Math, BetterExplained eBook Available!
Learn math intuitively. Math, BetterExplained captures key insights as a readable, printable ebook. It's not another math course -- experience the "aha!" moments that make ideas actually click.
You could never forget what a circle is for, right? I want you to have the same realization about e, the natural log, imaginary numbers, and more.
What's inside?
- 12 chapters drawn from the blog articles, essential to any student:
- Contents
- Introduction
- 1. Developing Math Intuition (Chapter preview)
- 2. The Pythagorean Theorem
- 3. Pythagorean Distance
- 4. Radians and Degrees
- 5. Imaginary Numbers
- 6. Complex Arithmetic
- 7. Exponential Functions & e
- 8. The Natural Logarithm (ln)
- 9. Interest Rates
- 10. Understanding Exponents
- 11. Euler’s Formula
- 12. Introduction To Calculus
- Afterword
- A bonus chapter on Euler's Formula, tying the above concepts together
- Print-quality design made for easy onscreen reading & printing
- PowerPoint slides and images for all diagrams used in the chapters (deluxe version)
Who's it for?
- Students: Save hours of frustration -- get things as I wish they were explained to me.
- Teachers/Home Schoolers: Get high-quality educational materials & ideas for your lesson plans.
- Self-learners: Go back and understand concepts at a level rarely discussed in textbooks or classrooms.
Testimonials
Doug Hogg, Former PrincipalI have several books on calculus (Calculus for Dummys, Math for the Millions, etc. etc. - never was able to read them) but your explanation is what I have needed all these years.
Ferose Khan JI am an engineer by profession... but never had that a-ha moment. I had it when I read your article. I don't have words to explain my happiness, you have unwound a knot that was tied 12 years before...
C. DhavejiThis is a great explanation! I am 49 years old and have never known what e is all about. It is thanks to your article that I get it and now can explain it to my son who is 13 years old...
Daniel EzellI've been following you for nearly two years...I find the intuitive approach to the subject and lucid writing unparalleled.
@mugunthkumarOne of the best e-books I've ever read in my life...
@anoemiJust started reading the ebook Math Better Explained by Kalid Azad, loving it so far
Explanations That Work
The explanations inside have been developed after years of study, and are consistently among the most popular in their field. I use analogies and diagrams to make concepts click: we're visual creatures, let's use that part of our brain!
For example: Concepts like imaginary numbers just pop into place when you see them as numbers in two dimensions:
We're used to the number line stretching left-to-right; when it spreads vertically, new numbers emerge. This simple insight saves hours of frustration when visualizing imaginary numbers.
Written For Human Beings
Rigid, stiff writing is uncomfortable for us both. I explain the way I wish I was taught: clearly, concisely, and with a sense of humor. Let's learn with conversations, not lectures.
For Your Computer, Phone or eReader
I don't like DRM restrictions any more than you. The ebook is an unrestricted PDF and can be enjoyed anywhere.
Quality Design
Some ebooks look like they were copied out of Word -- not this. Book-quality layout and typography mean it's a joy to print and read at your leisure. Readability is king: wide margins give plenty of room to write notes, and whitespace helps the words flow.
About Kalid Azad
I became fascinated with intuitive learning after a tough math class at Princeton University. After cramming for days, the formulas finally clicked -- "Argh! Why couldn't they explain it like that in the first place?" I had to share my insights to save other people my frustration.
That "aha!" moment spawned BetterExplained.com, whose articles have been read by millions worldwide. It's regarded as one of the best places to really understand math. Memorization is fragile, but insights stick.
I've been writing technically for a decade, from chapters in programming textbooks to whitepapers for Microsoft.
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The order goes through Paypal, but an account isn't required. And if you aren't satisfied, contact me for a refund at any time, if you have trouble with your download, or if you pre-ordered the beta but did not receive the final version.
Projects like this help transform BetterExplained into a sustainable venture. Readers have asked if they can donate; instead, I'd prefer you buy the ebook for yourself, a relative, or a friend. Thanks for your support!
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Have a question? Know an explanation that caused your own a-ha moment? Write about it here.
I’ve been following your website for months now; this is excellent news! And since this is the first time I’m posting I just wanted to say thank you Kalid, this site has gotten me excited about math again.
Sebastian Marquez — September 15, 2009 @ 2:31 pm
I’ve been following you for nearly two years. I have several sources for my math explorations (I put them all on the collaborative blog). Still, I find the intuitive approach to the subject and lucid writing unparalleled. What really sets you apart is your excitement about discovery.
I work through your articles with my tutoring students who want to work outside their math curriculum. I eagerly open any new Better Explained article that hits my newsreader. Thank you, Kalid.
Daniel Ezell — September 15, 2009 @ 6:04 pm
Awesome news!! Love your stuff. By chance, will there be a hard copy of the book too?
Karmen Blake — September 15, 2009 @ 8:19 pm
@Sebastian: Thank you for the kind words! You are more than welcome, and I’m really happy you were able to rekindle your interest
.
@Daniel: Thanks so much, it really means a lot to me when teachers are able to help other students learn. I get really excited when I finally get those breakthroughs and am thrilled they’re coming in useful — thanks again!
@Karmen: Thanks! I’d love to produce a hard copy of the ebook, I’m taking this as the first step to get experience with publishing
. If and when the hard copy comes out, I’ll do my best to make sure everyone who got the electronic copy gets a discount on the hardcopy as well.
Kalid — September 15, 2009 @ 9:22 pm
I agree with your comments. I think this is a great idea and would like to see a hard copy one day
I myself am a victim of being a critic to the theories behind math, but this step up approach to understanding it from “outside the box” of number crunching is essential. Thanks Kalid!
Valerie — September 15, 2009 @ 10:26 pm
I’ve been following your website for months.I think it’s great!
meng — September 16, 2009 @ 4:45 am
i just bought your ebook and as i was paying i got the idea that this could be a great concept for an iphone app or interactive ebook. i think its something you might want to consider depending on the book’s success.
hamad — September 16, 2009 @ 3:49 pm
Yes, this is great news. I’ve followed you for quite a while now and was recently thinking to myself that I wish you had a book that would incorporate website topics as well as others! Bought my copy today
Thanks for all your hard work.
ktr — September 16, 2009 @ 8:56 pm
@Valerie: You’re more than welcome! I’d love to see a hard copy too
.
@Meng: Thanks for the support!
@Hamad: That’s a great idea! I had thought about just reading the PDF, but there are so many more things you can do. Now you’ve got me thinking…
@ktr: You’re more than welcome, thanks for the kind words and support!
Kalid — September 17, 2009 @ 12:10 am
That’s great news Kalid!! I really like your blog and your approach towards life & maths
Your ebook will be a cherished collection in my library
Keep up the good work! All the best!
Regards,
Prateek.
Prateek Sharma — September 17, 2009 @ 1:03 am
@Prateek: Thanks for the note — I really appreciate your encouragement!
Kalid — September 17, 2009 @ 1:24 am
What do you use for typesetting ? (Just curious).
uwe — September 17, 2009 @ 4:14 pm
@uwe: The ebook was created using Adobe InDesign. I hired a designer, James Wondrack, to make the template.
Kalid — September 18, 2009 @ 1:11 pm
this will be money well spent.
Kenneth Rochester — September 21, 2009 @ 7:43 pm
Hi,
You seem to link to the articles on the website from the book. It would be a good idea to to have those articles included in the book because its very annoying to click those links.
I’ve been reading this site for some time now. Keep up the good work!
Maulin — September 22, 2009 @ 5:41 pm
@Maulin: Thanks for the feedback! Yes, I’ll be changing the links to be to the other chapters — I appreciate the note!
Kalid — September 24, 2009 @ 3:17 am
when can we expect a full version to be released?
John — September 24, 2009 @ 12:32 pm
@John: I’ve gotten some great feedback and am going to be doing some work to make the ebook very printer-friendly. I think there’ll be another beta coming out in early October, and assuming all goes well, the final version should be released near the end of that month or in early November.
Kalid — September 24, 2009 @ 1:46 pm
Hi Khalid,
I’ve just come across your site by recommendation through reddit. I really appreciate the work you’re putting in. I know my maths as much as I need to, but I’ve just bought your ebook because you explain concepts better than I do to my students.
I hope to send you tips and feedback for the final version!
Thanks,
Afsar
Afsar — September 24, 2009 @ 2:31 pm
Khalid,
thank you for releasing this – i have found this site endlessly useful. You put things in a way that just fits!
Its good to buy an ebook to take away with me and have things put into a more structured and familiar form (take as a compliment). Worth ever £ and i will be recommending to many!!
Kind Regards,
Doug
Douglas Rae — September 24, 2009 @ 3:03 pm
@Afsar: Thanks for the comment! I’m happy if anything can be used to help your students. Feedback is definitely welcome!
@Doug: You’re welcome, thanks for the comment and support! Yes, I want the ebook to be like a portable version of the site, I have some changes to the beta coming up that will help with just that
.
Kalid — September 26, 2009 @ 2:06 pm
I have some decent intuition (beyond the proofs
) of the Chain and Power rules for derivatives. Just thought I’d share, whether or not you already know.
Chain: This “rule” is really the simple concept of “correcting” for different variables when you’re looking at relationships. It says that d/dx f(g(x)) = f’(g(x)) times g’(x)
In other words, figure out the direct relationship between f and g, not thinking about x just yet, then multiply by the relationship between g and x.
Example: Let’s say Al takes 3 steps whenever Bill takes 1 step. That would mean the ratio of Al to Bill is 3:1, and if Al were the y-axis and Bill were x, then there would be a line of slope 3/1. Now let’s say that _Bill_ takes 2 steps whenever Carrie takes 1 step.
The question is, how many steps does _Al_ take when Carrie takes 1 step?
Not hard. When Carrie takes 1 step, Bill takes 2 steps. And when Bill takes 2 steps, Al will have to take 6 steps!
Rate of A wrt B = 3
Rate of B wrt C = 2
Rate of A wrt C = (3)(2) = 6
Maybe it’s already obvious to you and everyone else, but judging by the misleading use of the word “rule” to describe this simple concept, I can’t be too sure. Tell me if I haven’t been clear and detailed enough.
Power: Geez, I wish I could draw a picture. This is a new insight, and I have only a visual, rather than arithmetical, intuition. It says that d/dx x^n = nx^(n-1)
Looks really weird, and the best proof I’ve seen uses the binomial theorem, but hopefully it’ll make more sense now, if it doesn’t already. (You know so much!)
Imagine a square, x^2, to start. Imagine the side of the square grow a tiny bit, which will be “dx”. How much does the area of the square increase? Well, there are two parts to this; two rectangles are formed, each with a long side of x (the side of the square) and a short side of dx, along with a super small square of side dx. Think (a+b)^2=a^2+2ab+b^2. The key point here is that dx^2 so small, you don’t even have to think about it. So the square grows by two thin rectangles with total area 2xdx. But the derivative is a ratio, which means when you compare the amount the area grows, 2xdx, to the amount the side grows, dx, you get 2x. Imagine two _lines_ bulging out of the sides of the square! 2x!
Look at a cube, x^3. Using the same logic, imagine three _squares_ bulging out of the faces of the cube! 3x^2!
This is the pattern: If x^n is your n-dimensional object, and x is the length of a side, then the area/volume of each bulging cross section is x^(n-1)dx. Actually, this has the same number of dimensions, except one of the sides is now the growth in x. How many bulges will we need? One for each dimension, n (visualize the cube).
You might have figured this out yourself by now, if this blog is any indication. Just wanted to share anyway. I’m a 16 yr old homeschooler, and after I first met you via your post on e a while back, I really got inspired to truly become comfortable with math, instead of just preparing for the ap tests! I was sort of already trying to understand, but you boosted and energized my efforts. Now I’m past the stage where you think math is a mess of logic, formulas, and conventions, and I still have my whole life ahead of me! Thanks.
Also, a typo I caught in your ebook:
Pg. 1: “Afterward” might be “afterwOrd”
Kent — October 2, 2009 @ 1:34 am
@Kent: Thanks for the note! That’s really, really awesome that you’re starting to see math in this deeper way, I wish I had realized the importance when I was your age. I think you’ll find it helps you in a ton of subjects, not just math — looking for the deeper connections just helps everything click for me.
Chain rule: Yep, that’s a great way to look at it. Another way I’ve found is to think of it as a series of “wiggles”. That is, A moves 3x whenever you “wiggle” B, and B moves 2x whenever you wiggle C. So when you wiggle C just a bit, you get the multiplied effect you mention.
Power rule: That’s exactly how I think about it! For each dimension you have, you gain a “slab” on each side. So for x = 2 (square), you indeed gain 2 slabs, and so on.
It’s really great you’re finding these insights so early
[Thanks for the typo, it's fixed now].
Kalid — October 4, 2009 @ 5:46 pm
great ebook, i have purchase it hope to see more good sharing in the near future….keep it up!
See Zeng Hoe — October 11, 2009 @ 5:47 pm
@See Zeng Hoe: Thanks for the support!
Kalid — October 12, 2009 @ 1:05 am
when the final version will up?
See Zeng Hoe — October 12, 2009 @ 2:35 am
@See Zeng Hoe: I’m pulling in the final round of feedback now, and aiming for late October for the final version.
Kalid — October 12, 2009 @ 5:20 pm
UPDATE: Hi everyone, the final version is now available! If you have purchased a beta copy, you should receive the final version in your email. Please contact me if you didn’t receive it or are having trouble.
Kalid — October 27, 2009 @ 3:36 pm
hi khalid,
Do you plan to publish a new ebook related to math?
See Zeng Hoe — November 6, 2009 @ 2:25 am
@See Zeng Hoe: Yes, I’d love to publish another one — I’m thinking about what to include, and writing a few more posts
.
Kalid — November 7, 2009 @ 4:23 pm
Hi Khalid, I love your website and wanted to buy the Beta version but due to some problems (i.e. my tendency to procrastinate and my absent-mindedness), I didn’t. And now it’s gone up to a price I don’t have a budget for at the moment.. yikes! I’ll definitely buy it coz yr explanations on math concepts simply rock! *is still saving money*
I like a hard copy better tho, so if it’s out, pls announce it here, thanks!
Ami — November 10, 2009 @ 8:40 am
@Ami: Hi, thanks for the comment & feedback! I’m thinking about lowering the price which should hopefully be in the range of more people
. And yep, I’ll definitely be announcing the hard copy as soon as it’s ready.
Kalid — November 10, 2009 @ 3:30 pm
How much of this is articles from the website, other than the extra chapter?
Andy — January 1, 2010 @ 3:59 pm
@Andy: The extra chapter, foreward, and afterward are unique to the book (the premium version also includes the original powerpoint slides used to make the diagrams) . The other chapters are based on the articles, with changes/updates to make them flow nicely in a book format. The primary benefit of the book is having the content in a portable, DRM-free format for comfortable printing and reading. Hope this helps!
Kalid — January 1, 2010 @ 8:51 pm
Cool, I’ll probably pick it up, I’d like to support the site anyway. By the way, you should make a Facebook fan page, I’m sure your readers would be glad to give you a little extra publicity.
Andy — January 1, 2010 @ 10:13 pm
@Andy: Thanks for the support, and great idea on the facebook fan page. I’m traveling now but will probably set one up when I return
.
Kalid — January 2, 2010 @ 7:47 pm
I’m sad because I don’t have a credit card just cash. I think that if I had an organized ebook ot would be easier to understand because I would read in the right order. I can afford the ebook but don’t have a credit card
Seamus — January 13, 2010 @ 8:48 pm
@Seamus: I’ll see what I can do
.
Kalid — January 15, 2010 @ 4:38 pm
@Kent hey man that’s amazing that you’re getting such “deep” insights already. Man seriously, this stuff is what should be taught in schools. These insights are the real deal of what math’s about.
I never got till today any intuitive understanding of the chain or power rule. I only knew the algebraic proofs… I didn’t even think an intuitive understanding was possible.
Frank — February 27, 2010 @ 6:46 pm
put a link to this page on your main navigation, maybe you will get more sales
Anon — March 10, 2010 @ 5:06 pm
@Anon: Good idea, just added!
Kalid — March 11, 2010 @ 2:09 am
Thank you Kalid, very insightful information.
Thaer — March 14, 2010 @ 9:14 pm
@Thaer: You’re more than welcome!
Kalid — March 15, 2010 @ 8:19 pm
I recently was searching something about calculus and when i see this article of introduction to calculus. Its just amazing. I knew that all this Math had some thing basic like this which we were not told in our classes. But ur description is just awesome.Keep up the good work.
Anirudh — May 12, 2010 @ 7:42 pm
Actually i was searching for you and found u ……….so lucky
Anirudh — May 12, 2010 @ 7:51 pm
@Anirudh: Thanks for the encouragement! I’m happy you found the article helpful
.
Kalid — June 17, 2010 @ 7:53 am
can u make it a bit cheaper for asian friends
jan — June 25, 2010 @ 2:58 am
It’d be nice if this were a bit cheaper. A price like $9 (or $9.99) would attract more buyers. And of course, if it were $4.99, then it’d make it affordable to many more people (not necessarily increase the total volume of sales). There ought to be a betterexplained article on the psychology of pricing and the ways to make people buy instead of pirating.
Cheapo — June 26, 2010 @ 3:22 am
@Cheapo: Thanks for the feedback — I may consider a coupon or discount for educational users. The psychology of pricing is very interesting indeed
. I wanted a price which was comparable to a real book, and much, much cheaper than even an hour of tutoring.
Kalid — July 2, 2010 @ 10:34 pm
Greetings from Malaysia!
I just bought your ebook after browsing your explanation on “e” – which i simply loved….
thanx so much for your efforts and look forward to more postings…I’d love to see you take on and simplify various concepts in statistics as well….
randhill — July 11, 2010 @ 6:44 am
@randhill: Thanks for the support, glad you are enjoying it! Yes, I’d love to write more on stats, thanks for the suggestion.
Kalid — July 11, 2010 @ 9:33 pm