## Learn Everything For Free with Khan Academy

**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.”

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Algebra

Conceptual videos and worked examples from basic algebra through algebra 2. Includes videos from the former algebra worked examples playlists.

Algebra: Introduction to AlgebraVideos 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 CoordinatesAlgebra: 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 2Algebra: 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 Addition and Subtraction

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 3Algebra: Graphing linear equations and inequalities

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

Quadrants of Coordinate Plane

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 2Algebra: 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

Addition Elimination Method 1

Addition Elimination Method 2

Addition Elimination Method 3

Addition Elimination Method 4

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 ApplicationAlgebra: Ratios & 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)

Advanced ratio problems

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 2Algebra: 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 3Algebra: Exponents and Radicals

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

Radical Equivalent to Rational Exponents 2

Simplifying radicals

Simplifying Radical Expressions1

Simplifying Radical Expressions 2

Simplifying Radical Expressions 3

More Simplifying Radical Expressions

Radical Expressions with Higher Roots

Adding and Simplifying Radicals

Subtracting and Simplifying Radicals

Adding and Subtracting Rational Expressions

Multiply and Simplify a Radical Expression 1

Multiply and Simplify a Radical Expression 2

How to Rationalize a Denominator

Solving Radical Equations

Extraneous Solutions to Radical Equations

Solving Radical Equations 1

Solving Radical Equations 2

Solving Radical Equations 3

Applying Radical Equations 1

Applying Radical Equations 2

Applying Radical Equations 3Algebra: 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 FunctionAlgebra: 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

Adding Polynomials

Adding polynomials with multiple variables

Polynomials 2

Simplifying First for Subtracting Rational Expressions

Subtracting Rational Expressions

Subtracting Polynomials

Polynomials1

Subtracting polynomials with multiple variables

Adding and Subtracting Polynomials 1

Adding and Subtracting Polynomials 2

Adding and Subtracting Polynomials 3

Addition and Subtraction of Polynomials

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 Binomials with Radicals

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 Quadratic Expressions

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 a quadratic by factoringAlgebra: Quadratics

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

Factoring Quadratic Expressions

Solving Quadratic Equations by Factoring.avi

Solving Quadratic Equations by Factoring 2.avi

Solving Quadratic Equations by Factoring 3.avi

CA Algebra I: Factoring Quadratics

Solving a quadratic by factoring

Applications Problem Factoring Quadratics

Algebra II: Quadratics and Shifts

Algebra II: Shifting Quadratic Graphs

Graphing a Quadratic Function

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

Introduction to the quadratic equation

Quadratic Equation part 2

Quadratic Formula 1

Quadratic Formula 2

Quadratic Formula 3

Quadratic Equations in Standard Form

CA Algebra I: Quadratic Equation

CA Algebra I: Quadratic Roots

Simple Quadratic Equation

Applying the Quadratic Formula

Application Problem with Quadratic Formula

Discriminant for Types of Solutions for a Quadratic

Discriminant of Quadratic Equations

Proof of Quadratic Formula

Quadratic Formula (proof)

Complex Roots from the Quadratic FormulaAlgebra: 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

Domain of a Radical Function

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

Quadratic Functions 1

Quadratic Functions 2

Quadratic Functions 3

Applying Quadratic Functions 1

Applying Quadratic Functions 2

Applying Quadratic Functions 3

Graphing a Quadratic Function

Graphing Radical Functions

Graphing Exponential Functions

Graphs of Square Root FunctionsAlgebra: 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

Adding Complex Numbers

Subtracting Complex Numbers

Multiplying Complex Numbers

Dividing Complex Numbers

Complex Roots from the Quadratic FormulaAlgebra: 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 invertibilityAlgebra: 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

Addition of 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 Addition and Subtraction

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

Addition and Subtraction of Polynomials

Multiplication of Polynomials

Special Products of Binomials

Polynomial Equations in Factored Form

Factoring Quadratic Expressions

Factoring Special Products

Factor by Grouping and Factoring Completely

Graphs of Quadratic Functions

Solving Quadratic Equations by Graphing

Solving Quadratic Equations by Square Roots

Solving Quadratic Equations by Completing the Square

Using the Quadratic Formula

Proof of Quadratic Formula

Discriminant of Quadratic Equations

Linear, Quadratic, and Exponential Models

Identifying Quadratic Models

Identifying Exponential Models

Quadratic Regression

Graphs of Square Root Functions

Radical Expressions with Higher Roots

More Simplifying Radical Expressions

How to Rationalize a Denominator

Extraneous Solutions to Radical Equations

Radical Equation Examples

More Involved Radical Equation Example

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

Adding Rational Expressions Example 1

Adding Rational Expressions Example 2

Adding Rational Expressions Example 3

Solving Rational Equations

Two more examples of solving rational equations

Surveys and SamplesAmerican 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 PIPAArithmetic 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 subtractionAdding and subtracting positive and negative whole numbers. Starts with 1+1=2 and covers carrying, borrowing, and word problems.

Basic Addition

Addition 2

Basic Subtraction

Subtraction 2

Subtracting Whole Numbers

Level 2 Addition

Addition 3

Subtraction 3: Introduction to Borrowing or Regrouping

Why borrowing works

Addition 4

Level 4 Subtraction

Subtraction Word Problem

Alternate mental subtraction method

Negative Numbers Introduction

Adding Negative Numbers

Adding integers with different signs

Adding/Subtracting negative numbers

Adding Whole Numbers and Applications 1

u09 l1 t2 we4 Adding Real Numbers ApplicationArithmetic 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 3Arithmetic and Pre-Algebra: Negative numbers

Understanding and using negative numbers.

Negative Numbers Introduction

Ordering Negative Numbers

Adding Negative Numbers

Adding integers with different signs

Adding/Subtracting negative numbers

Multiplying Positive and Negative Numbers

Dividing Positive and Negative Numbers

Why a Negative Times a Negative is a PositiveArithmetic and Pre-Algebra: Number properties

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

Commutative Law of Addition

Commutative Law of Multiplication

Associative Law of Addition

Associative Law of Multiplication

Commutative Property for Addition

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 Addition

Inverse Property of Multiplication

Why Dividing by Zero is Undefined

Why Zero Divided by Zero is Undefined/Indeterminate

Undefined and IndeterminateArithmetic 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 1Arithmetic 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 MultipleArithmetic 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

Adding Fractions with Like Denominators

Subtracting Fractions

Finding Common Denominators

Adding Fractions with Unlike Denominators

Adding and subtracting fractions

Adding Mixed Numbers

Adding Mixed Numbers with Unlike Denominators

Subtracting Mixed Numbers

Subtracting Mixed Numbers 2

Adding Mixed Numbers Word Problem

Subtracting Mixed Numbers Word Problem

Adding fractions with different signs

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 expressionsArithmetic 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

Adding 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 expressionsArithmetic 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 expressionsArithmetic 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 translationArithmetic 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 2Art 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 CulturesSculpture from the Parthenon’s East Pediment

Head of Augustus

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

Hadrian’s Villa: A Virtual Tour

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, RomeArt 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 CupArt History: 1300-1400 Proto-Renaissance

Duccio, The Rucellai Madonna, 1285-86

Cimabue, Santa Trinita Madonna

Duccio’s Madonna and Child

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

Giotto, The Ognissanti Madonna

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 TriptychArt 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

Mantegna’s Dead Christ

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

Fra Angelico’s The Annunciation (Prado)

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

Donatello’s Madonna of the Clouds

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 & Ghiberti The Sacrifice of Isaac

Botticelli’s Primavera

Martini’s Architectural VedutaArt History: 1500-1600 End of the Renaissance and the Reformation

Parmigianino’s Madonna of the Long Neck

Michelangelo’s Piet�

Raphael, Madonna of the Goldfinch

Pontormo’s Entombment

Raphael’s La belle jardinière

Dürer’s Four Apostles

Leonardo, Adoration of the Magi

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

Raphael’s Alba Madonna

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

Cranach’s Adam and Eve

Michelangelo’s Slaves

Dürer’s Self-portrait

Holbein’s The Ambassadors

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

Titian’s Bacchus and Ariadne

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 WayArt 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 & 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 PhilipArt 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

Vigée Le Brun’s Madame Perregaux

Boucher’s Madame de Pompadour

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 BottomArt 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

Alma-Tadema’s Listening to Homer

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

Gaudí, Sagrada Família

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 & 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 & 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

Dada Duchamp and the Ready-Mades

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)

Braque’s The Viaduct at L’Estaque

Picasso’s The Reservoir, Horta de Ebro

Feininger’s Cathedral for the Bauhaus

De Stijl: Mondrian’s Composition No. II, with Red and Blue

Schad’s Self-Portrait

Cartier-Bresson’s Behind the Gare St. Lazare

Klee’s Twittering Machine

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 BuildingArt 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 & 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 DissentBanking 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

LIBORBiology

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

Sex-Linked Traits

Bacteria

Viruses

ATP: Adenosine Triphosphate

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

Brain Teaser: Blue Forehead Room

Blue Forehead Room Solution

Forehead Numbers Brain Teaser

Light Bulb Switching Brain Teaser

Path Counting Brain Teaser

3-D Path Counting Brain TeaserBrit Cruise

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

Journey into CryptographyPart 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 7: One-time pad

Part 8: Case Study: WW2 Encryption Machines

Part 9: Perfect Secrecy

Part 10: Pseudorandom Number Generators

Part 11: Diffie-Hellman key exchangeCAHSEE 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 52-53Calculus

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

Extreme Derivative Word Problem (advanced)

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)

Ladder rate-of-change problem

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&c

AP Calculus BC Exams: 2008 1 c&d

AP Calculus BC Exams: 2008 1 d

Calculus BC 2008 2 a

Calculus BC 2008 2 b &c

Calculus BC 2008 2d

Partial Derivatives

Partial Derivatives 2

Gradient 1

Gradient of a scalar field

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 & b)

2011 Calculus AB Free Response #2 (c & d)

2011 Calculus AB Free Response #3 (a & 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 & c)

2011 Calculus BC Free Response #1d

2011 Calculus BC Free Response #3a

2011 Calculus BC Free Response #3 (b & 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 AnswerCalifornia 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 ISal 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: Factoring Quadratics

CA Algebra I: Completing the Square

CA Algebra I: Quadratic Equation

CA Algebra I: Quadratic Roots

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: FunctionsCalifornia 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 II: Quadratics and Shifts

Algebra II: Shifting Quadratic Graphs

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 DeviationCalifornia 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: Proof by Contradiction

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 TranslationsChemistry

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

The Mole and Avogadro’s Number

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 ExampleCompetition 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

Area Circumradius Formula Proof

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 FunctionCosmology 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

Radius of Observable Universe

(Correction) Radius of Observable Universe

Red Shift

Cosmic Background Radiation

Cosmic Background Radiation 2

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 2060Credit 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 2Currency

Videos about currency exchange

Currency Exchange Introduction

Currency Effect on Trade

Currency Effect on Trade Review

Pegging the Yuan

Chinese Central Bank Buying Treasuries

American-Chinese Debt Loop

Debt Loops Rationale and Effects

China keeps peg but diversifies holdingsCurrent 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 & Capacity Utilization

Inflation, Deflation & Capacity Utilization 2

Inflation & Deflation 3: Obama Stimulus Plan

Unemployment

CPI Index

Simple Analysis of Cost per Job Saved from Stimulus

Unemployment Rate Primer

Floating Exchange Resolving Trade Imbalance

China Pegs to Dollar to Keep Trade Imbalance

China buys US Bonds

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 USDifferential 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 ProbFinance

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

Renting vs. buying a home (part 2)

Renting vs. Buying (detailed analysis)

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

Is short selling bad?

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

Traditional IRAs

Roth IRAs

401(k)s

Payday Loans

Institutional Roles in Issuing and Processing Credit Cards

Ponzi Schemes

Currency Exchange Introduction

Currency Effect on Trade

Currency Effect on Trade Review

Pegging the Yuan

Chinese Central Bank Buying Treasuries

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

Long Straddle

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

Contango from Trader Perspective

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

Exchange Traded Funds (ETFs)

Hedge Funds Intro

Hedge Fund Structure and Fees

Are Hedge Funds Bad?

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

Basic Leveraged Buyout (LBO)

Corporate Debt versus Traditional Mortgages

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

Carry Trade Basics

Interpretting Futures Fair Value in the PreMarket

Interest Rate Swap 1

Interest Rate Swap 2GMAT

Prepare for the Graduate Management Admission Test by going over these practice problems.

GMAT: Problem SolvingSal 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 54GMAT: 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 41Geithner 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 solutionGeometry

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 geometryFinding 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

Circles: Radius, Diameter and Circumference

Parts of a Circle

Area of a Circle

Solid Geometry Volume

Cylinder Volume and Surface Area

Volume of a SphereGeometry: 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 LinesGeometry: 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

Perpendicular Radius Bisects Chord

Inradius Perimeter and Area

2003 AIME II Problem 7Geometry: 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 CentroidGeometry: Polygons, quadrilaterals, and parallelograms

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

Quadrilateral Overview

Quadrilateral Properties

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 MeasuresGeometry: Circles

Finding measurements and applying and proving circle theorems.

Language and Notation of the Circle

Circles: Radius, Diameter and Circumference

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)

Perpendicular Radius Bisects Chord

Incenter and incircles of a triangle

Inradius Perimeter and AreaGeometry: 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: Proof by Contradiction

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 TranslationsHealthcare 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

Systemic Thinking About Cancer

Vitamin C and the Limeys

Inflammation

Blue Cross and Blue Shield

Conversation About Drug Pricing

Health Care Costs in US vs Europe

Healthcare System Overview

Paying Doctors

Medicare OverviewHistory

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 GrowthIIT 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 ExampleKhan Academy-Related Talks and Interviews

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

CNN: Google award to Khan Academy

Fareed Zakaria talks about Khan Academy on CNN GPS

Khan Academy on the Gates Notes

Sal on ABC News

Forbes Names You Need To Know: Khan Academy

Salman Khan on KQED MindShift

Khan Academy Exercise Software

Salman Khan talk at TED 2011 (from ted.com)

Khan Academy on Nightly News

Sal on Dylan Ratigan show

Authors@Google: Salman Khan

LinkedIn Speaker Series Salman Khan

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)

Answers for Malibu Magazine

NCSU Answers

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

Verbal Answers to “Ask Me Anything” on Reddit

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

60 minutes: Google’s Eric Schmidt on Khan Academy

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

Khan Academy at Marlborough School

Khan Academy at Summit Prep

Khan Academy at KIPP

MIT 2012 Commencement Address

Minli VirdoneLinear 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 PlanesMIT+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

Bread Mold Kills Bacteria

Bouncing Droplets: Superhydrophobic and Superhydrophilic SurfacesMacroeconomics

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

Actual CPI-U Basket of Goods

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

The Business Cycle

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 GreeceMicroeconomics

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

Comparative Advantage Specialization and Gains from Trade

Comparative Advantage and Absolute Advantage

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

Rent Control and Deadweight Loss

Minimum Wage and Price Floors

Taxation and Dead Weight Loss

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

Adding Demand CurvesOrganic 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

Addition of Water (Acid-Catalyzed) Mechanism

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

Free Radical Reactions

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

Friedel Crafts Acylation Addendum

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 ReactionPaulson 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 solutionPhysics

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

Introduction to mechanical advantage

Mechanical Advantage (part 2)

Mechanical Advantage (part 3)

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 SurfacePrecalculus

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

Addition Rule for Probability

Compound Probability of Independent Events

Probability 1 Module Examples

Independent Events 1

Independent Events 2

Independent Events 3

Coin Flipping Example

Getting At Least One Heads

Frequency Probability and Unfair Coins

Probability of Dependent Events

Probability of Dependent Events 2

Getting Exactly Two Heads (Combinatorics)

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

LeBron asks about the chances of making 10 free throwsSAT 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 3Singapore 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

Reading Pictographs

Reading Bar Graphs

u08_l1_t2_we2 Reading Line Graphs

Reading Pie Graphs (Circle Graphs)

Misleading Line Graphs

u08_l1_t2_we3 Stem-and-leaf Plots

Box-and-Whisker Plots

Reading 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 PatternsTrigonometry

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

Basic Trigonometry

Basic Trigonometry II

Radians and degrees

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

Navigation Word Problem

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 14Valuation 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

EBITDAVenture 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 RestructuringVi 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.”

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## Phonebloks – An Idea Worth Sharing | D4

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## David Donatello Vector | Donation

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