laplace Transform 6
Laplace Transform to solve an equation
Laplace Transform solves an equation 2
More Laplace Transform tools
Using the Laplace Transform to solve a nonhomogenous eq
Laplace Transform of : L{t}
Laplace Transform of t^n: L{t^n}
Laplace Transform of the Unit Step Function
Inverse Laplace Examples
Laplace/Step Function Differential Equation
Dirac Delta Function
Laplace Transform of the Dirac Delta Function
Introduction to the Convolution
The Convolution and the Laplace Transform
Using the Convolution Theorem to Solve an Initial Value Prob

Finance

Videos on finance and macroeconomics

Introduction to interest
Interest (part 2)
Introduction to Present Value
Present Value 2
Present Value 3
Present Value 4 (and discounted cash flow)
Introduction to Balance Sheets
More on balance sheets and equity
Home equity loans
Renting vs. buying a home (part 2)
The housing price conundrum
Housing price conundrum (part 2)
Housing Price Conundrum (part 3)
Housing Conundrum (part 4)
What it means to buy a company’s stock
Bonds vs. Stocks
Shorting Stock
Shorting Stock 2
Chapter 7:Bankruptcy Liquidation
Chapter 11: Bankruptcy Restructuring
Return on capital
Credit Default Swaps (CDS) Intro
Mortgage Back Security Overview
Collateralized Debt Obligation Overview
Mortgage-Backed Securities I
Mortgage-backed securities II
Mortgage-backed securities III
Collateralized Debt Obligation (CDO)
Introduction to the yield curve
Introduction to compound interest and e
Compound Interest and e (part 2)
Compound Interest and e (part 3)
Compound Interest and e (part 4)
Bailout 1: Liquidity vs. Solvency
Bailout 2: Book Value
Bailout 3: Book value vs. market value
Bailout 4: Mark-to-model vs. mark-to-market
Bailout 5: Paying off the debt
Bailout 6: Getting an equity infusion
Bailout 7: Bank goes into bankruptcy
Bailout 8: Systemic Risk
Bailout 9: Paulson’s Plan
Bailout 10: Moral Hazard
Credit Default Swaps
Credit Default Swaps 2
Investment vs. Consumption 1
Investment vs. Comsumption 2
Bailout 11: Why these CDOs could be worth nothing
Bailout 12: Lone Star Transaction
Bailout 13: Does the bailout have a chance of working?
Wealth Destruction 1
Wealth Destruction 2
Bailout 14: Possible Solution
Bailout 15: More on the solution
Banking 1
Banking 2: A bank’s income statement
Banking 3: Fractional Reserve Banking
Banking 4: Multiplier effect and the money supply
Personal Bankruptcy: Chapters 7 and 13
Introduction to Compound Interest
The Rule of 72 for Compound Interest
Annual Percentage Rate (APR) and Effective APR
Introduction to Bonds
Relationship between bond prices and interest rates
Introduction to Mortgage Loans
Roth IRAs
401(k)s
Payday Loans
Institutional Roles in Issuing and Processing Credit Cards
Ponzi Schemes
Currency Exchange Introduction
Pegging the Yuan
American-Chinese Debt Loop
Debt Loops Rationale and Effects
American Call Options
Basic Shorting
American Put Options
Call Option as Leverage
Put vs. Short and Leverage
Call Payoff Diagram
Put Payoff Diagram
Put as Insurance
Put-Call Parity
Put Writer Payoff Diagrams
Call Writer Payoff Diagram
Arbitrage Basics
Put-Call Parity Arbitrage I
Put-Call Parity Arbitrage II
Put-Call Parity Clarification
Actual Option Quotes
Option Expiration and Price
Forward Contract Introduction
Futures Introduction
Motivation for the Futures Exchange
Futures Margin Mechanics
Verifying Hedge with Futures Margin Mechanics
Futures and Forward Curves
Severe Contango Generally Bearish
Backwardation Bullish or Bearish
Futures Curves II
Contango
Backwardation
Contango and Backwardation Review
Upper Bound on Forward Settlement Price
Lower Bound on Forward Settlement Price
Arbitraging Futures Contract
Arbitraging Futures Contracts II
Cash Accounting
Accrual Basis of Accounting
Comparing Accrual and Cash Accounting
Balance Sheet and Income Statement Relationship
Basic Cash Flow Statement
Doing the example with Accounts Payable growing
Expensing a Truck leads to inconsistent performance
Depreciating the truck
Depreciation in Cash Flow
Amortization and Depreciation
Basic Capital Structure Differences
Market Capitalization
Market Value of Assets
LIBOR
Fair Value Accounting
Tax Deductions Introduction
Alternative Minimum Tax
Term Life Insurance and Death Probability
Back of Envelope Office Space Conundrum
Corporations and Limited Liability
Is Limited Liability or Double Taxation Fair
Open-Ended Mutual Fund (Part 1)
Open-End Mutual Fund Redemptions
Closed-End Mutual Funds
Hedge Funds Intro
Hedge Fund Structure and Fees
Hedge Funds, Venture Capital, and Private Equity
Treasury Bond Prices and Yields
Annual Interest Varying with Debt Maturity
The Yield Curve
Fed Open Market Operations
Quantitative Easing
More on Quantitative Easing (and Credit Easing)
Hedge Fund Strategies – Long Short 1
Hedge Fund Strategies – Long Short 2
Hedge Fund Strategies – Merger Arbitrage 1
Stock Dilution
Acquisitions with Shares
Price Behavior After Announced Acquisition
Simple Merger Arb with Share Acquisition
AMT Overview
Open market operations and Quantitative Easing Overview
Another Quantitative Easing Video
US and Japanese Quantitative Easing
Term and Whole Life Insurance Policies 2
Term and Whole Life Insurance Policies
Estate Tax Introduction
Human Capital
Risk and Reward Introduction
Futures Fair Value in the Pre-Market
What is Inflation
Inflation Data
Moderate Inflation in a Good Economy
Stagflation
Real and Nominal Return
Calculating Real Return in Last Year Dollars
Relation Between Nominal and Real Returns and Inflation
Use Cases for Credit Default Swaps
Financial Weapons of Mass Destruction
Deflation
Velocity of Money Rather than Quantity Driving Prices
Deflation Despite Increases in Money Supply
Deflationary Spiral
Hyperinflation
Estate Tax Basics
Term and Whole Life
Open-Ended Mutual Funds
Unemployment Rate Primer (v2)
Time Value of Money
Mortgage Interest Rates
Inflation Overview
Basics of US Income Tax Rate Schedule
Interpretting Futures Fair Value in the PreMarket
Interest Rate Swap 1
Interest Rate Swap 2

GMAT

Prepare for the Graduate Management Admission Test by going over these practice problems.
GMAT: Problem Solving

Sal works through the 249 math problem solving questions in the official GMAC GMAT book.

GMAT Math: 1
GMAT Math: 2
GMAT Math: 3
GMAT Math: 4
GMAT Math: 5
GMAT: Math 6
GMAT: Math 7
GMAT: Math 8
GMAT: Math 9
GMAT: Math 10
GMAT: Math 11
GMAT: Math 12
GMAT: Math 13
GMAT: Math 14
GMAT: Math 15
GMAT: Math 16
GMAT: Math 17
GMAT: Math 18
GMAT: Math 19
GMAT Math 20
GMAT Math 21
GMAT Math 22
GMAT Math 23
GMAT Math 24
GMAT Math 25
GMAT Math 26
GMAT Math 27
GMAT Math 28
GMAT Math 29
GMAT Math 30
GMAT Math 31
GMAT Math 32
GMAT Math 33
GMAT Math 34
GMAT Math 35
GMAT Math 36
GMAT Math 37
GMAT Math 38
GMAT Math 39
GMAT Math 40
GMAT Math 41
GMAT Math 42
GMAT Math 43
GMAT Math 44
GMAT Math 45
GMAT Math 46
GMAT Math 47
GMAT Math 48
GMAT Math 49
GMAT Math 50
GMAT Math 51
GMAT Math 52
GMAT Math 53
GMAT Math 54

GMAT: Data Sufficiency

Sal works through 155 data sufficiency problems in the GMAC GMAT Review book (so using real GMAT problems). Buy the book, then watch the videos.

GMAT: Data Sufficiency 1
GMAT: Data Sufficiency 2
GMAT: Data Sufficiency 3
GMAT: Data Sufficiency 4
GMAT: Data Sufficiency 5
GMAT: Data Sufficiency 6
GMAT: Data Sufficiency 7
GMAT: Data Sufficiency 8
GMAT: Data Sufficiency 9
GMAT: Data Sufficiency 10
GMAT: Data Sufficiency 11
GMAT: Data Sufficiency 12
GMAT: Data Sufficiency 13
GMAT: Data Sufficiency 14
GMAT: Data Sufficiency 15
GMAT: Data Sufficiency 16
GMAT: Data Sufficiency 17
GMAT: Data Sufficiency 18
GMAT: Data Sufficiency 19
GMAT: Data Sufficiency 20
GMAT: Data Sufficiency 21
GMAT Data Sufficiency 21 (correction)
GMAT: Data Sufficiency 22
GMAT: Data Sufficiency 23
GMAT: Data Sufficiency 24
GMAT: Data Sufficiency 25
GMAT: Data Sufficiency 26
GMAT: Data Sufficiency 27
GMAT: Data Sufficiency 28
GMAT: Data Sufficiency 29
GMAT: Data Sufficiency 30
GMAT: Data Sufficiency 31
GMAT: Data Sufficiency 32
GMAT: Data Sufficiency 33
GMAT: Data Sufficiency 34
GMAT: Data Sufficiency 35
GMAT: Data Sufficiency 36
GMAT: Data Sufficiency 37
GMAT: Data Sufficiency 38
GMAT: Data Sufficiency 39
GMAT Data Sufficiency 40
GMAT Data Sufficiency 41

Geithner Plan

Videos on the Geithner Plan to solve the banking crisis.

Geithner Plan I
Geithner Plan II
Geithner Plan 2.5
Geithner Plan III
Geithner Plan IV
Geithner 5: A better solution

Geometry

Videos on geometry. After Basic Geometry list, videos assume you know introductory algebra concepts. After these videos, you’ll be ready for Trigonometry.
Geometry: Basic geometry

Finding perimeter, volume, and area of basic shapes without algebra.

Perimeter and Area Basics
Area and Perimeter
Perimeter of a Polygon
Perimeter and Area of a Non-Standard Polygon
Parts of a Circle
Area of a Circle
Solid Geometry Volume
Cylinder Volume and Surface Area
Volume of a Sphere

Geometry: Introduction to Euclidean geometry

Understanding the purpose, notation, and building blocks of geometry.

Euclid as the Father of Geometry
Language and Notation of Basic Geometry
Lines, Line Segments, and Rays
Identifying Rays
Identifying Parallel and Perpendicular Lines

Geometry: Angles

Identifying, measuring, and calculating angles.

Angle Basics
Introduction to angles (old)
Measuring Angles in Degrees
Using a Protractor
Measuring Angles
Angle-a-trons
Acute Right and Obtuse Angles
Acute Obtuse and Right Angles
Complementary and Supplementary Angles
Identifying Complementary and Supplementary Angles
Angles (part 2)
Proof – Sum of Measures of Angles in a Triangle are 180
Triangle Angle Example 1
Angles at the intersection of two lines
Proof-Vertical Angles are Equal
Angles (part 3)
Angles formed between transversals and parallel lines
Proof – Corresponding Angle Equivalence Implies Parallel Lines
Angles of parallel lines 2
Triangle Angle Example 2
Triangle Angle Example 3
Finding Missing Angles
Finding more angles
The Angle Game
Angle Game (part 2)
More on why SSA is not a postulate
Angles Formed by Parallel Lines and Transversals
Point Line Distance and Angle Bisectors
Two column proof showing segments are perpendicular
Angle Bisector Theorem Examples
Angle Bisector Theorem Proof
Inscribed and Central Angles
2003 AIME II Problem 7

Geometry: Triangles

Identifying types of triangles, using principles of similarity and congruence, and applying and proving triangle postulates.

Proof – Sum of Measures of Angles in a Triangle are 180
Triangle Angle Example 1
Triangle Angle Example 2
Triangle Angle Example 3
Challenging Triangle Angle Problem
Congruent and Similar Triangles
Congruent Triangles and SSS
SSS to Show a Radius is Perpendicular to a Chord that it Bisects
Other Triangle Congruence Postulates
Finding Congruent Triangles
More on why SSA is not a postulate
Congruent Triangle Proof Example
Congruent Triangle Example 2
Congruent legs and base angles of Isosceles Triangles
Equilateral Triangle Sides and Angles Congruent
Equilateral and Isosceles Example Problems
Another Isosceles Example Problem
Example involving an isosceles triangle and parallel lines
Figuring out all the angles for congruent triangles example
Triangle Area Proofs
Area of an Equilateral Triangle
Koch Snowflake Fractal
Area of Koch Snowflake (part 1) – Advanced
Area of Koch Snowflake (part 2) – Advanced
Similar Triangle Basics
Similarity Postulates
Similar triangles
Similar triangles (part 2)
Similar Triangle Example Problems
Similarity Example Problems
Application of Similar Triangles
Challenging Similarity Problem
Similarity example where same side plays different roles
Finding Area Using Similarity and Congruence
Introduction to the Pythagorean Theorem
The Pythagorean Theorem
Pythagorean Theorem II
Pythagorean Theorem Proof Using Similarity
45-45-90 Triangles
45-45-90 Triangle Side Ratios
Intro to 30-60-90 Triangles
30-60-90 Triangles II
30-60-90 Triangle Side Ratios Proof
30-60-90 Triangle Example Problem
Heron’s Formula
Part 1 of Proof of Heron’s Formula
Part 2 of the Proof of Heron’s Formula
Area of Inscribed Equilateral Triangle (some basic trig used)
Right Triangles Inscribed in Circles (Proof)
Area of Diagonal Generated Triangles of Rectangle are Equal
Triangle Medians and Centroids
Triangle Medians and Centroids (2D Proof)
Circumcenter of a Triangle
Circumcenter of a Right Triangle
Incenter and incircles of a triangle
Medians divide into smaller triangles of equal area
Exploring Medial Triangles
Proving that the Centroid is 2-3rds along the Median
Median Centroid Right Triangle Example
Proof – Triangle Altitudes are Concurrent (Orthocenter)
Review of Triangle Properties
Euler Line
Euler’s Line Proof
Common Orthocenter and Centroid

Identifying types of quadrilaterals, finding measurements, and applying and proving postulates.

Area of a Parallelogram
Area of a Regular Hexagon
Sum of Interior Angles of a Polygon
Sum of the exterior angles of convex polygon
Proof – Opposite Angles of Parallelogram Congruent
Proof – Opposite Sides of Parallelogram Congruent
Proof – Diagonals of a Parallelogram Bisect Each Other
Rhombus Diagonals
Proof – Rhombus Diagonals are Perpendicular Bisectors
Proof – Rhombus Area Half Product of Diagonal Length
Area of a Parallelogram
Area of a Regular Hexagon
Problem involving angle derived from square and circle
2003 AIME II Problem 7
CA Geometry: Deducing Angle Measures

Geometry: Circles

Finding measurements and applying and proving circle theorems.

Language and Notation of the Circle
Parts of a Circle
Three Points Defining a Circle
Area of a Circle
Pi Is (still) Wrong.
Right Triangles Inscribed in Circles (Proof)
Right Triangles Inscribed in Circles (Proof)
Incenter and incircles of a triangle

Geometry: Worked Examples

Sal does the 80 problems from the released questions from the California Standards Test for Geometry. Basic understanding of Algebra I necessary.

Interesting Perimeter and Area Problems
Challenging Perimeter Problem
CA Geometry: deductive reasoning
CA Geometry: More Proofs
CA Geometry: Similar Triangles 1
CA Geometry: Similar Triangles 2
CA Geometry: More on congruent and similar triangles
CA Geometry: Triangles and Parallelograms
CA Geometry: Area, Pythagorean Theorem
CA Geometry: Area, Circumference, Volume
CA Geometry: Pythagorean Theorem, Area
CA Geometry: Exterior Angles
CA Geometry: Deducing Angle Measures
CA Geometry: Pythagorean Theorem, Compass Constructions
CA Geometry: Compass Construction
CA Geometry: Basic Trigonometry
CA Geometry: More Trig
CA Geometry: Circle Area Chords Tangent
CA Geometry: Secants and Translations

Healthcare and Medicine

Videos about medicine and the healthcare system

Glucose Insulin and Diabetes
Blood Sugar Levels
Glucose Concentration Conversion
A1C Levels
Heart Disease and Heart Attacks
Thrombo-emboli and Thromboembolisms
Stenosis, ischemia and heart failure
Strokes
Normal Colon Tissue
Hyperplasia in Colon Tissue
Colon Dysplasia
Cancerous Colon Tissue
Adequacy of the Lateral Cervical Spine X-Ray
Assessing Alignment of the Lateral Cervical Spine (neck) X-Ray
Cervical Spine Protection in Airway Management (not a substitute for formal training)
Intro to the Endocrine System
Bacterial Meningitis
Precocious Puberty
Childhood Growth
Ritual of the Bedside Exam
Vitamin C and the Limeys
Inflammation
Blue Cross and Blue Shield
Health Care Costs in US vs Europe
Healthcare System Overview
Paying Doctors
Medicare Overview

History

The history of the world (eventually)!

US History Overview 1: Jamestown to the Civil War
Appomattox Court House and Lincoln’s Assassination
US History Overview 2 – Reconstruction to the Great Depression
US History Overview 3 – WWII to Vietnam
Communism
Korean War Overview
Bay of Pigs Invasion
Cuban Missile Crisis
Vietnam War
Pattern of US Cold War Interventions
Allende and Pinochet in Chile
When Capitalism is Great and Not-so-great
20th Century Capitalism and Regulation in the United States
French Revolution (Part 1)
French Revolution (Part 2)
French Revolution (Part 3) – Reign of Terror
French Revolution (Part 4) – The Rise of Napoleon Bonaparte
Haitian Revolution (Part 1)
Haitian Revolution (Part 2)
Napoleon and the Wars of the First and Second Coalitions
Napoleon and the War of the Third Coalition
Napoleon and the War of the Fourth Coalition
Napoleon’s Peninsular Campaigns
French Invasion of Russia
Napoleon Forced to Abdicate
Thomas Malthus and Population Growth

IIT JEE Questions

Questions from previous IIT JEEs

IIT JEE Trigonometry Problem 1
IIT JEE Perpendicular Planes (Part 1)
IIT JEE Perpendicular Plane (part 2)
IIT JEE Complex Root Probability (part 1)
IIT JEE Complex Root Probability (part 2)
IIT JEE Position Vectors
IIT JEE Integral Limit
IIT JEE Algebraic Manipulation
IIT JEE Function Maxima
IIT JEE Diameter Slope
IIT JEE Hairy Trig and Algebra (part 1)
IIT JEE Hairy Trig and Algebra (Part 2)
IIT JEE Hairy Trig and Algebra (Part 3)
IIT JEE Complex Numbers (part 1)
IIT JEE Complex Numbers (part 2)
IIT JEE Complex Numbers (part 3)
IIT JEE Differentiability and Boundedness
IIT JEE Integral with Binomial Expansion
IIT JEE Symmetric and Skew-Symmetric Matrices
IIT JEE Trace and Determinant
IIT JEE Divisible Determinants
IIT JEE Circle Hyperbola Intersection
IIT JEE Circle Hyperbola Common Tangent Part 1
IIT JEE Circle Hyperbola Common Tangent Part 2
IIT JEE Circle Hyperbola Common Tangent Part 3
IIT JEE Circle Hyperbola Common Tangent Part 4
IIT JEE Circle Hyperbola Common Tangent Part 5
IIT JEE Trigonometric Constraints
IIT JEE Trigonometric Maximum
Vector Triple Product Expansion (very optional)
IIT JEE Lagrange’s Formula
Tangent Line Hyperbola Relationship (very optional)
2010 IIT JEE Paper 1 Problem 50 Hyperbola Eccentricity
Normal vector from plane equation
Point distance to plane
Distance Between Planes
Complex Determinant Example
Series Sum Example
Trigonometric System Example
Simple Differential Equation Example

Collection of interviews with and presentations by Salman Khan. Also a few other mentions of Khan Academy at other talks.

PBS NewsHour on the Khan Academy
Salman Khan on CNN
Salman Khan Speaks at GEL (Good Experience Live) Conference
Salman Khan Talk at the MIT Club of Northern California
Salman Khan talk at Castilleja School on January 5th, 2010
Sal Khan Interview with IT Conversations – January 31,2010
Salman Khan interview with NPR’s All Things Considered on 12/28/2009
Khan Academy on PBS NewsHour (Edited)
Sal Khan (with a severe cold!) on Future Talk
Brian Lehrer Interview with Salman Khan
Salman Khan Interview with Mixergy.com
Bill Gates talks about the Khan Academy at Aspen Ideas Festival 2010
Khan Academy Vision and Social Return
Bay Area CBS Station with Salman Khan
Khan Academy on the Gates Notes
Sal on ABC News
Forbes Names You Need To Know: Khan Academy
Salman Khan on KQED MindShift
Salman Khan talk at TED 2011 (from ted.com)
Sal on Dylan Ratigan show
TEDxSanJoseCA – Salman Khan – (Sequel to talk at TED)
Salman Khan on Charlie Rose
Salman Khan on Big Think
Salman Khan on Marketplace (NPR) on 5-24-2011
May 29th, 2011 CNN Piece
Salman Khan at TiEcon 2011
Khan Academy on Perry’s Principles (6/2/2011)
Khan Academy on California Report (June 2011)
Ideal Math and Science Class Time
NPR Story on KA Los Altos Pilots (June 2011)
Salman Khan interviewed on NPR’s On Point
21st Century Challenges (Royal Geographic Society)
Questions from Superinteressante (8-22-2011)
Answers to Questions from the Independent
The Gates Notes: Sal on Khan Academy
The Gates Notes: Students in Los Altos
The Gates Notes: Teachers in Los Altos
The Gates Notes: Administrators in Los Altos
The Gates Notes: Insights into students’ progress
Early Show
Brainwave Sep 2011
School Leadership Briefing Questions (Sep 12 2011) 2
School Leadership Briefing (Sep 12 2011)
Center for Future of Museums
Sal during Education Week (Sep 2011) 1
Khan Academy on 20 20 (Sep 2011)
KA on John Stossel Documentary
Tom Brokaw interviews Sal at Education Nation 2011
Financial Times October 2011
2011 Roundtable at Stanford: Education Nation 2.0
Year 2060: Education Predictions
Khan Academy Exercises and Data Reports Overview
Elizabeth Slavitt
Marcos Ojeda
60 minutes: The future of education?
60 minutes: Khan Academy’s “world-changing” plan for schools
60 minutes: School of the future
60 minutes: Khan Academy in the classroom
ED SESSION III with Sal Khan – Reactions in Idaho
Videocast with Sal Khan: Effectively Using Khan Academy
Salman Khan at Rice University’s 2012 commencement
Microsoft CEO Summit Innovation in Education
Khan Academy at Oakland Unity High School
Minli Virdone

Linear Algebra

Matrices, vectors, vector spaces, transformations. Covers all topics in a first year college linear algebra course. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn’t a prereq) so don’t confuse this with regular high school algebra.

Introduction to matrices
Matrix multiplication (part 1)
Matrix multiplication (part 2)
Inverse Matrix (part 1)
Inverting matrices (part 2)
Inverting Matrices (part 3)
Matrices to solve a system of equations
Matrices to solve a vector combination problem
Singular Matrices
3-variable linear equations (part 1)
Solving 3 Equations with 3 Unknowns
Linear Algebra: Introduction to Vectors
Linear Algebra: Vector Examples
Linear Algebra: Parametric Representations of Lines
Linear Combinations and Span
Linear Algebra: Introduction to Linear Independence
More on linear independence
Span and Linear Independence Example
Linear Subspaces
Linear Algebra: Basis of a Subspace
Vector Dot Product and Vector Length
Proving Vector Dot Product Properties
Proof of the Cauchy-Schwarz Inequality
Linear Algebra: Vector Triangle Inequality
Defining the angle between vectors
Defining a plane in R3 with a point and normal vector
Linear Algebra: Cross Product Introduction
Proof: Relationship between cross product and sin of angle
Dot and Cross Product Comparison/Intuition
Matrices: Reduced Row Echelon Form 1
Matrices: Reduced Row Echelon Form 2
Matrices: Reduced Row Echelon Form 3
Matrix Vector Products
Introduction to the Null Space of a Matrix
Null Space 2: Calculating the null space of a matrix
Null Space 3: Relation to Linear Independence
Column Space of a Matrix
Null Space and Column Space Basis
Visualizing a Column Space as a Plane in R3
Proof: Any subspace basis has same number of elements
Dimension of the Null Space or Nullity
Dimension of the Column Space or Rank
Showing relation between basis cols and pivot cols
Showing that the candidate basis does span C(A)
A more formal understanding of functions
Vector Transformations
Linear Transformations
Matrix Vector Products as Linear Transformations
Linear Transformations as Matrix Vector Products
Image of a subset under a transformation
im(T): Image of a Transformation
Preimage of a set
Preimage and Kernel Example
Sums and Scalar Multiples of Linear Transformations
More on Matrix Addition and Scalar Multiplication
Linear Transformation Examples: Scaling and Reflections
Linear Transformation Examples: Rotations in R2
Rotation in R3 around the X-axis
Unit Vectors
Introduction to Projections
Expressing a Projection on to a line as a Matrix Vector prod
Compositions of Linear Transformations 1
Compositions of Linear Transformations 2
Linear Algebra: Matrix Product Examples
Matrix Product Associativity
Distributive Property of Matrix Products
Linear Algebra: Introduction to the inverse of a function
Proof: Invertibility implies a unique solution to f(x)=y
Surjective (onto) and Injective (one-to-one) functions
Relating invertibility to being onto and one-to-one
Determining whether a transformation is onto
Linear Algebra: Exploring the solution set of Ax=b
Linear Algebra: Matrix condition for one-to-one trans
Linear Algebra: Simplifying conditions for invertibility
Linear Algebra: Showing that Inverses are Linear
Linear Algebra: Deriving a method for determining inverses
Linear Algebra: Example of Finding Matrix Inverse
Linear Algebra: Formula for 2×2 inverse
Linear Algebra: 3×3 Determinant
Linear Algebra: nxn Determinant
Linear Algebra: Determinants along other rows/cols
Linear Algebra: Rule of Sarrus of Determinants
Linear Algebra: Determinant when row multiplied by scalar
Linear Algebra: (correction) scalar muliplication of row
Linear Algebra: Determinant when row is added
Linear Algebra: Duplicate Row Determinant
Linear Algebra: Determinant after row operations
Linear Algebra: Upper Triangular Determinant
Linear Algebra: Simpler 4×4 determinant
Linear Algebra: Determinant and area of a parallelogram
Linear Algebra: Determinant as Scaling Factor
Linear Algebra: Transpose of a Matrix
Linear Algebra: Determinant of Transpose
Linear Algebra: Transpose of a Matrix Product
Linear Algebra: Transposes of sums and inverses
Linear Algebra: Transpose of a Vector
Linear Algebra: Rowspace and Left Nullspace
Lin Alg: Visualizations of Left Nullspace and Rowspace
Linear Algebra: Orthogonal Complements
Linear Algebra: Rank(A) = Rank(transpose of A)
Linear Algebra: dim(V) + dim(orthogonoal complelent of V)=n
Lin Alg: Representing vectors in Rn using subspace members
Lin Alg: Orthogonal Complement of the Orthogonal Complement
Lin Alg: Orthogonal Complement of the Nullspace
Lin Alg: Unique rowspace solution to Ax=b
Linear Alg: Rowspace Solution to Ax=b example
Lin Alg: Showing that A-transpose x A is invertible
Linear Algebra: Projections onto Subspaces
Linear Alg: Visualizing a projection onto a plane
Lin Alg: A Projection onto a Subspace is a Linear Transforma
Linear Algebra: Subspace Projection Matrix Example
Lin Alg: Another Example of a Projection Matrix
Linear Alg: Projection is closest vector in subspace
Linear Algebra: Least Squares Approximation
Linear Algebra: Least Squares Examples
Linear Algebra: Another Least Squares Example
Linear Algebra: Coordinates with Respect to a Basis
Linear Algebra: Change of Basis Matrix
Lin Alg: Invertible Change of Basis Matrix
Lin Alg: Transformation Matrix with Respect to a Basis
Lin Alg: Alternate Basis Tranformation Matrix Example
Lin Alg: Alternate Basis Tranformation Matrix Example Part 2
Lin Alg: Changing coordinate systems to help find a transformation matrix
Linear Algebra: Introduction to Orthonormal Bases
Linear Algebra: Coordinates with respect to orthonormal bases
Lin Alg: Projections onto subspaces with orthonormal bases
Lin Alg: Finding projection onto subspace with orthonormal basis example
Lin Alg: Example using orthogonal change-of-basis matrix to find transformation matrix
Lin Alg: Orthogonal matrices preserve angles and lengths
Linear Algebra: The Gram-Schmidt Process
Linear Algebra: Gram-Schmidt Process Example
Linear Algebra: Gram-Schmidt example with 3 basis vectors
Linear Algebra: Introduction to Eigenvalues and Eigenvectors
Linear Algebra: Proof of formula for determining Eigenvalues
Linear Algebra: Example solving for the eigenvalues of a 2×2 matrix
Linear Algebra: Finding Eigenvectors and Eigenspaces example
Linear Algebra: Eigenvalues of a 3×3 matrix
Linear Algebra: Eigenvectors and Eigenspaces for a 3×3 matrix
Linear Algebra: Showing that an eigenbasis makes for good coordinate systems
Vector Triple Product Expansion (very optional)
Normal vector from plane equation
Point distance to plane
Distance Between Planes

MIT+K12

A Crash Course on Indoor Flying Robots
The Invention of the Battery
The Forces on an Airplane
Flocculation: Making Clean Water
A Voyage to Mars: Bone Loss in Space
Bouncing Droplets: Superhydrophobic and Superhydrophilic Surfaces

Macroeconomics

Topics covered in a traditional college level introductory macroeconomics course

Circular Flow of Income and Expenditures
Parsing Gross Domestic Product
More on Final and Intermediate GDP Contributions
Investment and Consumption
Income and Expenditure Views of GDP
Components of GDP
Examples of Accounting for GDP
Real GDP and Nominal GDP
GDP Deflator
Example Calculating Real GDP with a Deflator
Introduction to Inflation
Inflation Data
Moderate Inflation in a Good Economy
Stagflation
Real and Nominal Return
Calculating Real Return in Last Year Dollars
Relation Between Nominal and Real Returns and Inflation
Deflation
Velocity of Money Rather than Quantity Driving Prices
Deflation Despite Increases in Money Supply
Deflationary Spiral
Hyperinflation
Unemployment Rate Primer
Phillips Curve
Interest as Rent for Money
Money Supply and Demand Impacting Interest Rates
Aggregate Demand
Shifts in Aggregate Demand
Long-Run Aggregate Supply
Short Run Aggregate Supply
Demand-Pull Inflation under Johnson
Real GDP driving Price
Cost Push Inflation
Monetary and Fiscal Policy
Tax Lever of Fiscal Policy
Breakdown of Gas Prices
Short-Run Oil Prices
Keynesian Economics
Risks of Keynesian Thinking
Overview of Fractional Reserve Banking
Weaknesses of Fractional Reserve Lending
Full Reserve Banking
Money Supply- M0 M1 and M2
Simple Fractional Reserve Accounting part 1
Simple Fractional Reserve Accounting (part 2)
MPC and Multiplier
Mathy Version of MPC and Multiplier (optional)
Consumption Function Basics
Generalized Linear Consumption Function
Consumption Function with Income Dependent Taxes
Keynesian Cross
Details on Shifting Aggregate Planned Expenditures
Keynesian Cross and the Multiplier
Investment and Real Interest Rates
Connecting the Keynesian Cross to the IS-Curve
Loanable Funds Interpretation of IS Curve
LM part of the IS-LM model
Government Spending and the IS-LM model
Balance of Payments- Current Account
Balance of Payments- Capital Account
Why Current and Capital Accounts Net Out
Accumulating Foreign Currency Reserves
Using Reserves to Stablize Currency
Speculative Attack on a Currency
Financial Crisis in Thailand Caused by Speculative Attack
Math Mechanics of Thai Banking Crisis
Greek Debt Recession and Austerity (part 1)
Greek Financial Crisis (part 2)
How and why Greece would leave the Euro (part 3)
Why Europe is worried about Greece

Microeconomics

Topics covered in a traditional college level introductory microeconomics course

Production Possibilities Frontier
Opportunity Cost
Increasing Opportunity Cost
Allocative Efficiency and Marginal Benefit
Economic Growth through Investment
Law of Demand
Price of Related Products and Demand
Changes in Income, Population, or Preferences
Normal and Inferior Goods
Inferior Goods Clarification
Law of Supply
Factors Affecting Supply
Market Equilibrium
Changes in Market Equilibrium
Price Elasticity of Demand
More on Elasticity of Demand
Perfect Inelasticity and Perfect Elasticity of Demand
Constant Unit Elasticity
Total Revenue and Elasticity
More on Total Revenue and Elasticity
Cross Elasticity of Demand
Elasticity of Supply
Elasticity and Strange Percent Changes
Demand Curve as Marginal Benefit Curve
Consumer Surplus Introduction
Total Consumer Surplus as Area
Producer Surplus
Minimum Wage and Price Floors
Percentage Tax on Hamburgers
Taxes and Perfectly Inelastic Demand
Taxes and Perfectly Elastic Demand
Marginal Utility
Equalizing Marginal Utility per Dollar Spent
Deriving Demand Curve from Tweaking Marginal Utility per Dollar
Budget Line
Optimal Point on Budget Line
Types of Indifference Curves
Economic Profit vs Accounting Profit
Depreciation and Opportunity Cost of Capital
Fixed, Variable, and Marginal Cost.
Visualizing Average Costs and Marginal Costs as Slope
Marginal Cost and Average Total Cost
Marginal Revenue and Marginal Cost
Marginal Revenue Below Average Total Cost
Long Term Supply Curve and Economic Profit
Perfect Competition
Monopoly Basics
Review of Revenue and Cost Graphs for a Monopoly
Monopolist Optimizing Price (part 1)- Total Revenue.
Monopolist Optimizing Price (part 2)- Marginal Revenue
Monopolist Optimizing Price (part 3)- Dead Weight Loss.avi
Optional Calculus Proof to Show that MR has Twice Slope of Demand
Oligopolies and Monopolisitc Competition
Monopolistic Competition and Economic Profit
Oligopolies, Duopolies, Collusion, and Cartels
Prisoners’ Dilemma and Nash Equilibrium
More on Nash Equilibrium
Why Parties to Cartels Cheat
Game Theory of Cheating Firms
Negative Externalities
Taxes for Factoring in Negative Externalities
Positive Externalities
Tragedy of the Commons
First Degree Price Discrimination
A Firm’s Marginal Product Revenue Curve
How Many People to Hire Given the MPR curve

Organic Chemistry

Topics covered in college organic chemistry course. Basic understanding of basic high school or college chemistry assumed

Representing Structures of Organic Molecules
Naming Simple Alkanes
Naming Alkanes with Alkyl Groups
Correction – 2-Propylheptane should never be the name!
Common and Systematic Naming-Iso, Sec and Tert Prefixes
More Organic Chemistry Naming Examples 1
Organic Chemistry Naming Examples 2
Organic Chemistry Naming Examples 3
Organic Chemistry Naming Examples 4
Organic Chemistry Naming Examples 5
Naming Alkenes Examples
Naming Alkyl Halides
sp3 Hybridized Orbitals and Sigma Bonds
Pi bonds and sp2 Hybridized Orbitals
Newman Projections
Newman Projections 2
Chair and Boat Shapes for Cyclohexane
Double Newman Diagram for Methcyclohexane
Introduction to Chirality
Chiral Examples 1
Chiral Examples 2
Cahn-Ingold-Prelog System for Naming Enantiomers
R,S (Cahn-Ingold-Prelog) Naming System Example 2
Stereoisomers, Enantiomers, Diastereomers, Constitutional Isomers and Meso Compounds
Cis-Trans and E-Z Naming Scheme for Alkenes
Entgegen-Zusammen Naming Scheme for Alkenes Examples
Introduction to Reaction Mechanisms
Markovnikov’s Rule and Carbocations
Polymerization of Alkenes with Acid
Sn2 Reactions
Sn1 Reactions
Steric Hindrance
Sn2 Stereochemistry
Solvent Effects on Sn1 and Sn2 Reactions
Nucleophilicity (Nucleophile Strength)
Nucleophilicity vs. Basicity
E2 Reactions
E1 Reactions
Zaitsev’s Rule
Comparing E2 E1 Sn2 Sn1 Reactions
E2 E1 Sn2 Sn1 Reactions Example 2
E2 E1 Sn2 Sn1 Reactions Example 3
Alcohols
Alcohol Properties
Resonance
Ether Naming and Introduction
Cyclic ethers and epoxide naming
Ring-opening Sn2 reaction of expoxides
Sn1 and Sn2 epoxide opening discussion
Aromatic Compounds and Huckel’s Rule
Naming Benzene Derivatives Introduction
Electrophilic Aromatic Substitution
Bromination of Benzene
Amine Naming Introduction
Amine Naming 2
Amine as Nucleophile in Sn2 Reaction
Amine in Sn2 part 2
Sn1 Amine Reaction
Aldehyde Introduction
Ketone Naming
Friedel Crafts Acylation
Keto Enol Tautomerization
Carboxlic Acid Introduction
Carboxylic Acid Naming
Fisher Esterification
Acid Chloride Formation
Amides, Anhydrides, Esters and Acyl Chlorides
Relative Stability of Amides Esters Anhydrides and Acyl Chlorides
Amide Formation from Acyl Chloride
Aldol Reaction

Paulson Bailout

Videos to help understand the bailout.

Bailout 1: Liquidity vs. Solvency
Bailout 2: Book Value
Bailout 3: Book value vs. market value
Bailout 4: Mark-to-model vs. mark-to-market
Bailout 5: Paying off the debt
Bailout 6: Getting an equity infusion
Bailout 7: Bank goes into bankruptcy
Bailout 8: Systemic Risk
Bailout 9: Paulson’s Plan
Bailout 10: Moral Hazard
Bailout 11: Why these CDOs could be worth nothing
Bailout 12: Lone Star Transaction
Bailout 14: Possible Solution
Bailout 15: More on the solution

Physics

Projectile motion, mechanics and electricity and magnetism. Solid understanding of algebra and a basic understanding of trigonometry necessary.

Introduction to Vectors and Scalars
Calculating Average Velocity or Speed
Solving for Time
Displacement from Time and Velocity Example
Acceleration
Newton’s First Law of Motion
Newton’s Second Law of Motion
Newton’s Third Law of Motion
Airbus A380 Take-off Time
Airbus A380 Take-off Distance
Why Distance is Area under Velocity-Time Line
Average Velocity for Constant Acceleration
Acceleration of Aircraft Carrier Takeoff
Race Cars with Constant Speed Around Curve
Introduction to Gravity
Mass and Weight Clarification
Gravity for Astronauts in Orbit
Would a Brick or Feather Fall Faster
Deriving Displacement as a Function of Time, Acceleration and Initial Velocity
Plotting Projectile Displacement, Acceleration, and Velocity
Projectile Height Given Time
Deriving Max Projectile Displacement Given Time
Impact Velocity From Given Height
Visualizing Vectors in 2 Dimensions
Projectile at an Angle
Different Way to Determine Time in Air
Launching and Landing on Different Elevations
Total Displacement for Projectile
Total Final Velocity for Projectile
Correction to Total Final Velocity for Projectile
Projectile on an Incline
Unit Vectors and Engineering Notation
Clearing the Green Monster at Fenway
Green Monster at Fenway Part 2
Optimal angle for a projectile part 1
Optimal angle for a projectile part 2 – Hangtime
Optimal angle for a projectile part 3 – Horizontal distance as a function of angle (and speed)
Optimal angle for a projectile part 4 Finding the optimal angle and distance with a bit of calculus
Normal Force and Contact Force
Normal Force in an Elevator
Inclined Plane Force Components
Ice Accelerating Down an Incline
Force of Friction Keeping the Block Stationary
Correction to Force of Friction Keeping the Block Stationary
Force of Friction Keeping Velocity Constant
Intuition on Static and Kinetic Friction Comparisons
Static and Kinetic Friction Example
Introduction to Tension
Tension (part 2)
Tension in an accelerating system and pie in the face
Moving pulley problem (part 1)
Moving pulley problem (part 2)
Introduction to Momentum
Momentum: Ice skater throws a ball
2-dimensional momentum problem
2-dimensional momentum problem (part 2)
Introduction to work and energy
Work and Energy (part 2)
Conservation of Energy
Work/Energy problem with Friction
Center of Mass
Introduction to Torque
Moments
Moments (part 2)
Unit Vector Notation
Unit Vector Notation (part 2)
Projectile Motion with Unit Vectors
Projectile Motion with Unit Vectors (part 2)
Projectile Motion with Ordered Set Notation
Projectile motion (part 1)
Projectile motion (part 2)
Projectile motion (part 3)
Projectile motion (part 4)
Projectile motion (part 5)
Centripetal Force and Acceleration Intuition
Visual Understanding of Centripetal Acceleration Formula
Relationship between angular velocity and speed
Calculus proof of centripetal acceleration formula
Loop De Loop Question
Loop De Loop Answer part 1
Loop De Loop Answer part 2
Acceleration Due to Gravity at the Space Station
Space Station Speed in Orbit
Conservation of angular momemtum
Introduction to Newton’s Law of Gravitation
Gravitation (part 2)
Intro to springs and Hooke’s Law
Potential energy stored in a spring
Spring potential energy example (mistake in math)
Introduction to Harmonic Motion
Harmonic Motion Part 2 (calculus)
Harmonic Motion Part 3 (no calculus)
Fluids (part 1)
Fluids (part 2)
Fluids (part 3)
Fluids (part 4)
Fluids (part 5)
Fluids (part 6)
Fluids (part 7)
Fluids (part 8 )
Fluids (part 9)
Fluids (part 10)
Fluids (part 11)
Fluids (part 12)
Thermodynamics (part 1)
Thermodynamics (part 2)
Thermodynamics (part 3)
Thermodynamics (part 4)
Thermodynamics (part 5)
Electrostatics (part 1): Introduction to Charge and Coulomb’s Law
Electrostatics (part 2)
Proof (Advanced): Field from infinite plate (part 1)
Proof (Advanced): Field from infinite plate (part 2)
Electric Potential Energy
Electric Potential Energy (part 2– involves calculus)
Voltage
Capacitance
Circuits (part 1)
Circuits (part 2)
Circuits (part 3)
Circuits (part 4)
Cross product 1
Cross Product 2
Cross Product and Torque
Introduction to Magnetism
Magnetism 2
Magnetism 3
Magnetism 4
Magnetism 5
Magnetism 6: Magnetic field due to current
Magnetism 7
Magnetism 8
Magnetism 9: Electric Motors
Magnetism 10: Electric Motors
Magnetism 11: Electric Motors
Magnetism 12: Induced Current in a Wire
The dot product
Dot vs. Cross Product
Calculating dot and cross products with unit vector notation
Introduction to Waves
Amplitude, Period, Frequency and Wavelength of Periodic Waves
Introduction to the Doppler Effect
Doppler effect formula for observed frequency
Doppler effect formula when source is moving away
When the source and the wave move at the same velocity
Mach Numbers
Specular and Diffuse Reflection
Specular and Diffuse Reflection 2
Refraction and Snell’s Law
Refraction in Water
Snell’s Law Examples 1
Snell’s Law Example 2
Total Internal Reflection
Virtual Image
Parabolic Mirrors and Real Images
Parabolic Mirrors 2
Convex Parabolic Mirrors
Convex Lenses
Convex Lens Examples
Concave Lenses
Object Image and Focal Distance Relationship (Proof of Formula)
Object Image Height and Distance Relationship
Viewing g as the value of Earth’s Gravitational Field Near the Surface

Precalculus

Non-trigonometry pre-calculus topics. Solid understanding of all of the topics in the “Algebra” playlist should make this playlist pretty digestible.

Introduction to Limits (HD)
Introduction to Limits
Limit Examples (part 1)
Limit Examples (part 2)
Limit Examples (part3)
Limit Examples w/ brain malfunction on first prob (part 4)
Squeeze Theorem
Proof: lim (sin x)/x
More Limits
Sequences and Series (part 1)
Sequences and series (part 2)
Permutations
Combinations
Binomial Theorem (part 1)
Binomial Theorem (part 2)
Binomial Theorem (part 3)
Introduction to interest
Interest (part 2)
Introduction to compound interest and e
Compound Interest and e (part 2)
Compound Interest and e (part 3)
Compound Interest and e (part 4)
Exponential Growth
Polar Coordinates 1
Polar Coordinates 2
Polar Coordinates 3
Parametric Equations 1
Parametric Equations 2
Parametric Equations 3
Parametric Equations 4
Introduction to Function Inverses
Function Inverse Example 1
Function Inverses Example 2
Function Inverses Example 3
Basic Complex Analysis
Exponential form to find complex roots
Complex Conjugates
Series Sum Example
Complex Determinant Example
2003 AIME II Problem 8
Logarithmic Scale
Vi and Sal Explore How We Think About Scale
Vi and Sal Talk About the Mysteries of Benford’s Law
Benford’s Law Explanation (Sequel to Mysteries of Benford’s Law)

Probability

Basic probability. Should have a reasonable grounding in basic algebra before watching.

Basic Probability
Simple Probability
Probability with Playing Cards and Venn Diagrams
Compound Probability of Independent Events
Probability 1 Module Examples
Independent Events 1
Independent Events 2
Independent Events 3
Coin Flipping Example
Frequency Probability and Unfair Coins
Probability of Dependent Events
Probability of Dependent Events 2
Exactly Three Heads in Five Flips
Generalizing with Binomial Coefficients (bit advanced)
Probability (part 1)
Probability (part 2)
Probability (part 3)
Probability (part 4)
Probability (part 5)
Probability (part 6)
Events and Outcomes 1
Events and Outcomes 2
Events and Outcomes 3
Dependent Probability Example 1
Dependent Probability Example 2
Probability (part 7)
Probability (part 8 )
Probability of More Complex Outcome
Permutations
Combinations
Permutations and Combinations 1
Permutations and Combinations 2
Permutations and Combinations 3
Permutations and Combinations 4
Probability using Combinations
Probability and Combinations (part 2)
Mega Millions Jackpot Probability
Conditional Probability and Combinations
Birthday Probability Problem
Introduction to Random Variables
Probability Density Functions
Binomial Distribution 1
Binomial Distribution 2
Binomial Distribution 3
Binomial Distribution 4
Expected Value: E(X)
Expected Value of Binomial Distribution
Poisson Process 1
Poisson Process 2
Law of Large Numbers
Term Life Insurance and Death Probability

SAT Preparation

I am going to work through every problem in the College Board “Official SAT Study Guide.” You should take the practice tests on your own, grade them and then use these videos to understand the problems you didn’t get or review. Have fun!

SAT prep: test 1 section3 part 1
SAT Prep: Test 1 Section 3 Part 2
SAT Prep: Test 1 Section 3 Part 3
SAT Prep: Test 1 Section 3 Part 4
SAT Prep: Test 1 Section 3 Part 5
SAT Prep: Test 1 Section 3 Part 6
SAT Prep: Test 1 Section 3 Part 7
SAT Prep: Test 1 Section 3 Part 8
SAT Prep: Test 1 Section 6 Part 1
SAT Prep: Test 1 Section 6 Part 2
SAT Prep: Test 1 Section 6 Part 3
SAT Prep: Test 1 Section 6 Part 4
SAT Prep: Test 1 Section 6 Part 5
SAT Prep: Test 1 Section 6 Part 6
SAT Prep: Test 1 Section 9 Part 1
SAT Prep: Test 1 Section 9 Part 2
SAT Prep: Test 1 Section 9 Part 3
SAT Prep: Test 1 Section 9 Part 4
SAT Prep: Test 1 Section 9 Part 5
SAT Prep: Test 2 Section 3 part 1
SAT Prep: Test 2 Section 3 Part 2
SAT Prep: Test 2 Section 3 Part 3
SAT Prep: Test 2 Section 3 Part 4
SAT Prep: Test 2 Section 3 Part 5
SAT Prep: Test 2 Section 3 Part 6
SAT Prep: Test 2 Section 6 Part 1
SAT Prep: Test 2 Section 6 Part 2
SAT Prep: Test 2 Section 6 Part 3
SAT Prep: Test 2 Section 6 Part 4
SAT Prep: Test 2 Section 6 Part 5
SAT Prep: Test 2 Section 6 Part 6
SAT Prep: Test 2 Section 9 Part 1
SAT Prep: Test 2 Section 9 Part 2
SAT Prep: Test 2 Section 9 Part 3
SAT Prep: Test 2 Section 9 Part 4
SAT Prep: Test 3 Section 2 Part 1
SAT Prep: Test 3 Section 2 Part 2
SAT Prep: Test 3 Section 2 Part 3
SAT Prep: Test 3 Section 2 Part 4
Test 3 Section 2 Part 5
SAT Prep: Test 3 Section 4 Part 1
SAT Prep: Test 3 Section 4 Part 2
SAT Prep: Test 3 Section 4 Part 3
SAT Prep: Test 3 Section 4 Part 4
SAT Prep: Test 3 Section 4 Part 5
SAT Prep: Test 3 Section 8 Part 1
SAT Prep: Test 3 Section 8 Part 2
SAT Prep: Test 3 Section 8 Part 3
SAT Prep: Test 3 Section 8 Part 4
SAT Prep: Test 4 Section 2 Part 1
SAT Prep: Test 4 Section 2 Part 2
SAT Prep: Test 4 Section 2 Part 3
SAT Prep: Test 4 Section 2 Part 4
SAT Prep: Test 4 Section 2 Part 5
SAT Prep: Test 4 Section 2 Part 6
SAT Prep: Test 4 Section 4 Part 1
SAT Prep: Test 4 Section 4 Part 2
SAT Prep: Test 4 Section 4 Part 3
SAT Prep: Test 4 Section 4 Part 4
SAT Prep: Test 4 Section 8 Part 1
SAT Prep: Test 4 Section 8 Part 2
SAT Prep: Test 4 Section 8 Part 3
SAT Prep: Test 4 Section 8 Part 4
SAT Prep: Test 5 Section 3 Part 1
SAT Prep: Test 5 Section 3 Part 2
SAT Prep: Test 5 Section 3 Part 3
SAT Prep: Test 5 Section 3 Part 4
SAT Prep: Test 5 Section 3 Part 5
SAT Prep: Test 5 Section 3 Part 6
SAT Prep: Test 5 Section 7 Part 1
SAT Prep: Test 5 Section 7 Part 2
SAT Prep: Test 5 Section 7 Part 3
SAT Prep: Test 5 Section 7 Part 4
SAT Prep: Test 5 Section 7 Part 5
SAT Prep: Test 5 Section 7 Part 6
SAT Prep: Test 5 Section 9 Part 1
SAT Prep: Test 5 Section 9 Part 2
SAT Prep: Test 5 Section 9 Part 3
SAT Prep: Test 5 Section 9 Part 4
SAT Prep: Test 6 Section 3 Part 1
SAT Prep: Test 6 Section 3 Part 2
SAT Prep: Test 6 Section 3 Part 3
SAT Prep: Test 6 Section 3 Part 4
SAT Prep: Test 6 Section 3 Part 5
SAT Prep: Test 6 Section 7 Part 1
SAT Prep: Test 6 Section 7 Part 2
SAT Prep: Test 6 Section 7 Part 3
SAT Prep: Test 6 Section 7 Part 4
SAT Prep: Test 6 Section 7 Part 5
SAT Prep: Test 6 Section 7 Part 6
SAT Prep: Test 6 Section 9 Part 1
SAT Prep: Test 6 Section 9 Part 2
SAT Prep: Test 6 Section 9 Part 3
SAT Prep: Test 6 Section 9 Part 4
SAT Prep: Test 7 Section 2 Part 1
SAT Prep: Test 7 Section 2 Part 2
SAT Prep: Test 7 Section 2 Part 3
SAT Prep: Test 7 Section 2 Part 4
SAT Prep: Test 7 Section 5 Part 1
SAT Prep: Test 7 Section 5 Part 2
SAT Prep: Test 7 Section 5 Part 3
SAT Prep: Test 7 Section 5 Part 4
SAT Prep: Test 7 Section 5 Part 5
SAT Prep: Test 7 Section 8 Part 1
SAT Prep: Test 7 Section 8 Part 2
SAT Prep: Test 7 Section 8 Part 3
SAT Prep: Test 7 Section 8 Part 4
SAT Prep: Test 8 Section 2 Part 1
SAT Prep: Test 8 Section 2 Part 2
SAT Prep: Test 8 Section 2 Part 3
SAT Prep: Test 8 Section 2 Part 4
SAT Prep: Test 8 Section 5 Part 1
SAT Prep: Test 8 Section 5 Part 2
SAT Prep: Test 8 Section 5 Part 3
SAT Prep: Test 8 Section 5 Part 4
SAT Prep: Test 8 Section 8 Part 1
SAT Prep: Test 8 Section 8 Part 2
SAT Prep: Test 8 Section 8 Part 3

Singapore Math

Lectures based on the Singapore Math curriculum. You can follow along through the workbooks available at singaporemath.com

Singapore Math: Grade 3a, Unit 1 (part 1)
Singapore Math: Grade 3a Unit 1 (part 2)
Singapore Math: Grade 3a, Unit 1 (part 3)
Singapore Math: Grade 3a, Unit 1 (part 4)
Singapore Math: Grade 3a, Unit 1 (part 5)
Singapore Math: Grade 3a, Unit 1 (part 6)
Singapore Math: Grade 3a, Unit 1 (part 7)
Singapore Math: Grade 3a, Unit 1 (part 8 )
Singapore Math: Grade 3a, Unit 1 (part 9)
Singapore Math: Grade 3a Unit 2 (part 1)
Singapore Math: Grade 3a Unit 2 (part 2)
Singapore Math: Grade 3a Unit 2 (part 3)
Singapore Math: Grade 3a Unit 2 (part 4)
Singapore Math: Grade 3a Unit 2 (part 5)
Singapore Math: Grade 3a Unit 2 (part 6)
Singapore Math: Grade 3a Unit 2 (part 7)
Singapore Math: Grade 3a Unit 2 (part 8 )
Singapore Math: Grade 3a Unit 2 (part 9)
Singapore Math: Grade 3a Unit 2 (part 10)
Singapore Math: Grade 3a Unit 2 (part 11)

Statistics

Introduction to statistics. Will eventually cover all of the major topics in a first-year statistics course (not there yet!)

Mean Median and Mode
Range and Mid-range
u08_l1_t2_we3 Stem-and-leaf Plots
Box-and-Whisker Plots
Statistics: The Average
Statistics: Sample vs. Population Mean
Statistics: Variance of a Population
Statistics: Sample Variance
Statistics: Standard Deviation
Statistics: Alternate Variance Formulas
Introduction to Random Variables
Probability Density Functions
Binomial Distribution 1
Binomial Distribution 2
Binomial Distribution 3
Binomial Distribution 4
Expected Value: E(X)
Expected Value of Binomial Distribution
Poisson Process 1
Poisson Process 2
Law of Large Numbers
Normal Distribution Excel Exercise
Introduction to the Normal Distribution
ck12.org Normal Distribution Problems: Qualitative sense of normal distributions
ck12.org Normal Distribution Problems: z-score
ck12.org Normal Distribution Problems: Empirical Rule
ck12.org Exercise: Standard Normal Distribution and the Empirical Rule
ck12.org: More Empirical Rule and Z-score practice
Central Limit Theorem
Sampling Distribution of the Sample Mean
Sampling Distribution of the Sample Mean 2
Standard Error of the Mean
Sampling Distribution Example Problem
Confidence Interval 1
Mean and Variance of Bernoulli Distribution Example
Bernoulli Distribution Mean and Variance Formulas
Margin of Error 1
Margin of Error 2
Confidence Interval Example
Small Sample Size Confidence Intervals
Hypothesis Testing and P-values
One-Tailed and Two-Tailed Tests
Z-statistics vs. T-statistics
Type 1 Errors
Small Sample Hypothesis Test
T-Statistic Confidence Interval
Large Sample Proportion Hypothesis Testing
Variance of Differences of Random Variables
Difference of Sample Means Distribution
Confidence Interval of Difference of Means
Clarification of Confidence Interval of Difference of Means
Hypothesis Test for Difference of Means
Comparing Population Proportions 1
Comparing Population Proportions 2
Hypothesis Test Comparing Population Proportions
Squared Error of Regression Line
Proof (Part 1) Minimizing Squared Error to Regression Line
Proof (Part 3) Minimizing Squared Error to Regression Line
Proof (Part 4) Minimizing Squared Error to Regression Line
Regression Line Example
Proof Part 2 Minimizing Squared Error to Line
R-Squared or Coefficient of Determination
Second Regression Example
Calculating R-Squared
Covariance and the Regression Line
Chi-Square Distribution Introduction
Pearson’s Chi Square Test (Goodness of Fit)
Contingency Table Chi-Square Test
ANOVA 1 – Calculating SST (Total Sum of Squares)
ANOVA 2 – Calculating SSW and SSB (Total Sum of Squares Within and Between).avi
ANOVA 3 -Hypothesis Test with F-Statistic
Correlation and Causality
Deductive Reasoning 1
Deductive Reasoning 2
Deductive Reasoning 3
U12_L1_T3_we1 Inductive Reasoning 1
Inductive Reasoning 2
Inductive Reasoning 3
U03_L1_T1_we2 Inductive Patterns

Trigonometry

Videos on trigonometry. Watch the “Geometry” playlist first if you have trouble understanding the topics covered here.

Basic Trigonometry
Basic Trigonometry II
Using Trig Functions
Using Trig Functions Part II
The unit circle definition of trigonometric function
Unit Circle Definition of Trig Functions
Graph of the sine function
Graphs of trig functions
Graphing trig functions
More trig graphs
Determining the equation of a trigonometric function
Trigonometric Identities
Proof: sin(a+b) = (cos a)(sin b) + (sin a)(cos b)
Proof: cos(a+b) = (cos a)(cos b)-(sin a)(sin b)
Trig identities part 2 (parr 4 if you watch the proofs)
Trig identies part 3 (part 5 if you watch the proofs)
Trigonometry word problems (part 1)
Trigonometry word problems (part 2)
Law of cosines
Proof: Law of Sines
Ferris Wheel Trig Problem
Ferris Wheel Trig Problem (part 2)
Fun Trig Problem
Polar Coordinates 1
Polar Coordinates 2
Polar Coordinates 3
Inverse Trig Functions: Arcsin
Inverse Trig Functions: Arctan
Inverse Trig Functions: Arccos
Trigonometry Identity Review/Fun
Tau versus Pi
IIT JEE Trigonometry Problem 1
IIT JEE Trigonometric Maximum
IIT JEE Trigonometric Constraints
Trigonometric System Example
2003 AIME II Problem 11.avi
2003 AIME II Problem 14

Valuation and Investing

Building blocks and case studies on the financial analysis and valuation of public equities.

Price and Market Capitalization
Introduction to the Income Statement
Earnings and EPS
Introduction to the Price-to-Earnings Ratio
P/E Discussion
ROA Discussion 1
ROA Discussion 2
Depreciation
Amortization
P/E Conundrum
Enterprise Value
EBITDA

Venture Capital and Capital Markets

All of the sources of funding (capital) for a business.

Raising money for a startup
Getting a seed round from a VC
Going back to the till: Series B
An IPO
More on IPOs
Equity vs. Debt
Bonds vs. Stocks
Chapter 7:Bankruptcy Liquidation
Chapter 11: Bankruptcy Restructuring

Vi Hart

Recreational mathematics and inspirational videos by resident mathemusician Vi Hart

Doodling in Math: Spirals, Fibonacci, and Being a Plant [1 of 3]
Doodling in Math Class: Spirals, Fibonacci, and Being a Plant [2 of 3]
Doodling in Math: Spirals, Fibonacci, and Being a Plant [Part 3 of 3]
Doodling in Math Class: Binary Trees
Doodling in Math Class: Stars
Doodling in Math Class: Snakes + Graphs
Doodling in Math Class: Infinity Elephants
Doodling in Math: Sick Number Games
Doodling in Math Class: Squiggle Inception
Doodling in Math Class: Triangle Party
Mobius Story: Wind and Mr. Ug
Math Improv: Fruit by the Foot
Wau: The Most Amazing, Ancient, and Singular Number
Are Shakespeare’s Plays Encoded within Pi?
What is up with Noises? (The Science and Mathematics of Sound, Frequency, and Pitch)
Open Letter to Nickelodeon, Re: SpongeBob’s Pineapple under the Sea
How To Snakes
Origami Proof of the Pythagorean Theorem
9.999… reasons that .999… = 1
Pi Is (still) Wrong.
Fractal Fractions
Angle-a-trons
Binary Hand Dance
Re: Visual Multiplication and 48/2(9+3)
The Gauss Christmath Special
Rhapsody on the Proof of Pi = 4
Doodle Music
What was up with Pythagoras?
A Song About A Circle Constant

You: “Wow. That’s a pretty impressive list. But surely that’s not everything.”
Me: “Close enough.”

##### Jeremy Hoke
jeremy.hoke@d4online.com

When Jeremy isn't leading the development of our digital projects, he's following the latest developments in technology, analysing insane amounts of data, and having yet another cup of coffee.

• ##### Phonebloks – An Idea Worth Sharing | D4
Posted at 13:04h, 12 September Reply

[…] Whilst I was on the bus this morning surfing the Internet (yes, I just said ‘surfing the Internet’ which means that you now know I’m at least in my mid-30s!), I stumbled upon an idea so good, I just had to write a blog about it – something I haven’t done since June of last year! […]