Online courses directory (381)

Basics of probability and combinatorics. Basic Probability. Example: Marbles from a bag. Example: Picking a non-blue marble. Example: Picking a yellow marble. Probability 1. 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. Independent probability. Introduction to dependent probability. Example: Dependent probability. Example: Is an event independent or dependent?. Example: Bag of unfair coins. Dependent probability. Monty Hall Problem. Permutations. Combinations. Counting 2. Example: Ways to arrange colors. Example: 9 card hands. Example: Ways to pick officers. Permutations. Combinations. Permutations and combinations. Example: Probability through counting outcomes. Example: All the ways you can flip a coin. Getting Exactly Two Heads (Combinatorics). Probability and Combinations (part 2). Probability using Combinations. Exactly Three Heads in Five Flips. Example: Different ways to pick officers. Example: Combinatorics and probability. Example: Lottery probability. Mega Millions Jackpot Probability. Generalizing with Binomial Coefficients (bit advanced). Conditional Probability and Combinations. Conditional Probability (Bayes Theorem) Visualized. Birthday Probability Problem. Probability with permutations and combinations. Basic Probability. Example: Marbles from a bag. Example: Picking a non-blue marble. Example: Picking a yellow marble. Probability 1. 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. Independent probability. Introduction to dependent probability. Example: Dependent probability. Example: Is an event independent or dependent?. Example: Bag of unfair coins. Dependent probability. Monty Hall Problem. Permutations. Combinations. Counting 2. Example: Ways to arrange colors. Example: 9 card hands. Example: Ways to pick officers. Permutations. Combinations. Permutations and combinations. Example: Probability through counting outcomes. Example: All the ways you can flip a coin. Getting Exactly Two Heads (Combinatorics). Probability and Combinations (part 2). Probability using Combinations. Exactly Three Heads in Five Flips. Example: Different ways to pick officers. Example: Combinatorics and probability. Example: Lottery probability. Mega Millions Jackpot Probability. Generalizing with Binomial Coefficients (bit advanced). Conditional Probability and Combinations. Conditional Probability (Bayes Theorem) Visualized. Birthday Probability Problem. Probability with permutations and combinations.

Understanding i and the complex plane. Introduction to i and Imaginary Numbers. Calculating i Raised to Arbitrary Exponents. Imaginary unit powers. Imaginary Roots of Negative Numbers. i as the Principal Root of -1 (a little technical). Complex numbers. Complex numbers (part 1). Complex numbers (part 2). The complex plane. Adding Complex Numbers. Subtracting Complex Numbers. Complex number polar form intuition. Complex plane operations. Adding and subtracting complex numbers. Multiplying Complex Numbers. Multiplying complex numbers. Dividing Complex Numbers. Dividing complex numbers. Multiplying and dividing complex numbers in polar form. Complex Conjugates. Complex Conjugates Example. Absolute value of complex numbers. Basic Complex Analysis. Complex number polar form intuition exercise. Complex number polar form intuition. Exponential form to find complex roots. Multiplying and dividing complex numbers in polar form. Powers of complex numbers. Complex Conjugates. IIT JEE Complex Numbers (part 1). IIT JEE Complex Numbers (part 2). IIT JEE Complex Numbers (part 3). Complex Determinant Example. Introduction to i and Imaginary Numbers. Calculating i Raised to Arbitrary Exponents. Imaginary unit powers. Imaginary Roots of Negative Numbers. i as the Principal Root of -1 (a little technical). Complex numbers. Complex numbers (part 1). Complex numbers (part 2). The complex plane. Adding Complex Numbers. Subtracting Complex Numbers. Complex number polar form intuition. Complex plane operations. Adding and subtracting complex numbers. Multiplying Complex Numbers. Multiplying complex numbers. Dividing Complex Numbers. Dividing complex numbers. Multiplying and dividing complex numbers in polar form. Complex Conjugates. Complex Conjugates Example. Absolute value of complex numbers. Basic Complex Analysis. Complex number polar form intuition exercise. Complex number polar form intuition. Exponential form to find complex roots. Multiplying and dividing complex numbers in polar form. Powers of complex numbers. Complex Conjugates. IIT JEE Complex Numbers (part 1). IIT JEE Complex Numbers (part 2). IIT JEE Complex Numbers (part 3). Complex Determinant Example.

Motivation and understanding of hyperbolic trig functions. Hyperbolic Trig Function Inspiration. Hyperbolic Trig Functions and the Unit Hyperbola. Hyperbolic Trig Function Inspiration. Hyperbolic Trig Functions and the Unit Hyperbola.

Preview of the calculus topic of limits. Introduction to limits. Introduction to Limits. Limits 1. Limits 2. Limit Examples (part 1). Limit Examples (part 2). Limit Examples (part 3). Limit Examples w/ brain malfunction on first prob (part 4). More Limits. Introduction to limits. Introduction to Limits. Limits 1. Limits 2. Limit Examples (part 1). Limit Examples (part 2). Limit Examples (part 3). Limit Examples w/ brain malfunction on first prob (part 4). More Limits.

Topics covered in a traditional college level introductory macroeconomics course. Introduction to Economics. 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 Stabilize Currency. Speculative Attack on a Currency. Financial Crisis in Thailand Caused by Speculative Attack. Math Mechanics of Thai Banking Crisis.

Our universe is defined by stars. This topic explores how they came to be and where they end up. This includes a discussion of black holes and galaxies. Birth of Stars. Accreting mass due to gravity simulation. Challenge: Modeling Accretion Disks. Becoming a Red Giant. White and Black Dwarfs. Star Field and Nebula Images. Lifecycle of Massive Stars. Supernova (Supernovae). Supernova clarification. Black Holes. Supermassive Black Holes. Quasars. Quasar Correction. Galactic Collisions. Parallax in Observing Stars. Stellar Parallax. Stellar Distance Using Parallax. Stellar Parallax Clarification. Parsec Definition. Cepheid Variables 1. Why Cepheids Pulsate. Why Gravity Gets So Strong Near Dense Objects. Birth of Stars. Accreting mass due to gravity simulation. Challenge: Modeling Accretion Disks. Becoming a Red Giant. White and Black Dwarfs. Star Field and Nebula Images. Lifecycle of Massive Stars. Supernova (Supernovae). Supernova clarification. Black Holes. Supermassive Black Holes. Quasars. Quasar Correction. Galactic Collisions. Parallax in Observing Stars. Stellar Parallax. Stellar Distance Using Parallax. Stellar Parallax Clarification. Parsec Definition. Cepheid Variables 1. Why Cepheids Pulsate. Why Gravity Gets So Strong Near Dense Objects.

What is the Earth made up of and how do we know? What causes the seasons? Are there longer-ranging cycles in Earth's climate?. 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. Pangaea. Compositional and Mechanical Layers of the Earth. How we know about the Earth's core. Seismic Waves. Why S-Waves Only Travel in Solids. Refraction of Seismic Waves. The Mohorovicic Seismic Discontinuity. Seasons Aren't Dictated by Closeness to Sun. How Earth's Tilt Causes Seasons. Are Southern Hemisphere Seasons More Severe?. Milankovitch Cycles Precession and Obliquity. Precession Causing Perihelion to Happen Later. What Causes Precession and Other Orbital Changes. Apsidal Precession (Perihelion Precession) and Milankovitch Cycles. 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. Pangaea. Compositional and Mechanical Layers of the Earth. How we know about the Earth's core. Seismic Waves. Why S-Waves Only Travel in Solids. Refraction of Seismic Waves. The Mohorovicic Seismic Discontinuity. Seasons Aren't Dictated by Closeness to Sun. How Earth's Tilt Causes Seasons. Are Southern Hemisphere Seasons More Severe?. Milankovitch Cycles Precession and Obliquity. Precession Causing Perihelion to Happen Later. What Causes Precession and Other Orbital Changes. Apsidal Precession (Perihelion Precession) and Milankovitch Cycles.

When and how did life emerge on Earth? How did humanity develop a civilization? Is there other intelligent life out there?. 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. Human Evolution Overview. Understanding Calendar Notation. Correction Calendar Notation. Development of Agriculture and Writing. Firestick Farming. Collective Learning. Thomas Malthus and Population Growth. Land Productivity Limiting Human Population. Energy Inputs for Tilling a Hectare of Land. Random Predictions for 2060. Chronometric Revolution. Carbon 14 Dating 1. Carbon 14 Dating 2. Potassium-Argon (K-Ar) Dating. K-Ar Dating Calculation. 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. 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. Human Evolution Overview. Understanding Calendar Notation. Correction Calendar Notation. Development of Agriculture and Writing. Firestick Farming. Collective Learning. Thomas Malthus and Population Growth. Land Productivity Limiting Human Population. Energy Inputs for Tilling a Hectare of Land. Random Predictions for 2060. Chronometric Revolution. Carbon 14 Dating 1. Carbon 14 Dating 2. Potassium-Argon (K-Ar) Dating. K-Ar Dating Calculation. 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.

Circular flow of income and expenditure. Gross domestic product. Introduction to Economics. 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 Economics. 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.

Inflation and deflation. CPI-U. Real and nominal return. Phillips Curve. Introduction to Inflation. Actual CPI-U Basket of Goods. Inflation Data. 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. Moderate Inflation in a Good Economy. Stagflation. Deflationary Spiral. Hyperinflation. Unemployment Rate Primer. Phillips Curve. Introduction to Inflation. Actual CPI-U Basket of Goods. Inflation Data. 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. Moderate Inflation in a Good Economy. Stagflation. Deflationary Spiral. Hyperinflation. Unemployment Rate Primer. Phillips Curve.

Find out how the heart and circulatory system work in the fetus!. Meet the Placenta!. Umbilical vessels and the Ductus Venosus. Flow through the Heart. Hypoxic Pulmonary Vasoconstriction. Foramen Ovale and Ductus Arteriosus. Fetal Hemoglobin and Hematocrit. Double Bohr Effect. Fetal Circulation Right Before Birth. Baby Circulation Right After Birth. Fetal Structures in an Adult. Meet the Placenta!. Umbilical vessels and the Ductus Venosus. Flow through the Heart. Hypoxic Pulmonary Vasoconstriction. Foramen Ovale and Ductus Arteriosus. Fetal Hemoglobin and Hematocrit. Double Bohr Effect. Fetal Circulation Right Before Birth. Baby Circulation Right After Birth. Fetal Structures in an Adult.

Using definite integrals with the shell and disc methods to find volumes of solids of revolution. Disk method around x-axis. Generalizing disc method around x-axis. Disc method around y-axis. Disc method (washer method) for rotation around x-axis. Generalizing the washer method. Disc method rotation around horizontal line. Washer method rotating around non-axis. Part 2 of washer for non axis rotation. Disc method rotating around vertical line. Calculating integral disc method around vertical line. Washer or ring method for vertical line rotation. Evaluating integral for washer method around vertical line. Shell method for rotating around vertical line. Evaluating integral for shell method example. Shell method for rotating around horizontal line. Shell method with two functions of x. Calculating integral with shell method. Shell method with two functions of y. Part 2 of shell method with 2 functions of y. Disc method: function rotated about x-axis. Disc method (rotating f(x) about x axis). Volume of a sphere. Disc method with outer and inner function boundaries. Shell method to rotate around y-axis. Disk method: rotating x=f(y) around the y-axis. Shell method around a non-axis line. Shell method around a non-axis line 2. Disk method around x-axis. Generalizing disc method around x-axis. Disc method around y-axis. Disc method (washer method) for rotation around x-axis. Generalizing the washer method. Disc method rotation around horizontal line. Washer method rotating around non-axis. Part 2 of washer for non axis rotation. Disc method rotating around vertical line. Calculating integral disc method around vertical line. Washer or ring method for vertical line rotation. Evaluating integral for washer method around vertical line. Shell method for rotating around vertical line. Evaluating integral for shell method example. Shell method for rotating around horizontal line. Shell method with two functions of x. Calculating integral with shell method. Shell method with two functions of y. Part 2 of shell method with 2 functions of y. Disc method: function rotated about x-axis. Disc method (rotating f(x) about x axis). Volume of a sphere. Disc method with outer and inner function boundaries. Shell method to rotate around y-axis. Disk method: rotating x=f(y) around the y-axis. Shell method around a non-axis line. Shell method around a non-axis line 2.

Limit introduction, squeeze theorem, and epsilon-delta definition of limits. Introduction to limits. Limit at a point of discontinuity. Determining which limit statements are true. Limit properties. Limit example 1. Limits 1. One-sided limits from graphs. One-sided limits from graphs. Introduction to Limits. Limit Examples (part 1). Limit Examples (part 2). Limit Examples (part 3). Limit Examples w/ brain malfunction on first prob (part 4). More Limits. Limits 1. Limits and infinity. Limits at positive and negative infinity. More limits at infinity. Limits with two horizontal asymptotes. Limits 2. Squeeze Theorem. Proof: lim (sin x)/x. Limit intuition review. Building the idea of epsilon-delta definition. Epsilon-delta definition of limits. Proving a limit using epsilon-delta definition. Limits to define continuity. Continuity. Epsilon Delta Limit Definition 1. Epsilon Delta Limit Definition 2. Introduction to limits. Limit at a point of discontinuity. Determining which limit statements are true. Limit properties. Limit example 1. Limits 1. One-sided limits from graphs. One-sided limits from graphs. Introduction to Limits. Limit Examples (part 1). Limit Examples (part 2). Limit Examples (part 3). Limit Examples w/ brain malfunction on first prob (part 4). More Limits. Limits 1. Limits and infinity. Limits at positive and negative infinity. More limits at infinity. Limits with two horizontal asymptotes. Limits 2. Squeeze Theorem. Proof: lim (sin x)/x. Limit intuition review. Building the idea of epsilon-delta definition. Epsilon-delta definition of limits. Proving a limit using epsilon-delta definition. Limits to define continuity. Continuity. Epsilon Delta Limit Definition 1. Epsilon Delta Limit Definition 2.

Divergence theorem intuition. Divergence theorem examples and proofs. Types of regions in 3D. 3-D Divergence Theorem Intuition. Divergence Theorem Example 1. Why we got zero flux in Divergence Theorem Example 1. Type I Regions in Three Dimensions. Type II Regions in Three Dimensions. Type III Regions in Three Dimensions. Divergence Theorem Proof (part 1). Divergence Theorem Proof (part 2). Divergence Theorem Proof (part 3). Divergence Theorem Proof (part 4). Divergence Theorem Proof (part 5). 3-D Divergence Theorem Intuition. Divergence Theorem Example 1. Why we got zero flux in Divergence Theorem Example 1. Type I Regions in Three Dimensions. Type II Regions in Three Dimensions. Type III Regions in Three Dimensions. Divergence Theorem Proof (part 1). Divergence Theorem Proof (part 2). Divergence Theorem Proof (part 3). Divergence Theorem Proof (part 4). Divergence Theorem Proof (part 5).

This topic continues our journey through the world of Euclid by helping us understand angles and how they can relate to each other. Angle basics. Measuring angles in degrees. Using a protractor. Measuring angles. Measuring angles. Acute right and obtuse angles. Angle types. Vertical, adjacent and linearly paired angles. Exploring angle pairs. Introduction to vertical angles. Vertical angles. Using algebra to find the measures of vertical angles. Vertical angles 2. Proof-Vertical Angles are Equal. Angles Formed by Parallel Lines and Transversals. Identifying Parallel and Perpendicular Lines. Figuring out angles between transversal and parallel lines. Congruent angles. Parallel lines 1. Using algebra to find measures of angles formed from transversal. Parallel lines 2. CA Geometry: Deducing Angle Measures. 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. Proof - Corresponding Angle Equivalence Implies Parallel Lines. Finding more angles. Angles 1. Angles 2. Sum of Interior Angles of a Polygon. Angles of a polygon. Sum of the exterior angles of convex polygon. Introduction to angles (old). Angles (part 2). Angles (part 3). Angles formed between transversals and parallel lines. Angles of parallel lines 2. The Angle Game. Angle Game (part 2). Acute right and obtuse angles. Complementary and supplementary angles. Complementary and supplementary angles. Example using algebra to find measure of complementary angles. Example using algebra to find measure of supplementary angles. Angle addition postulate. Angle basics. Measuring angles in degrees. Using a protractor. Measuring angles. Measuring angles. Acute right and obtuse angles. Angle types. Vertical, adjacent and linearly paired angles. Exploring angle pairs. Introduction to vertical angles. Vertical angles. Using algebra to find the measures of vertical angles. Vertical angles 2. Proof-Vertical Angles are Equal. Angles Formed by Parallel Lines and Transversals. Identifying Parallel and Perpendicular Lines. Figuring out angles between transversal and parallel lines. Congruent angles. Parallel lines 1. Using algebra to find measures of angles formed from transversal. Parallel lines 2. CA Geometry: Deducing Angle Measures. 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. Proof - Corresponding Angle Equivalence Implies Parallel Lines. Finding more angles. Angles 1. Angles 2. Sum of Interior Angles of a Polygon. Angles of a polygon. Sum of the exterior angles of convex polygon. Introduction to angles (old). Angles (part 2). Angles (part 3). Angles formed between transversals and parallel lines. Angles of parallel lines 2. The Angle Game. Angle Game (part 2). Acute right and obtuse angles. Complementary and supplementary angles. Complementary and supplementary angles. Example using algebra to find measure of complementary angles. Example using algebra to find measure of supplementary angles. Angle addition postulate.

Conditional statements and deductive reasoning. Conditional statements exercise examples. Logical argument and deductive reasoning exercise example. Conditional statements and deductive reasoning. Conditional statements exercise examples. Logical argument and deductive reasoning exercise example.

Watch fun, educational videos on all sorts of Physics questions. Thomas Young's Double Slit Experiment. Newton's Prism Experiment. Bridge Design and Destruction! (part 1). Bridge Design (and Destruction!) Part 2. Shifts in Equilibrium. The Marangoni Effect: How to make a soap propelled boat!. The Invention of the Battery. The Forces on an Airplane. Bouncing Droplets: Superhydrophobic and Superhydrophilic Surfaces. A Crash Course on Indoor Flying Robots. Heat Transfer. Thomas Young's Double Slit Experiment. Newton's Prism Experiment. Bridge Design and Destruction! (part 1). Bridge Design (and Destruction!) Part 2. Shifts in Equilibrium. The Marangoni Effect: How to make a soap propelled boat!. The Invention of the Battery. The Forces on an Airplane. Bouncing Droplets: Superhydrophobic and Superhydrophilic Surfaces. A Crash Course on Indoor Flying Robots. Heat Transfer.

What makes living (and nonliving) things tick?. Homeostasis. Bread Mold Kills Bacteria. Glaciers With Chocolate. Rock Cycle. Homeostasis. Bread Mold Kills Bacteria. Glaciers With Chocolate. Rock Cycle.

Watch fun, educational videos on all sorts of Materials, how they're created and what they can do. Whats all the matter? Atoms and Molecules. What is Soap?. Flocculation: Making Clean Water. Manufacturing Processes: Hands On to Hands Off. Whats all the matter? Atoms and Molecules. What is Soap?. Flocculation: Making Clean Water. Manufacturing Processes: Hands On to Hands Off.