Math, BetterExplained eBook Available!
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
Never before have I heard such a clear and concise explanation of the fundamentals... I seriously could have saved hours of hair-pulling in university had I had access to this article years ago.
I 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.
Your book is extremely well written – if only all books on this subject matter could be written in this style. I utterly enjoy reading your book. Thank you.
This 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...
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| Site license for 100 users | (Just $2/copy!) |
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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.
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