Online courses directory (107)

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 Measures.

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 Area.

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 Translations. 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 Translations.

Relationship between angular velocity and speed. Why Distance is Area under Velocity-Time Line. Introduction to Vectors and Scalars. Calculating Average Velocity or Speed. Solving for Time. Displacement from Time and Velocity Example. Acceleration. Balanced and Unbalanced Forces. Unbalanced Forces and Motion. Newton's First Law of Motion. Newton's First Law of Motion Concepts. 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. 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. Slow Sock on Lubricon VI. Normal Forces on Lubricon VI. 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. Introduction to Tension (Part 2). Tension in an accelerating system and pie in the face. 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 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. 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 momentum. Introduction to Newton's Law of Gravitation. Gravitation (part 2). Viewing g as the value of Earth's Gravitational Field Near the Surface. 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).

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. 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.

Random logic puzzles and brain teasers. Fun to do and useful for many job interviews!. Liar Truth-teller Brain Teaser. Toggler Brain Teaser. Alien Abduction Brain Teaser. Blue Forehead Room Brain Teaser. Blue Forehead Room Solution. Forehead Numbers Brain Teaser. Light Bulb Switching Brain Teaser. Path Counting Brain Teaser. 3-D Path Counting Brain Teaser. Liar Truth-teller Brain Teaser. Toggler Brain Teaser. Alien Abduction Brain Teaser. Blue Forehead Room Brain Teaser. Blue Forehead Room Solution. Forehead Numbers Brain Teaser. Light Bulb Switching Brain Teaser. Path Counting Brain Teaser. 3-D Path Counting Brain Teaser.

Sal working through the 53 problems from the practice test available at http://www.cde.ca.gov/ta/tg/hs/documents/mathpractest.pdf for the CAHSEE (California High School Exit Examination). Clearly useful if you're looking to take that exam. Probably still useful if you want to make sure you have a solid understanding of basic high school math. CAHSEE Practice: Problems 1-3. CAHSEE Practice: Problems 4-9. CAHSEE Practice: Problems 10-12. CAHSEE Practice: Problems 13-14. CAHSEE Practice: Problems 15-16. CAHSEE Practice: Problems 17-19. CAHSEE Practice: Problems 20-22. CAHSEE Practice: Problems 23-27. CAHSEE Practice: Problems 28-31. CAHSEE Practice: Problems 32-34. CAHSEE Practice: Problems 35-37. CAHSEE Practice: Problems 38-42. CAHSEE Practice: Problems 43-46. CAHSEE Practice: Problems 47-51. CAHSEE Practice: Problems 52-53. CAHSEE Practice: Problems 1-3. CAHSEE Practice: Problems 4-9. CAHSEE Practice: Problems 10-12. CAHSEE Practice: Problems 13-14. CAHSEE Practice: Problems 15-16. CAHSEE Practice: Problems 17-19. CAHSEE Practice: Problems 20-22. CAHSEE Practice: Problems 23-27. CAHSEE Practice: Problems 28-31. CAHSEE Practice: Problems 32-34. CAHSEE Practice: Problems 35-37. CAHSEE Practice: Problems 38-42. CAHSEE Practice: Problems 43-46. CAHSEE Practice: Problems 47-51. CAHSEE Practice: Problems 52-53.

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. 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. 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). 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. 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. 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).

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 homogeneous 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 characteristic 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 nonhomogeneous eq. Laplace Transform of : L{t}. Laplace Transform of t^n: L{t^n}. Laplace Transform of the Unit Step Function. Inverse Laplace Examples. Laplace/Step Function Differential Equation. Dirac Delta Function. Laplace Transform of the Dirac Delta Function. Introduction to the Convolution. The Convolution and the Laplace Transform. Using the Convolution Theorem to Solve an Initial Value Prob.

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

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). Idea Behind Inverting a 2x2 Matrix. 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. Introduction to Vectors. Vector Examples. Parametric Representations of Lines. Linear Combinations and Span. Introduction to Linear Independence. More on linear independence. Span and Linear Independence Example. Linear Subspaces. Basis of a Subspace. Vector Dot Product and Vector Length. Proving Vector Dot Product Properties. Proof of the Cauchy-Schwarz Inequality. Vector Triangle Inequality. Defining the angle between vectors. Defining a plane in R3 with a point and normal vector. 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. Matrix Product Examples. Matrix Product Associativity. Distributive Property of Matrix Products. 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. Exploring the solution set of Ax=b. Matrix condition for one-to-one trans. Simplifying conditions for invertibility. Showing that Inverses are Linear. Deriving a method for determining inverses. Example of Finding Matrix Inverse. Formula for 2x2 inverse. 3x3 Determinant. nxn Determinant. Determinants along other rows/cols. Rule of Sarrus of Determinants. Determinant when row multiplied by scalar. (correction) scalar multiplication of row. Determinant when row is added. Duplicate Row Determinant. Determinant after row operations. Upper Triangular Determinant. Simpler 4x4 determinant. Determinant and area of a parallelogram. Determinant as Scaling Factor. Transpose of a Matrix. Determinant of Transpose. Transpose of a Matrix Product. Transposes of sums and inverses. Transpose of a Vector. Rowspace and Left Nullspace. Visualizations of Left Nullspace and Rowspace. Orthogonal Complements. Rank(A) = Rank(transpose of A). dim(V) + dim(orthogonal complement of V)=n. Representing vectors in Rn using subspace members. Orthogonal Complement of the Orthogonal Complement. Orthogonal Complement of the Nullspace. Unique rowspace solution to Ax=b. Rowspace Solution to Ax=b example. Showing that A-transpose x A is invertible. Projections onto Subspaces. Visualizing a projection onto a plane. A Projection onto a Subspace is a Linear Transforma. Subspace Projection Matrix Example. Another Example of a Projection Matrix. Projection is closest vector in subspace. Least Squares Approximation. Least Squares Examples. Another Least Squares Example. Coordinates with Respect to a Basis. Change of Basis Matrix. Invertible Change of Basis Matrix. Transformation Matrix with Respect to a Basis. Alternate Basis Transformation Matrix Example. Alternate Basis Transformation Matrix Example Part 2. Changing coordinate systems to help find a transformation matrix. Introduction to Orthonormal Bases. Coordinates with respect to orthonormal bases. Projections onto subspaces with orthonormal bases. Finding projection onto subspace with orthonormal basis example. Example using orthogonal change-of-basis matrix to find transformation matrix. Orthogonal matrices preserve angles and lengths. The Gram-Schmidt Process. Gram-Schmidt Process Example. Gram-Schmidt example with 3 basis vectors. Introduction to Eigenvalues and Eigenvectors. Proof of formula for determining Eigenvalues. Example solving for the eigenvalues of a 2x2 matrix. Finding Eigenvectors and Eigenspaces example. Eigenvalues of a 3x3 matrix. Eigenvectors and Eigenspaces for a 3x3 matrix. Showing that an eigenbasis makes for good coordinate systems. Vector Triple Product Expansion (very optional). Normal vector from plane equation. Point distance to plane. Distance Between Planes.

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 Monopolistic 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 Curves.

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).

Basic probability. Should have a reasonable grounding in basic algebra before watching. Basic Probability. Example: Marbles from a bag. Example: Picking a non-blue marble. Example: Picking a yellow marble. Term Life Insurance and Death Probability. Probability with Playing Cards and Venn Diagrams. Addition Rule for Probability. Compound Probability of Independent Events. Getting At Least One Heads. Example: Probability of rolling doubles. LeBron Asks: What are the chances of making 10 free throws in a row?. LeBron Asks: What are the chances of three free throws versus one three pointer?. Frequency Probability and Unfair Coins. Example: Getting two questions right on an exam. Example: Rolling even three times. Introduction to dependent probability. Example: Dependent probability. Example: Is an event independent or dependent?. Example: Bag of unfair coins. Monty Hall Problem. Example: All the ways you can flip a coin. Example: Probability through counting outcomes. Permutations. Combinations. Example: Ways to arrange colors. Example: 9 card hands. Example: Ways to pick officers. Getting Exactly Two Heads (Combinatorics). Probability and Combinations (part 2). Probability using Combinations. Exactly Three Heads in Five Flips. Generalizing with Binomial Coefficients (bit advanced). Example: Different ways to pick officers. Example: Combinatorics and probability. Example: Lottery probability. Mega Millions Jackpot Probability. Conditional Probability and Combinations. Birthday Probability Problem. Random Variables. Discrete and continuous random variables. Probability Density Functions. Expected Value: E(X). Binomial Distribution 1. Binomial Distribution 2. Binomial Distribution 3. Binomial Distribution 4. Expected Value of Binomial Distribution. Poisson Process 1. Poisson Process 2. Law of Large Numbers. Introduction to Random Variables. Probability (part 1). Probability (part 2). Probability (part 3). Probability (part 4). Probability (part 5). Probability (part 6). Probability (part 7). Probability (part 8).

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). 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).

Introduction to statistics. We start with the basics of reading and interpretting data and then build into descriptive and inferential statistics that are typically covered in an introductory course on the subject. Overview of Khan Academy statistics. Statistics intro: mean, median and mode. Constructing a box-and-whisker plot. Sample mean versus population mean.. Variance of a population. Sample variance. Review and intuition why we divide by n-1 for the unbiased sample variance. Simulation showing bias in sample variance. Simulation providing evidence that (n-1) gives us unbiased estimate. 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. Introduction to the Normal Distribution. Normal Distribution Excel Exercise. Law of Large Numbers. ck12.org Normal Distribution Problems: Qualitative sense of normal distributions. ck12.org Normal Distribution Problems: Empirical Rule. ck12.org Normal Distribution Problems: z-score. 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. Confidence Interval Example. Mean and Variance of Bernoulli Distribution Example. Bernoulli Distribution Mean and Variance Formulas. Margin of Error 1. Margin of Error 2. 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 2 Minimizing Squared Error to Line. Proof (Part 3) Minimizing Squared Error to Regression Line. Proof (Part 4) Minimizing Squared Error to Regression Line. Regression Line Example. Second Regression Example. R-Squared or Coefficient of Determination. Calculating R-Squared. Covariance and the Regression Line. Correlation and Causality. 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. Another simulation giving evidence that (n-1) gives us an unbiased estimate of variance. Mean Median and Mode. Range and Mid-range. Reading Pictographs. Reading Bar Graphs. Reading Line Graphs. Reading Pie Graphs (Circle Graphs). Misleading Line Graphs. Stem-and-leaf Plots. Box-and-Whisker Plots. Reading Box-and-Whisker Plots. Statistics: The Average. Statistics: Variance of a Population. Statistics: Sample Variance. Deductive Reasoning 1. Deductive Reasoning 2. Deductive Reasoning 3. Inductive Reasoning 1. Inductive Reasoning 2. Inductive Reasoning 3. Inductive Patterns.

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 14.

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. Dialogue for 2. Doodling in Math Class: Connecting Dots. Hexaflexagons. Hexaflexagons 2. Hexaflexagon Safety Guide. Flex Mex. Optimal Potatoes. Green Bean Matherole. Borromean Onion Rings. Thanksgiving Turduckenen-duckenen. Snowflakes, Starflakes, and Swirlflakes. 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. Dialogue for 2. Doodling in Math Class: Connecting Dots. Hexaflexagons. Hexaflexagons 2. Hexaflexagon Safety Guide. Flex Mex. Optimal Potatoes. Green Bean Matherole. Borromean Onion Rings. Thanksgiving Turduckenen-duckenen. Snowflakes, Starflakes, and Swirlflakes.