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Math, Better Explained: Learn to Unlock Your Math Intuition
"Math, Better Explained" is a clear, intuitive guide to math topics essential for high school, college and beyond. Whether you're a student, parent, or teacher, this book is your key to unlocking the aha! moments that make math truly click -- and make learning enjoyable.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 Intuition2. The Pythagorean Theorem3. Pythagorean Distance4. Radians and Degrees5. Imaginary Numbers6. Complex Arithmetic7. Exponential Functions & e8. The Natural Logarithm (ln)9. Interest Rates10. Understanding Exponents11. Euler
98 pages, Paperback
First published December 6, 2011
194 people are currently reading
1318 people want to read
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Displaying 1 - 30 of 40 reviews
May 6, 2020
3.4 stars. Math better explained but NOT MUCH better.
An interesting book that I think would work much better if read alongside a more rigorous math text. It has some interesting parts but the examples offer no practical help and all the joking around gets tiresome after a while. The chapters about interest rates and the natural logarithm were particularly good.
An interesting book that I think would work much better if read alongside a more rigorous math text. It has some interesting parts but the examples offer no practical help and all the joking around gets tiresome after a while. The chapters about interest rates and the natural logarithm were particularly good.
June 30, 2015
Kalid made an amazing job in developing mathematical intuition. Looking at math concepts the way the scientist first discovered them is much beneficial to learners than the rigorous proofs!
I like what he said at the end of the book:
"We’ve created complex mechanical constructs to “rigorously” prove Calcu-
lus, but have lost our intuition in the process"
For more and recent articles, visit Kalid website: http://betterexplained.com/
Happy Math :)
I like what he said at the end of the book:
"We’ve created complex mechanical constructs to “rigorously” prove Calcu-
lus, but have lost our intuition in the process"
For more and recent articles, visit Kalid website: http://betterexplained.com/
Happy Math :)
February 25, 2019
This book is an outstanding demonstration of how math should be taught at the beginner level. Memorizing formulas and working out contrived examples do not help us truly understand the beauty of mathematics. We MUST dig deeper beyond the surface and into the INTUITION! That way results can flow naturally out of our understanding, and instead of looking at a gibberish formula, we can say AHA! That makes perfect sense, and DAMN that is SO cool! I never would have guessed those ideas were connected in such a way! Formulas, examples, proofs, and rigor all have their place, but we must first start by "just plain talkin'"
Kalid Azad has a wonderful way of building intuition for math concepts. In this book he discusses concepts such as the pythagorean theorem, radians, and exponential growth. He even took on the most elegant and grand formula in all of mathematics: Euler's formula. Believe it or not, he was able to tie everything together to make sense of how the heck "e" raised to the imaginary number "i" multiplied by pi is somehow a clean -1! Like... what!? Yea... that's mathematics for ya! Crazy seemingly unrelated ideas can join together to create something truly amazing.
Anyway, this book is definitely worth the read, and it's not necessary to have a strong background in mathematics because like I said, Azad understands that before we bring in the rigor, we must first have a conversation.
"Knowledge isn’t about acing a quiz: it’s about letting ideas become natural and automatic extensions to the way you think. New concepts snap into place because they’re based on a solid intuitive foundation, not a fragile memorized one."
Kalid Azad has a wonderful way of building intuition for math concepts. In this book he discusses concepts such as the pythagorean theorem, radians, and exponential growth. He even took on the most elegant and grand formula in all of mathematics: Euler's formula. Believe it or not, he was able to tie everything together to make sense of how the heck "e" raised to the imaginary number "i" multiplied by pi is somehow a clean -1! Like... what!? Yea... that's mathematics for ya! Crazy seemingly unrelated ideas can join together to create something truly amazing.
Anyway, this book is definitely worth the read, and it's not necessary to have a strong background in mathematics because like I said, Azad understands that before we bring in the rigor, we must first have a conversation.
"Knowledge isn’t about acing a quiz: it’s about letting ideas become natural and automatic extensions to the way you think. New concepts snap into place because they’re based on a solid intuitive foundation, not a fragile memorized one."
October 23, 2014
It's a book that I've been skimming from time to time from over a year now and recently I made a serious review and finished the whole text.
Each time it was such a joy to read, because it puts a completely new, intuitive perspective on ideas that seem boring and grinding on the surface, such as imaginary numbers. (but that's just the problem with math education)
Be notified that is not a textbook - this book should be used as intuitive introduction into various areas of mathematics, that will help you better appreciate the baffling equations and keep you motivated, because you will know that there is such a depth underneath these abstract concepts.
Kalid was a better teacher through these pages than any kind of classroom math studying - and I honestly think that it would've been much better to have such a book for a high school textbook instead of a standard one - because not everyone has to be doing math and not everyone will even touch math after getting a diploma - but at least he'd have a rough, approximate understanding of what mathematics really is, why it's so important in the modern world and that it isn't boring in the least - it's just the way it is presented to most of us.
Each time it was such a joy to read, because it puts a completely new, intuitive perspective on ideas that seem boring and grinding on the surface, such as imaginary numbers. (but that's just the problem with math education)
Be notified that is not a textbook - this book should be used as intuitive introduction into various areas of mathematics, that will help you better appreciate the baffling equations and keep you motivated, because you will know that there is such a depth underneath these abstract concepts.
Kalid was a better teacher through these pages than any kind of classroom math studying - and I honestly think that it would've been much better to have such a book for a high school textbook instead of a standard one - because not everyone has to be doing math and not everyone will even touch math after getting a diploma - but at least he'd have a rough, approximate understanding of what mathematics really is, why it's so important in the modern world and that it isn't boring in the least - it's just the way it is presented to most of us.
August 5, 2024
Short and sweet set of intuitive models for some math topics such as imaginary numbers and e/ln(x). Not every explanation clicked for me, but still a very pragmatic approach to developing a conceptual understanding.
Definitely more of a supplement to a more computationally-inclined text than a full replacement.
Definitely more of a supplement to a more computationally-inclined text than a full replacement.
February 22, 2021
A short book that gives an intuition on Pythagorian theorem, e, ln(x), radians/degrees, Euler's formula. Written in a rather easy language with a lot of pictures/graphs.
It's like 3blue1brown videos, even simpler explained.
It's like 3blue1brown videos, even simpler explained.
April 1, 2016
author tried to be hilarious , he made just one point that intuition does helps. But he confused me more than the Maths Textbooks i had to face in school. Three Stars Because , there were some origins Which were very well explained !
July 9, 2016
Great little read! Wish I could have read this years back; before I learned some of these concepts the harder way, or just took longer to arrive at the interesting ways to look at various maths concepts. A job well done by the author! Recommended.
April 8, 2018
Excellent book
The book delves into a high school math education. It takes topics that from the outset look unintuitive, and makes them intuitive. I really liked the explanation of e & ln.
The book delves into a high school math education. It takes topics that from the outset look unintuitive, and makes them intuitive. I really liked the explanation of e & ln.
May 25, 2015
A little bit overkill sometimes, but definitely thought provoking.
December 5, 2019
A good and fun book to learn about the intuition behind common math concepts such as logarithm, Euler's number / Napier's constant, Euler's formula, imaginary numbers, and growth rates. If this book is the first serving of these topics, then the reader should be ready to work out calculations on pen and paper to grok the intuition behind the topics. If not, then paying attention should suffice to grok the intuition behind the topics. All of the covered topics are accessible as promised with the exception of Euler's formula being a bit hurried and the language used in growth rates being a bit complex.
Ideal for math enthusiasts and for math/science-oriented middle/high schoolers
Ideal for math enthusiasts and for math/science-oriented middle/high schoolers
August 29, 2022
To quote the author, "Knowledge isn’t about acing a quiz: it’s about letting ideas become natural and automatic extensions to the way you think. New concepts snap into place because they’re based on a solid intuitive foundation, not a fragile memorized one."
A short book that explains Mathematical ideas in an intuitive way. I cannot emphasize how much I appreciated the author's approach to explain these mathematical concepts that I had to learn the non-intuitive way. I wish the author huge success so he can write a second and a third part to this book.
A short book that explains Mathematical ideas in an intuitive way. I cannot emphasize how much I appreciated the author's approach to explain these mathematical concepts that I had to learn the non-intuitive way. I wish the author huge success so he can write a second and a third part to this book.
Read
January 9, 2025#cal 2024.02.06.
#w [ euler's formula . rule of 72 . bacteria can split and double in 24 hours . conjucate . space mars 680 degrees longer days . circle 360 degrees years 365 days . the area of any shape is any line segment squared . Pythagoras theorem works on any shape / formula that squares with a number ]
#$ [ APY and pay early #$ APR speed that money grows #$ pay mortgage beginning of month #$ compound growth #$ interest trajectory #$ annual percentage yield #$ annual percentage rate . graph results ]
#me we get twice as many noodles if we fold them in half
#w [ euler's formula . rule of 72 . bacteria can split and double in 24 hours . conjucate . space mars 680 degrees longer days . circle 360 degrees years 365 days . the area of any shape is any line segment squared . Pythagoras theorem works on any shape / formula that squares with a number ]
#$ [ APY and pay early #$ APR speed that money grows #$ pay mortgage beginning of month #$ compound growth #$ interest trajectory #$ annual percentage yield #$ annual percentage rate . graph results ]
#me we get twice as many noodles if we fold them in half
September 23, 2020
One who runs away from maths sink this book in don't consume it at once take some time for intuition to develop. This book is the math teacher we all imagined we had but never had.
very basic concepts are explained but they may shake the foundation of our perception of those concepts and let us rethink our whole model of maths we created in our mind.
this is really math better explained.
very basic concepts are explained but they may shake the foundation of our perception of those concepts and let us rethink our whole model of maths we created in our mind.
this is really math better explained.
June 2, 2022
This book is an example of how Maths should be taught in schools! in an engaging refreshing and interesting way, I was able to understand certain really brilliant mathematical ideas like Euler's formula, imaginary numbers, etc in a lucid way which was rather scary for me years ago! now ready to delve deeper into the amazing world of Mathematics!
November 3, 2018
Beat book I’ve read in years
It’s been a while since I took a look at math since university. This approach is really enlightening. I’m so glad to get into this book. Amazing book. Thanks a lot.
It’s been a while since I took a look at math since university. This approach is really enlightening. I’m so glad to get into this book. Amazing book. Thanks a lot.
December 19, 2019
Fun and intuitive introduction to some of the most useful math rules and constants applicable in real-life scenarios, such as taking a bank loan. Some of the explanations seemed a bit unclear and would definitely benefit from some more visualisations/graphs illustrating the problem essence.
December 27, 2020
Much needed method
Kalid Azad has opened up math understanding for a much wider audience than traditional teaching methods can. His books are a service to humanity. If you're interested in math, buy them.
Kalid Azad has opened up math understanding for a much wider audience than traditional teaching methods can. His books are a service to humanity. If you're interested in math, buy them.
July 26, 2017
Nice, short, and to the point. It does indeed help with understanding math. Guess will read again when Eliott is ready to understand things.
This entire review has been hidden because of spoilers.
June 8, 2020
Inspiring, easy to read, amazing
May 20, 2023
tl:dr version:
Look at modern application of concepts and connect concept to a flexible idea/understanding if it doesn't click initially.
Look at modern application of concepts and connect concept to a flexible idea/understanding if it doesn't click initially.
March 7, 2024
Excellent book. Wish I read this earlier when I was still in school 😂 But better late than never 👏
October 7, 2016
ڕەنگە هەڵە نەبم ئەگەر بلێم ئەستەمە ئەم شتانە لەمە ڕوونتر و سادەتر و جوانتر باس بکرێن، بەم شێوازە باسکردنە هەموو کەس دەتوانێت لە قورسترین و نامۆترین و بێزراوترین شتەکانی ماتماتیک تێبگات، بۆ نمونە شتانێکی وەک
e
یاخود
ln
کە زۆرێک هەر بە بیستنی ناویان یان بینینیان گیانیان ئێش ئەکات. لێرە زۆر بە شێوازێکی سادە لەو شتە بنچینەییە قورسانە تێدەگەیت و هەر شتێک لەوانەی کە لەم کتێبەدا باس کراون ئەگەر دواتر لە هاوکێشەیەکدا بیانبینیت یەکسەر تێدەگەیت بۆ دەبێ لەو هاوکێشەیەدا یان لە وەسفی فڵان دیاردەدا ئەمە بەکار بهێنرێت و ڕۆڵی ئەمە چییە و چۆن وەسفی بابەتەکە دەکات.
هەر بۆیە بە ڕای من پێویستە هەموو کەسێک کە لە هەر ئاستێکدا دەرگیری ماتماتیک دەبێت ئەم کتێبە بخوێنێتەوە. سەرەڕای ئەوەی کتێبەکە لە ١٠٠ لاپەڕە کەمترە بەڵام شتانێکی زۆر گرنگ و بنچینەییت زۆر بە تێگەیاندنێکی باشەوە بۆ ڕوون دەکاتەوە، جا ئەگەر کاتی خۆی کە ئەم بابەتانەمان لە خوێندنگا یان لە زانکۆ دەخوێند شتێکی وا بەردەست بوایە یان کەسێک هەبوایە بەم شێوەیە باسی ئەم بابەتانە یان هەر بابەتێکی تری ماتماتیکی بکردایە، ئەوا زۆر کاتمان بۆ دەگەڕایەوە و دەکرا لە زۆرێک لە شتەکان زۆر جیاوز لەم بە حساب تێگەیشتنەی ئێستا تێبگەین.
e
یاخود
ln
کە زۆرێک هەر بە بیستنی ناویان یان بینینیان گیانیان ئێش ئەکات. لێرە زۆر بە شێوازێکی سادە لەو شتە بنچینەییە قورسانە تێدەگەیت و هەر شتێک لەوانەی کە لەم کتێبەدا باس کراون ئەگەر دواتر لە هاوکێشەیەکدا بیانبینیت یەکسەر تێدەگەیت بۆ دەبێ لەو هاوکێشەیەدا یان لە وەسفی فڵان دیاردەدا ئەمە بەکار بهێنرێت و ڕۆڵی ئەمە چییە و چۆن وەسفی بابەتەکە دەکات.
هەر بۆیە بە ڕای من پێویستە هەموو کەسێک کە لە هەر ئاستێکدا دەرگیری ماتماتیک دەبێت ئەم کتێبە بخوێنێتەوە. سەرەڕای ئەوەی کتێبەکە لە ١٠٠ لاپەڕە کەمترە بەڵام شتانێکی زۆر گرنگ و بنچینەییت زۆر بە تێگەیاندنێکی باشەوە بۆ ڕوون دەکاتەوە، جا ئەگەر کاتی خۆی کە ئەم بابەتانەمان لە خوێندنگا یان لە زانکۆ دەخوێند شتێکی وا بەردەست بوایە یان کەسێک هەبوایە بەم شێوەیە باسی ئەم بابەتانە یان هەر بابەتێکی تری ماتماتیکی بکردایە، ئەوا زۆر کاتمان بۆ دەگەڕایەوە و دەکرا لە زۆرێک لە شتەکان زۆر جیاوز لەم بە حساب تێگەیشتنەی ئێستا تێبگەین.
June 12, 2016
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.
2. What radians really are and the insights into trigonometry. His website talks trigonometry in lot more detail and that was mind blowing.
3. It's about 'i' - I never understood complex numbers and it's use. This book demystifies 'i'.
4. 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.
Here are some of the things I learnt:
1. Pythagoras theorem is not just about right triangles, but lot more than that.
2. What radians really are and the insights into trigonometry. His website talks trigonometry in lot more detail and that was mind blowing.
3. It's about 'i' - I never understood complex numbers and it's use. This book demystifies 'i'.
4. 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.
April 1, 2013
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."
It's a little perverse though: unless you've actually strugged w/ the nonsensical way they teach algebra, geometry, and trigonometry in high school, you might not appreciate the ways Azad links seemingly disparate subjects.
Too short, IMO, but a perfect bridge for a high school graduate about to start college.
"Children are expected to cope with mathematics that drove educated adults insane hundreds of years ago."
It's a little perverse though: unless you've actually strugged w/ the nonsensical way they teach algebra, geometry, and trigonometry in high school, you might not appreciate the ways Azad links seemingly disparate subjects.
Too short, IMO, but a perfect bridge for a high school graduate about to start college.
December 2, 2016
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 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.
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 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.
March 1, 2013
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 it, but not so good for bringing in the outsider.
January 7, 2015
...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...
[see my entire review up at MAA Reviews]
[see my entire review up at MAA Reviews]
August 3, 2016
Absolutely, jaw-droppingly fantastic. I've a BSC in Engineering, but I struggled with math throughout my whole education. This short (but very dense!) book caused so many AHA! moments, I can't even start to count them. 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.
July 5, 2015
Shorter than expected but feels very rewarding. A playful return to a subject long time not practiced, in my case.
Much of physics (and life!) involves leaving your perspective and seeing things from another viewpoint.
Left me wanting more.
Throughout our school life we think the Pythagorean Theorem is about triangles and geometry. It’s not.
Much of physics (and life!) involves leaving your perspective and seeing things from another viewpoint.
Left me wanting more.
Throughout our school life we think the Pythagorean Theorem is about triangles and geometry. It’s not.
Displaying 1 - 30 of 40 reviews