We can check this works. Definition 4: Define e using the natural log This definition is the most gnarly: instead of talking about e directly, we work backwards.
In other words: Here, e is the "base of the natural logarithm". Trace the similarities I feel comfortable with an idea when I can hop between definitions and notice similarities.
Happy math. Continuous Growth What does an exponent really mean? Q: Why is e special? Join k Monthly Readers Enjoy the article? There's plenty more to help you build a lasting, intuitive understanding of math. Join the newsletter for bonus content and the latest updates. Join for Free Lessons. Green The 25 cents Mr. Green made Mr. Month 4: Mr. Green, shoveling along 33 cents.
Month 8: Mr. Blue earns another 33 cents and gives it to Mr. Green, bringing Mr. Green up to 66 cents. This 11 cents becomes Mr. Month Things get a bit crazy. Blue earns another 33 cents and shovels it to Mr. Green to a full dollar. This 22 cents gets added to Mr. Red, who now totals 33 cents. And Mr. The newly-created money can earn money of its own, and on the cycle goes. I like to think of the original amount Mr. Blue as never changing.
Blue shovels money to create Mr. Green, a steady 33 every 4 months since Mr. Blue does not change. In the diagram, Mr. Blue has a blue arrow showing how he feeds Mr. Green just happens to create and feed Mr.
Red green arrow , but Mr. As Mr. Green grows over time being constantly fed by Mr. Blue , he contributes more and more to Mr. Between months Mr. Green gives 11 cents to Mr. Green gives 22 cents to Mr. Red, since Mr. Green was at 66 cents during Month 8. If we expanded the chart, Mr. Green would give 33 cents to Mr. Green reached a full dollar by Month Can We Get Infinite Money?
Enter pincode. Usually delivered in 8 days? JaroBooks 2. Whether you're a student, parent, or teacher, this book is your key to unlocking the aha! The book intentionally avoids mindless definitions and focuses on building a deep, natural intuition so you can integrate the ideas into your everyday thinking.
Its explanations on the natural logarithm, imaginary numbers, exponents and the Pythagorean Theorem are among the most-visited in the world.
The topics in Math, Better Explained include: 1. Developing Math Intuition 2. I am developing a strong inclination towards understanding the basic concepts of mathematics. I'm looking for books and blogs that quench this thirst of mine. I hit Khalid's blog - it was like a whole new world. Here are some of the things I learnt: 1. Pythagoras theorem is not just about right triangles, but lot more than that. What radians really are and the insights into trigonometry. His website talks trigonometry in lot more detail and that was mind blowing.
It's about 'i' - I never under I am developing a strong inclination towards understanding the basic concepts of mathematics. It's about 'i' - I never understood complex numbers and it's use. This book demystifies 'i'. The exponent e and the plethora of its uses and implications. I know the author has a book on Calculus as well and I'll definitely read it. Khalid, any plans to write a book about Statistics?
I'm sure thousands will be enlightened by your way of thinking the most common and yet the least understood subject of probability. Mar 31, Jean-Luc rated it really liked it. The author, Kalid Azad, claims he wrote this book because he was tired of seeing students "learn" by rote memorization, and he wanted to help people understand the simple beauty behind basic mathematical concepts.
I believe this quote is what really drove him to create his blog and this book: "Children are expected to cope with mathematics that drove educated adults insane hundreds of years ago.
Too short, IMO, but a perfect bridge for a high school graduate about to start college. Dec 01, Janis rated it it was amazing. High school revisited from a whole new perspective Math was my strong side when I was younger. With every new formula and equation I gradually lost it.
My college years was a big confusion all together. This book revived my interest in algebra again, showing fresh new ways of looking at well known things. I'd recommend this book to any student, parent, or teacher. This will give you a solid ground to build upon. This is about principles understanding not formulas remembering. I gave five stars High school revisited from a whole new perspective Math was my strong side when I was younger. I gave five stars because this book was a clear and enlightening experience for me.
I'm eager to read the next book about calculus from the same author. Feb 28, Daftwullie rated it liked it. I'm not sure that it really is better explained. I think it depends on your purpose for reading. If you have ever learned the math and you want a refresher or want to play with the ideas, then the style is fun and engaging. However, I was looking for context and reasoning behind and around the math to enrich my kids' education.
It's not so great for that purpose. I moves too fast and shifts around within the topic too much. It's more like an inside joke--fun for the people who are already in on I'm not sure that it really is better explained. It's more like an inside joke--fun for the people who are already in on it, but not so good for bringing in the outsider.
Parents can find their own path to insight here while teachers may find some classroom capsules to enliven lectures. The author tries very hard, almost with exasperation, to avoid any definition without motivation, any explanation with linkage to intuition. Azad excitedly brings light to imaginary numbers as the arithmetic of rotation, natural logarithms in terms of time to grow, and exponentials as growth over time Absolutely, jaw-droppingly fantastic.
This short but very dense! Will definitely reread it, as this was just a "first immersion", when I will need it. Brilliant, and absolutely recommended to everyone who just wants to understand our world a bit better. Oct 18, Dave Murray rated it really liked it. An enjoyable math book I enjoyed reading this and recommend reading it twice it's short. Once without getting carried away with detail to see where it all goes.
0コメント