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BETTEREXPLAINED
Most lessons offer low-level details in a linear, seemingly logical sequence. Better Explained focuses on the big picture — the Aha! moment — and then the specifics. Here’s the difference: I know which approach keeps my curiosity and enthusiasm. The learning strategy is the ADEPT Method : Learning isn’t about memorizing factsto pass a
A GENTLE INTRODUCTION TO LEARNING CALCULUS EASY PERMUTATIONS AND COMBINATIONS LEARN DIFFICULT CONCEPTS WITH THE ADEPT METHOD Learn Difficult Concepts with the ADEPT Method. After a decade of writing explanations, I’ve simplified the strategy I use to get new concepts to click. Make explanations ADEPT: Use an Analogy, Diagram, Example, Plain-English description, and then a Technical description. Here’s how to teach yourself a difficult idea, or explain one toothers.
UNDERSTANDING THE MONTY HALL PROBLEM Understanding the Monty Hall Problem. The Monty Hall problem is a counter-intuitive statistics puzzle: There are 3 doors, behind which are two goats and a car. You pick a door (call it door A). You’re hoping for the car of course. Monty Hall, the game show host, examinesthe other doors (B
HOW TO LEARN TRIGONOMETRY INTUITIVELY Pretend you’re in the middle of your dome, about to hang up a movie screen. You point to some angle “x”, and that’s where the screen will hang. The angle you point at determines: sine (x) = sin (x) = height of the screen, hanging like a sign. cosine (x) = cos (x) =distance
UNDERSTANDING THE BIRTHDAY PARADOX Here are a few lessons from the birthday paradox: n is roughly the number you need to have a 50% chance of a match with n items. 365 is about 20. This comes into play in cryptography for the birthday attack. Even though there are 2 128 (1e38) GUID s, we only have 2 64 (1e19) to use up before a 50% chance of collision. UNDERSTANDING ACCOUNTING BASICS (ALOE AND BALANCE SHEETS)SEE MORE ONBETTEREXPLAINED.COM
UNDERSTANDING THE PARETO PRINCIPLE (THE 80/20 RULESEE MORE ONBETTEREXPLAINED.COM
NAVIGATE A GRID USING COMBINATIONS AND PERMUTATIONS And 9 for the second, 8 for the third, and 7 choices for the final right-to-up conversion. There are 10 * 9 * 8 * 7 = 10!/6! = 5040 possibilities. But, wait! We need to remove the redundancies: after all, converting moves #1 #2 #3 and #4 (in that order) is the same as converting #4 #3 #2 #1. We have 4! (4 * 3 * 2 * 1 = 24) ways torearrange the
BETTEREXPLAINED
Most lessons offer low-level details in a linear, seemingly logical sequence. Better Explained focuses on the big picture — the Aha! moment — and then the specifics. Here’s the difference: I know which approach keeps my curiosity and enthusiasm. The learning strategy is the ADEPT Method : Learning isn’t about memorizing factsto pass a
A GENTLE INTRODUCTION TO LEARNING CALCULUS EASY PERMUTATIONS AND COMBINATIONS LEARN DIFFICULT CONCEPTS WITH THE ADEPT METHOD Learn Difficult Concepts with the ADEPT Method. After a decade of writing explanations, I’ve simplified the strategy I use to get new concepts to click. Make explanations ADEPT: Use an Analogy, Diagram, Example, Plain-English description, and then a Technical description. Here’s how to teach yourself a difficult idea, or explain one toothers.
UNDERSTANDING THE MONTY HALL PROBLEM Understanding the Monty Hall Problem. The Monty Hall problem is a counter-intuitive statistics puzzle: There are 3 doors, behind which are two goats and a car. You pick a door (call it door A). You’re hoping for the car of course. Monty Hall, the game show host, examinesthe other doors (B
HOW TO LEARN TRIGONOMETRY INTUITIVELY Pretend you’re in the middle of your dome, about to hang up a movie screen. You point to some angle “x”, and that’s where the screen will hang. The angle you point at determines: sine (x) = sin (x) = height of the screen, hanging like a sign. cosine (x) = cos (x) =distance
UNDERSTANDING THE BIRTHDAY PARADOX Here are a few lessons from the birthday paradox: n is roughly the number you need to have a 50% chance of a match with n items. 365 is about 20. This comes into play in cryptography for the birthday attack. Even though there are 2 128 (1e38) GUID s, we only have 2 64 (1e19) to use up before a 50% chance of collision. UNDERSTANDING ACCOUNTING BASICS (ALOE AND BALANCE SHEETS)SEE MORE ONBETTEREXPLAINED.COM
UNDERSTANDING THE PARETO PRINCIPLE (THE 80/20 RULESEE MORE ONBETTEREXPLAINED.COM
NAVIGATE A GRID USING COMBINATIONS AND PERMUTATIONS And 9 for the second, 8 for the third, and 7 choices for the final right-to-up conversion. There are 10 * 9 * 8 * 7 = 10!/6! = 5040 possibilities. But, wait! We need to remove the redundancies: after all, converting moves #1 #2 #3 and #4 (in that order) is the same as converting #4 #3 #2 #1. We have 4! (4 * 3 * 2 * 1 = 24) ways torearrange the
A VISUAL GUIDE TO SIMPLE, COMPOUND AND CONTINUOUS INTEREST Corporate bonds: A bond with a face value of $ 1000 and 5% interest rate (coupon) pays you $ 50 per year until it expires. You can’t increase the face value, so $ 50/year is what you will get from the bond. (In reality, the bond would pay $ 25 every 6 months). Simple interest is the most basic type of return. NAVIGATE A GRID USING COMBINATIONS AND PERMUTATIONS And 9 for the second, 8 for the third, and 7 choices for the final right-to-up conversion. There are 10 * 9 * 8 * 7 = 10!/6! = 5040 possibilities. But, wait! We need to remove the redundancies: after all, converting moves #1 #2 #3 and #4 (in that order) is the same as converting #4 #3 #2 #1. We have 4! (4 * 3 * 2 * 1 = 24) ways torearrange the
UNDERSTANDING ACCOUNTING BASICS (ALOE AND BALANCE SHEETS) A balance sheet is a document that tracks a company's assets, liabilities and owner's equity at a specific point in time. As you know, if the company's has something, it belongs to someone. The sides must balance. So let's do an example. Suppose we start a company with$ 100 cash:
THE QUICK GUIDE TO GUIDS GUIDs to the Rescue. GUIDs are large, enormous numbers that are nearly guaranteed to be unique. They are usually 128 bits long and look like this in hexadecimal: 30dd879c-ee2f-11db-8314-0800200c9a66. The format is a well-defined sequence of 32 hex digits grouped into chunks of 8-4-4-4-12. This gives us 2^128 or about 10^38 numbers. IT’S TIME FOR AN INTUITION-FIRST CALCULUS COURSE Algebra Robot: Calculating change in circumference: 2*pi* (r + 1) - 2*pi*r = 2*pi. They are the same. Calculation complete. Calculus Disciple: Oh! We know circumference = 2*pi*r. The derivative is 2*pi, a constant, which means the current radius has no impact on a changing circumference. Calculus Zen master: I see the true nature of things. WHY DO WE MULTIPLY COMBINATIONS? So, the total is. choices we want = (1 + 10 + 45 + 120) = 176. And for kicks, the chance of seeing this happen is: 176 / 1024 = 17.2%. Multiplication goes beyond "repeated addition". It's a general notion of combining for which I'm still discovering interpretations. Let's not get tied into a single meaning. QUICK INSIGHT: SUBTRACTING NEGATIVE NUMBERS For older students, "subtracting a negative" can be seen as "cancelling a debt". If I have a debt of $ 30, and someone "subtracts it", I've effectively gained $ 30. In general, if you remove a disadvantage, you have improved your situation -- a positive. Theseexplanations are a
VECTOR CALCULUS
“If you can't explain it simply, you don't understand it well enough.” —Einstein AN INTUITIVE (AND SHORT) EXPLANATION OF BAYES’ THEOREM An Intuitive (and Short) Explanation of Bayes’ Theorem. Bayes’ theorem was the subject of a detailed article. The essay is good, but over 15,000 words long — here’s the condensed version for Bayesian newcomers like myself: Tests are not the event. We have a cancer test, separate from the event of actually having cancer. UNDERSTANDING PYTHAGOREAN DISTANCE AND THE GRADIENT Understanding Pythagorean Distance and the Gradient. The Pythagorean Theorem shows how strange our concept of distance is. Using the rule a 2 + b 2 = c 2, we can trade some "a" to get more "b". Starting with. means "A 13-inch pizza equals a 13-inch pizza". Sure.BETTEREXPLAINED
Most lessons offer low-level details in a linear, seemingly logical sequence. Better Explained focuses on the big picture — the Aha! moment — and then the specifics. Here’s the difference: I know which approach keeps my curiosity and enthusiasm. The learning strategy is the ADEPT Method : Learning isn’t about memorizing factsto pass a
INTUITION FOR GRAPHED FUNCTIONS Intuition For Graphed Functions. When we graph a function f ( x), there's a few ways we can modify it: Using f ( a x + b) + c instead of f ( x) has a few effects: What's going on? Well, we're describing the visual result on the graph, but aren't describing that underlying process that made the change. Let's take a look at the root cause. LEARN DIFFICULT CONCEPTS WITH THE ADEPT METHOD Learn Difficult Concepts with the ADEPT Method. After a decade of writing explanations, I’ve simplified the strategy I use to get new concepts to click. Make explanations ADEPT: Use an Analogy, Diagram, Example, Plain-English description, and then a Technical description. Here’s how to teach yourself a difficult idea, or explain one toothers.
UNDERSTANDING THE PARETO PRINCIPLE (THE 80/20 RULESEE MORE ONBETTEREXPLAINED.COM
UNDERSTANDING ACCOUNTING BASICS (ALOE AND BALANCE SHEETS)SEE MORE ONBETTEREXPLAINED.COM
QUICK INSIGHT: SUBTRACTING NEGATIVE NUMBERS For older students, "subtracting a negative" can be seen as "cancelling a debt". If I have a debt of $ 30, and someone "subtracts it", I've effectively gained $ 30. In general, if you remove a disadvantage, you have improved your situation -- a positive. Theseexplanations are a
WHY DO WE MULTIPLY COMBINATIONS? So, the total is. choices we want = (1 + 10 + 45 + 120) = 176. And for kicks, the chance of seeing this happen is: 176 / 1024 = 17.2%. Multiplication goes beyond "repeated addition". It's a general notion of combining for which I'm still discovering interpretations. Let's not get tied into a single meaning. HOW TO LEARN TRIGONOMETRY INTUITIVELY Pretend you’re in the middle of your dome, about to hang up a movie screen. You point to some angle “x”, and that’s where the screen will hang. The angle you point at determines: sine (x) = sin (x) = height of the screen, hanging like a sign. cosine (x) = cos (x) =distance
IMAGINARY MULTIPLICATION VS. IMAGINARY EXPONENTS Imaginary multiplication directly rotates our position. Imaginary exponents rotate the direction of our exponential growth; we compute our position after the sideways growth is complete. I think of imaginary multiplication as turning your map 90 degrees. East becomes North; no matter how long you drove East, now you're going North. Q: WHY IS E SPECIAL? (2.718…, NOT 2, 3.7 OR ANOTHER NUMBER?) Yes, you can beat e x in an exponential footrace, if you use a rate more than 100%. 13.74 x is really x. Because ln (13.74) ~ 2.6, you are assuming a 260% continuous interest rate, more than the 100% e x uses. (Alternatively, you can grow for 260% of the unit time period that e x uses.) Related:BETTEREXPLAINED
Most lessons offer low-level details in a linear, seemingly logical sequence. Better Explained focuses on the big picture — the Aha! moment — and then the specifics. Here’s the difference: I know which approach keeps my curiosity and enthusiasm. The learning strategy is the ADEPT Method : Learning isn’t about memorizing factsto pass a
INTUITION FOR GRAPHED FUNCTIONS Intuition For Graphed Functions. When we graph a function f ( x), there's a few ways we can modify it: Using f ( a x + b) + c instead of f ( x) has a few effects: What's going on? Well, we're describing the visual result on the graph, but aren't describing that underlying process that made the change. Let's take a look at the root cause. LEARN DIFFICULT CONCEPTS WITH THE ADEPT METHOD Learn Difficult Concepts with the ADEPT Method. After a decade of writing explanations, I’ve simplified the strategy I use to get new concepts to click. Make explanations ADEPT: Use an Analogy, Diagram, Example, Plain-English description, and then a Technical description. Here’s how to teach yourself a difficult idea, or explain one toothers.
UNDERSTANDING THE PARETO PRINCIPLE (THE 80/20 RULESEE MORE ONBETTEREXPLAINED.COM
UNDERSTANDING ACCOUNTING BASICS (ALOE AND BALANCE SHEETS)SEE MORE ONBETTEREXPLAINED.COM
QUICK INSIGHT: SUBTRACTING NEGATIVE NUMBERS For older students, "subtracting a negative" can be seen as "cancelling a debt". If I have a debt of $ 30, and someone "subtracts it", I've effectively gained $ 30. In general, if you remove a disadvantage, you have improved your situation -- a positive. Theseexplanations are a
WHY DO WE MULTIPLY COMBINATIONS? So, the total is. choices we want = (1 + 10 + 45 + 120) = 176. And for kicks, the chance of seeing this happen is: 176 / 1024 = 17.2%. Multiplication goes beyond "repeated addition". It's a general notion of combining for which I'm still discovering interpretations. Let's not get tied into a single meaning. HOW TO LEARN TRIGONOMETRY INTUITIVELY Pretend you’re in the middle of your dome, about to hang up a movie screen. You point to some angle “x”, and that’s where the screen will hang. The angle you point at determines: sine (x) = sin (x) = height of the screen, hanging like a sign. cosine (x) = cos (x) =distance
IMAGINARY MULTIPLICATION VS. IMAGINARY EXPONENTS Imaginary multiplication directly rotates our position. Imaginary exponents rotate the direction of our exponential growth; we compute our position after the sideways growth is complete. I think of imaginary multiplication as turning your map 90 degrees. East becomes North; no matter how long you drove East, now you're going North. Q: WHY IS E SPECIAL? (2.718…, NOT 2, 3.7 OR ANOTHER NUMBER?) Yes, you can beat e x in an exponential footrace, if you use a rate more than 100%. 13.74 x is really x. Because ln (13.74) ~ 2.6, you are assuming a 260% continuous interest rate, more than the 100% e x uses. (Alternatively, you can grow for 260% of the unit time period that e x uses.) Related: HOW TO ADD 1 THROUGH 100 USING CALCULUS Intuitively, the integral is "repeatedly adding a bunch of stuff" -- it seems like we could put it to work. From the rules of Calculus (or using Wolfram Alpha) we get this: Intuitively: Add up things following the f ( x) = x pattern and you end up with 1 2 x 2. Well, let's see: the actual sum from 1 to 100 is 5050. THE LESSON AND THE META-LESSON A few of my scattered meta-lessons: Analogies, while imperfect, are a huge jump start. It's motivating to get the ball rolling and course correct along the way, vs. waiting to line things up perfectly. Nearly every explanation is improved with a visual or diagram. Humor and empathy put the reader at ease so they can tell you when they'reVECTOR CALCULUS
Vector Calculus: Understanding the Cross Product. Taking two vectors, we can write every combination of components in a grid: This completed grid is the outer product, which can be separated into the: Dot product, the interactions between similar dimensions ( x*x, y*y, z*z) Cross product, the interactions between different dimensions ( x*y,y*z
IT’S TIME FOR AN INTUITION-FIRST CALCULUS COURSE Algebra Robot: Calculating change in circumference: 2*pi* (r + 1) - 2*pi*r = 2*pi. They are the same. Calculation complete. Calculus Disciple: Oh! We know circumference = 2*pi*r. The derivative is 2*pi, a constant, which means the current radius has no impact on a changing circumference. Calculus Zen master: I see the true nature of things. LEARN DIFFICULT CONCEPTS WITH THE ADEPT METHOD Learn Difficult Concepts with the ADEPT Method. After a decade of writing explanations, I’ve simplified the strategy I use to get new concepts to click. Make explanations ADEPT: Use an Analogy, Diagram, Example, Plain-English description, and then a Technical description. Here’s how to teach yourself a difficult idea, or explain one toothers.
UNDERSTANDING THE PARETO PRINCIPLE (THE 80/20 RULE Understanding the Pareto Principle (The 80/20 Rule) Originally, the Pareto Principle referred to the observation that 80% of Italy’s wealth belonged to only 20% of the population. More generally, the Pareto Principle is the observation (not law) that most things in life are not distributed evenly. It can mean all of the following things:And
QUICK INSIGHT: INTUITIVE MEANING OF DIVISION The division in the permutation formula acts as a boundary, and the division in the combination formula is a type of "group up". I imagine the variations being merged into a single option: The words we pick frame how we think about an equation. "Divide" implies we're splittingthings apart.
A QUICK INTUITION FOR PARAMETRIC EQUATIONS A Quick Intuition For Parametric Equations. Algebra is really about relationships. How are things connected? Do they move together, or apart, or maybe they’re completely independent? Normal equations assume an “input to output” connection. That is, we take an input (x=3), plug it into the relationship ( y = x 2 ), and observe theresult
USING LOGARITHMS IN THE REAL WORLD With logarithms a ".5" means halfway in terms of multiplication, i.e the square root ( 9 .5 means the square root of 9 -- 3 is halfway in terms of multiplication because it's 1 to 3 and 3 to 9). Taking log (500,000) we get 5.7, add 1 for the extra digit, and we can say WHAT YOU SHOULD KNOW ABOUT THE STOCK MARKET They match buyers and sellers efficiently. All prices are completely transparent and you see what other people have paid/sold for. You pick your own price and will get that amount if there’s a willing partner. Most explanations jump into the minor details — not here. Today we’ll see why theBETTEREXPLAINED
Most lessons offer low-level details in a linear, seemingly logical sequence. Better Explained focuses on the big picture — the Aha! moment — and then the specifics. Here’s the difference: I know which approach keeps my curiosity and enthusiasm. The learning strategy is the ADEPT Method : Learning isn’t about memorizing factsto pass a
CALCULUS, BETTER EXPLAINED EBOOK + VIDEO COURSELESSON 1CALCULUS These lessons are based on articles read by millions of readers, and evolved with thousands of comments and direct feedback. Here's what's you'll get in the course: 15-chapter eBook with a professional layout ( sample) 15 video lessons walking through each chapter (2.5 hours total) YouTube. Better Explained. 14.4K subscribers. A GENTLE INTRODUCTION TO LEARNING CALCULUS CALCULUS LEARNING GUIDE Calculus is the art of splitting patterns apart (X-rays, derivatives) and gluing patterns together (Time-lapses, integrals). Sometimes we can cleverly re-arrange the pattern to find a new insight. A circle can be split into rings: And the rings turned into a triangle: Wow! We found the circle's area in a simpler way. INTUITION FOR TAYLOR SERIES (DNA ANALOGY) Intuition for Taylor Series (DNA Analogy) Your body has a strange property: you can learn information about the entire organism from a single cell. Pick a cell, dive into the nucleus, and extract the DNA. You can now regrow the entire creature from that tiny sample. There's a math analogy here. Take a function, pick a specific point, and divein.
VECTOR CALCULUS: UNDERSTANDING THE DOT PRODUCTSEE MORE ONBETTEREXPLAINED.COM
UNDERSTANDING THE MONTY HALL PROBLEM Understanding the Monty Hall Problem. The Monty Hall problem is a counter-intuitive statistics puzzle: There are 3 doors, behind which are two goats and a car. You pick a door (call it door A). You’re hoping for the car of course. Monty Hall, the game show host, examinesthe other doors (B
QUICK INSIGHT: SUBTRACTING NEGATIVE NUMBERS For older students, "subtracting a negative" can be seen as "cancelling a debt". If I have a debt of $ 30, and someone "subtracts it", I've effectively gained $ 30. In general, if you remove a disadvantage, you have improved your situation -- a positive. Theseexplanations are a
UNDERSTANDING THE PARETO PRINCIPLE (THE 80/20 RULESEE MORE ONBETTEREXPLAINED.COM
UNDERSTANDING PYTHAGOREAN DISTANCE AND THE GRADIENT Understanding Pythagorean Distance and the Gradient. The Pythagorean Theorem shows how strange our concept of distance is. Using the rule a 2 + b 2 = c 2, we can trade some "a" to get more "b". Starting with. means "A 13-inch pizza equals a 13-inch pizza". Sure.BETTEREXPLAINED
Most lessons offer low-level details in a linear, seemingly logical sequence. Better Explained focuses on the big picture — the Aha! moment — and then the specifics. Here’s the difference: I know which approach keeps my curiosity and enthusiasm. The learning strategy is the ADEPT Method : Learning isn’t about memorizing factsto pass a
CALCULUS, BETTER EXPLAINED EBOOK + VIDEO COURSELESSON 1CALCULUS These lessons are based on articles read by millions of readers, and evolved with thousands of comments and direct feedback. Here's what's you'll get in the course: 15-chapter eBook with a professional layout ( sample) 15 video lessons walking through each chapter (2.5 hours total) YouTube. Better Explained. 14.4K subscribers. A GENTLE INTRODUCTION TO LEARNING CALCULUS CALCULUS LEARNING GUIDE Calculus is the art of splitting patterns apart (X-rays, derivatives) and gluing patterns together (Time-lapses, integrals). Sometimes we can cleverly re-arrange the pattern to find a new insight. A circle can be split into rings: And the rings turned into a triangle: Wow! We found the circle's area in a simpler way. INTUITION FOR TAYLOR SERIES (DNA ANALOGY) Intuition for Taylor Series (DNA Analogy) Your body has a strange property: you can learn information about the entire organism from a single cell. Pick a cell, dive into the nucleus, and extract the DNA. You can now regrow the entire creature from that tiny sample. There's a math analogy here. Take a function, pick a specific point, and divein.
UNDERSTANDING THE MONTY HALL PROBLEM Understanding the Monty Hall Problem. The Monty Hall problem is a counter-intuitive statistics puzzle: There are 3 doors, behind which are two goats and a car. You pick a door (call it door A). You’re hoping for the car of course. Monty Hall, the game show host, examinesthe other doors (B
VECTOR CALCULUS: UNDERSTANDING THE DOT PRODUCTSEE MORE ONBETTEREXPLAINED.COM
QUICK INSIGHT: SUBTRACTING NEGATIVE NUMBERS For older students, "subtracting a negative" can be seen as "cancelling a debt". If I have a debt of $ 30, and someone "subtracts it", I've effectively gained $ 30. In general, if you remove a disadvantage, you have improved your situation -- a positive. Theseexplanations are a
UNDERSTANDING THE PARETO PRINCIPLE (THE 80/20 RULESEE MORE ONBETTEREXPLAINED.COM
UNDERSTANDING PYTHAGOREAN DISTANCE AND THE GRADIENT Understanding Pythagorean Distance and the Gradient. The Pythagorean Theorem shows how strange our concept of distance is. Using the rule a 2 + b 2 = c 2, we can trade some "a" to get more "b". Starting with. means "A 13-inch pizza equals a 13-inch pizza". Sure. CALCULUS, BETTER EXPLAINED EBOOK + VIDEO COURSE These lessons are based on articles read by millions of readers, and evolved with thousands of comments and direct feedback. Here's what's you'll get in the course: 15-chapter eBook with a professional layout ( sample) 15 video lessons walking through each chapter (2.5 hours total) YouTube. Better Explained. 14.4K subscribers. CALCULUS LEARNING GUIDE Calculus is the art of splitting patterns apart (X-rays, derivatives) and gluing patterns together (Time-lapses, integrals). Sometimes we can cleverly re-arrange the pattern to find a new insight. A circle can be split into rings: And the rings turned into a triangle: Wow! We found the circle's area in a simpler way. LESSON 12: THE BASIC ARITHMETIC OF CALCULUS Chapter 12 The Basic Arithmetic Of Calculus. Remember learning arithmetic? After seeing how to multiply small numbers, we learned how to multiply numbers with several digits: 13 × 15 = ( 10 + 3) ( 10 + 5) = 100 + 30 + 50 + 15. We can’t just combine the first digits (10 A GENTLE INTRODUCTION TO LEARNING CALCULUS A Gentle Introduction To Learning Calculus. I have a love/hate relationship with calculus: it demonstrates the beauty of math and the agony of math education. Calculus relates topics in an elegant, brain-bending manner. My closest analogy is Darwin’s Theory of Evolution: once understood, you start seeing Nature in terms ofsurvival.
HOW TO OPTIMIZE YOUR SITE WITH GZIP COMPRESSION Compression is a simple, effective way to save bandwidth and speed up your site. I hesitated when recommending gzip compression when speeding up your javascript because of problems in older browsers.. But it’s the 21st century. LEARN DIFFICULT CONCEPTS WITH THE ADEPT METHOD Learn Difficult Concepts with the ADEPT Method. After a decade of writing explanations, I’ve simplified the strategy I use to get new concepts to click. Make explanations ADEPT: Use an Analogy, Diagram, Example, Plain-English description, and then a Technical description. Here’s how to teach yourself a difficult idea, or explain one toothers.
UNDERSTANDING ACCOUNTING BASICS (ALOE AND BALANCE SHEETS) A balance sheet is a document that tracks a company's assets, liabilities and owner's equity at a specific point in time. As you know, if the company's has something, it belongs to someone. The sides must balance. So let's do an example. Suppose we start a company with$ 100 cash:
UNDERSTANDING THE BIRTHDAY PARADOX Here are a few lessons from the birthday paradox: n is roughly the number you need to have a 50% chance of a match with n items. 365 is about 20. This comes into play in cryptography for the birthday attack. Even though there are 2 128 (1e38) GUID s, we only have 2 64 (1e19) to use up before a 50% chance of collision. AN INTUITIVE (AND SHORT) EXPLANATION OF BAYES’ THEOREM An Intuitive (and Short) Explanation of Bayes’ Theorem. Bayes’ theorem was the subject of a detailed article. The essay is good, but over 15,000 words long — here’s the condensed version for Bayesian newcomers like myself: Tests are not the event. We have a cancer test, separate from the event of actually having cancer. VECTOR CALCULUS: UNDERSTANDING THE CROSS PRODUCT Taking two vectors, we can write every combination of components in a grid: This completed grid is the outer product, which can be separated into the:. Dot product, the interactions between similar dimensions (x*x, y*y, z*z). Cross product, the interactions between different dimensions (x*y,y*z, z*x, etc.). The dot product ($\vec{a} \cdot \vec{b}$) measures similarity because it only__Menu
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PYTHAGOREAN THEOREM AS SWEEPING AREAJune 19th, 2019|
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INTUITION FOR THE QUADRATIC FORMULAMay 1st, 2019|
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INTUITION FOR POLYNOMIALSMarch 26th, 2019|
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ANALOGY: MATH AND COOKING February 28th, 2019|*
INTUITION FOR TAYLOR SERIES (DNA ANALOGY)January 23rd, 2019|
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WHAT DOES AN EXPONENT REALLY MEAN?December 6th, 2018|
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INTUITION FOR GRAPHED FUNCTIONSNovember 1st, 2018|
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LEARNING TIP: THE 5 SECOND GUTCHECKOctober 2nd, 2018|
WHY IS BETTEREXPLAINED DIFFERENT? Most lessons offer low-level details in a linear, seemingly logical sequence. Better Explained focuses on the big picture — the Aha! moment — and then the specifics. Here’s the difference: I know which approach keeps my curiosity and enthusiasm. The general strategy is the ADEPT Method: (read about the ADEPT method) Learning isn’t about memorizing facts to pass a test. It’s about unlocking the joy of discovery when an idea finally makes sense. If this approach resonates with you, welcome aboard.ABOUT KALID AZAD
I enjoyed math until a poorly-taught class nearly destroyed that passion. A last-minute Aha! moment showed me math could make sense, even be enjoyable, when presented with: * A friendly, curious attitude * A mix of intuitive and technical understanding * A focus on lasting insight I share explanations that helped, hoping they help you too. I’m thrilled that BetterExplained now reaches millions every year, and has appeared in blogs for the New York Times and Scientific American. Readmore…
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AN INTUITIVE GUIDE TO LINEAR ALGEBRA*
INTUITIVE UNDERSTANDING OF EULER’S FORMULA*
DEVELOPING YOUR INTUITION FOR MATH*
INTUITIVE GUIDE TO ANGLES, DEGREES AND RADIANS*
A VISUAL, INTUITIVE GUIDE TO IMAGINARY NUMBERS*
RETHINKING ARITHMETIC: A VISUAL GUIDE*
SURPRISING USES OF THE PYTHAGOREAN THEOREM*
DEMYSTIFYING THE NATURAL LOGARITHM (LN)*
AN INTUITIVE (AND SHORT) EXPLANATION OF BAYES’ THEOREM*
AN INTUITIVE GUIDE TO EXPONENTIAL FUNCTIONS & EINTUITIVE LEARNING
ADEPT METHOD
Learning starts with an analogy.WHY LEARN MATH?
Vocabulary for thinkingMATH INTUITION
Start with the cat, not its DNA BOW & ARROW INTUITION First, have a good shot.PENCIL, THEN INK
Don't hide the processANALOGIES
Useful, even if "wrong"CARTOONS
Simplify ideas to a caricature INTUITION ISN'T OPTIONAL The recipe for knowledge that lasts. ARITHMETIC & NUMBERS MENTAL MATH SHORTCUTS A few memorable conversionsSUM 1 TO 100
Rearrange to simplifyVISUAL ARITHMETIC
Every operation is a transformationSENSE OF SCALE
Bring large numbers down to everyday termsFENCEPOST PROBLEM
Counting spans or points?NUMBER SYSTEMS
When the odometer ticks overEVERYDAY LOGARITHMS
Counting digits
MODULAR ARITHMETIC
Variations on clocksALGEBRA & COUNTING
COMBINATIONS
Multiply possibilities, divide redundanciesPRIMES
Atoms within numbersTHE EQUALS SIGN
Set, check, or define?FACTORING EQUATIONS
Break down the tepee PARAMETRIC EQUATIONS Extract the true causeTYPES OF GRAPHS
Map (distance matters) or non-mapSQUARE NUMBERS
Use geometry, algebra, calculusNAVIGATE A GRID
Convert decisions to letters & permute COMBINATIONS & MULTIPLICATIONChoices multiply.
RATIOS
How much oomph, how often?GEOMETRY
PYTHAGOREAN THEOREM
How every shape changes PYTHAGOREAN DISTANCE Compare any quantitiesSIMILARITY
Step back. Smaller shape, same ratios.PYTHAGOREAN RESCALE
Work from a unit triangle PRECALCULUS & TRIGONOMETRYRADIANS
Angles from the mover’s perspectiveFINDING PI
Surround that critterSINE WAVES
The natural sway found in circles, springsTHE NUMBER E
Perfectly smooth growthNATURAL LOG
Time needed to grow
IMAGINARY NUMBERS
Numbers can rotate
COMPLEX NUMBERS
Arithmetic goes 2d
COMPLEX MULTIPLICATIONScale & rotate
EXPONENTS
Grow numbers in the expand-o-tron THINK WITH EXPONENTS Logs are causes, exponents are effectsTRIGONOMETRY
Visualize a dome, wall, and ceilingLAW OF SINES
Every angle has an equal perspective.LAW OF COSINES
Keep track of interacting parts.TRIG IDENTITIES
Draw the circles yourself.STATISTICS
STATISTICS
See footprints, guess the animalAVERAGES
"Typical" depends on the relationshipBIRTHDAY PARADOX
23 people, many possibilitiesBAYES THEOREM
Extra info? Adjust the odds. SHORT BAYES’ THEOREM Track new info in a tableMONTY HALL
Original door vs. best of the other twoCALCULUS COURSE
CALCULUS GUIDE
Learn the basics, fast.LESSON 1
1-Minute Summary
LESSON 2
X-Ray Vision
LESSON 3
3D intuition
LESSON 4
Integrals, DerivativesLESSON 5
Computer Notation
LESSON 6
Improved Algebra
LESSON 7
Linear Changes
LESSON 8
Squared Changes
LESSON 9
Infinity
LESSON 10
Derivatives
LESSON 11
Fundamental Theorem of CalculusLESSON 12
Rules: Add, Multiply, InvertLESSON 13
Patterns In the RulesLESSON 14
Rules: Powers, DivisionLESSON 15
Archimedes' FormulasCALCULUS SUMMARY
The big insights. All together now.CALCULUS (ARTICLES)
1 MINUTE CALCULUS
Analyze patterns with x-ray and time-lapse vision0.999… = 1?
What's your number system?LIMITS
Guess what happened when you blinked LIMITS / INFINITESIMALS Make a model perfectINTEGRATION
Piece-by-piece multiplicationDERIVATIVE INTRO
Measurements depend on the instrumentDERIVATIVES II
Imagine linked machinesDERIVATIVES III
Quotient, exponents, logs CALCULUS BANK ACCOUNT Raises change income, changing the balanceVECTOR CALCULUS
CIRCULATION & CURL
Total twist, twist at a pointTHE GRADIENT
Microwave the doughboy, quickGRADIENT DETAILS
Follow the best tradeoffFLUX
Amount of bananas crossing a surfaceDIVERGENCE
Flux per unit volumeDOT PRODUCT
Mario Kart speed boostCROSS PRODUCT
All the uneven parts ENGINEERING / UNIVERSITY MATHLINEAR ALGEBRA
Math with mini-spreadsheetsEULER’S FORMULA
Imaginary exponents make circlesFOURIER TRANSFORM
Patterns have circular ingredientsPROGRAMMING TOOLS
VERSION CONTROL
Track files over timeDISTRIBUTED VCS
Pass around changes
GIT INSIGHTS
#1: There's a staging areaGDB DEBUGGING
A quickstart guide
WEB DEVELOPMENT
FASTER JAVASCRIPT
Minify, compress, move to endHTTP CACHING
Don't redownload until expiredGZIP COMPRESSION
Zip files before sending STARTING RUBY ON RAILS Get past the gotchasUNDERSTANDING MVC
Fat models, thin controller, thin view JAVASCRIPT REFERENCE1-page summary
LOAD XML/JSON
Treat a script as dataXSRF ATTACKS
Attacker spoofs a legit request DEBUGGING WITH FIREFOXUse firebug
MAKING BOOKMARKLETS
A quick javascript snippet LOW-LEVEL PROGRAMMINGGUIDS
You'll never run out. Ever.BINARY FILES
Space efficiency vs. marshallingBYTE ORDER
Computers speak different languagesUNICODE
Not every char is 2 bytesXOR SWAP
Cleverness, not for real lifeFAST 1/SQRT(X)
Newton's method, magic initializerSYMBOL TABLES
Deobfuscate object codeNETWORKING
Telnet is an IM conversationBUSINESS
RULE OF 72
time = 72/interest
PARETO PRINCIPLE
Sometimes 80% is enoughSTOCK MARKET
A transparent store
ACCOUNTING BASICS
Everything is owned by someoneINTEREST RATES
A formula for every type of interestDEBT & LEVERAGE
Invested debt multiplies returnASSORTED MUSINGS
KNOW THYSELF
If you're Hulk, be Hulk. SIMPLICITY VS. COMPLEXITY Complexity, not power, is the enemy.NOTES ON HAPPINESS
Passion, foolishness, dancing BREVITY IS BEAUTIFULZero guilt.
“If you can't explain it simply, you don't understand it well enough.” —Einstein (more ) | Privacy |CC-BY-NC-SA
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