A website that explains maths concepts in very intuitive way so you don't have to memorize them.

I have struggled with these concepts from Precalc to calc 2 and I never had a firm understanding of the subjects. I felt like I was just memorizing equations and computations. This is the first time I can actually say that I understand a trig concept after reading your explanations. Thank you so much!

We love you! In all seriousness, I struggled so much with more basic math (statistics/calculus) when I was younger, and simply couldn't "get it". (Also, the teacher's method of teaching was to write the formulas on the board and yell if we didn't get it.

I admire this guy's Reddit hustle.

I just read two of your articles, and man, you just blew my mind.

Absolutely amazing. Thank you!

Sorry for Reddit Hug of Death.

Tons of calculus, diff-eq, lin-al, and a few EE classes, and no one ever said the word "rotation" when talking about complex numbers. This is what pisses me off so much about uni. It's always "this is some shit, accept it, and use it for this over here" instead of understanding what the hell it is in the first place.

That was really straightforward. Kudos.

We’re at a 45 degree angle, with equal parts in the real and imaginary (1 + i). It’s like a hotdog with both mustard and ketchup — who says you need to choose?

Now I'm fucking hungry and have to run out to the store. Thanks.

Your site is great!

Have exams in January. You sir just saved my life. Live long and may the force be with you (wasn't sure which one to go with if any at all :P)

As someone with autism/retardation I want to thank you from the bottom of my heart. I only started reading about imaginary numbers but the way you put "i" as a pattern of "X,Y,-X,-Y" finally made it click in my head.

God I wish resources like your website and special ed in general was as good as it is now when I was growing up, Might actually have had a chance...

I just read the first one about imaginary numbers, and the idea of using it to know how to move across the water in a boat is what makes this seem useful.

This being said, when you described i as flipping 90 degrees, I immediately wanted there to be a third...set of numbers? With the "normal" numbers being negative and positive, and i being perpendicular to that, why not have a third set of numbers perpendicular to the plane of those two sets? This way the analogy of the boat on water translates to a submarine under water, or a spaceship in space.

Does such a set of numbers exist? Can there be a fourth set of numbers to represent the dimension of time, parallel? to the "space" of the other set of numbers? If yes, it would make sense to me that there be a fifth set of "numbers" to represent whatever is perpendicular to time.

Tl;dr: This article answered one math question, but has given me even more math questions, and I'm not sure what words to use to make sense anymore.

You sir.

just saved my math classes.

MVP right here.

Key to success right here. Major.

This is great

I'm gonna be using your site a lot next term. Thank you.

I've only just started looking, but I'm a maths student looking to go into teaching, and this site is amazing. One critique from what I've seen so far is that I think going into complex numbers to explain addition formulae is unnecessarily complicated; the same process could be done with coördinates in R², and while I like the complex numbers approach, students who haven't met them before are likely to struggle with them (at the very least, it's a significant complication for those who struggle with abstraction). Nonetheless, in general, I like what I see, and will definitely keep this site in mind in the future (assuming it stays up until I start teaching).

Hello Kalid, I am a student who has always had trouble understanding concepts in math. I know that I can get it eventually, but explanations don't normally click for me.

I just want to say that your explanation on imaginary numbers just clicked for me. Now I am inspired to learn more. You have a gift sir, and I thank you for your awesome service.

Give this man a sub!

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Great site! I was using it last week to learn how to use Baye's theorem. Keep up the good work!

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Kalid I've followed your blog for years now, and it's still my fav math-related one!

Hi thanks so much for this. It's an amazing resource.

I hope I wont be taking away from your spotlight too much if I ask you what kind of resources it took to develop this incredible tool, and what you think the barriers to implementing solutions like this at state and federal levels are.

Given that most students have a web browser in their pocket, shouldn't they already have a product like yours ready at hand?

I feel like this is something that should be implemented in education nationwide. It seems like a no-brainer to me. So I just hoped you might have some insight into what the reality of that kind of implementation is.

Thanks for taking the time to answer, should you; I'm sure you're preoccupied with new-found success. Congratulations!

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Responding to bookmark. I can't figure out how to star or favorite from my phone.

Anything for people trying to learn just basic math? Fractions and multiplication?

Your host's error site is beautiful. That is all.

Bookmarked!

Hey! Kalid from BetterExplained here. Woke up this morning to crazy site alerts. I'm working to get it online but here's a few popular articles:

• Imaginary numbers: http://webcache.googleusercontent.com/search?q=cache:http://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/

• Understanding e: http://webcache.googleusercontent.com/search?q=cache:http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/

• Intuitive Trig: http://webcache.googleusercontent.com/search?q=cache:http://betterexplained.com/articles/intuitive-trigonometry/

• Calculus intro: http://webcache.googleusercontent.com/search?q=cache:http://betterexplained.com/calculus/lesson-1

• Sine waves: http://webcache.googleusercontent.com/search?q=cache:http://betterexplained.com/articles/intuitive-understanding-of-sine-waves/

• Euler's Formula: http://webcache.googleusercontent.com/search?q=cache:http://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/

• Linear Algebra: http://webcache.googleusercontent.com/search?q=cache:http://betterexplained.com/articles/linear-algebra-guide/

• Pareto Principle (80/20 rule): http://webcache.googleusercontent.com/search?q=cache:http://betterexplained.com/articles/understanding-the-pareto-principle-the-8020-rule/

Working to get the site up, thanks!

────────

Welp, I guess I can use Reddit as my blog until things are working normally. AMA and I'll answer as best I can.

General Learning Philosophy: Anything can be understood if we approach it the right way. Spoken language, writing, number systems, we figured these out. We can learn math too. The system I like (ADEPT) is

• Analogy - Tell me what it's like

• Diagram - Help me visualize it

• Example - Allow me to experience it

• Plain English - Describe it with everyday words

• Technical - Discuss the formal details

Example: Negative numbers were finally understood in the late 1700s. When the American Revolution was happening. They baffled people for so long because "How can you have less than nothing?". Something can be there, or not there, but what does "negative there" mean?

Doesn't make sense! So, we have BC and AD (before 0, after 0) and debits and credits (two ways to track your balance, not a negative balance), East and West (not negative West) and so on.

But with the analogy of a number line, boom, negatives make sense. You have a single scale, with a neutral point, and you can go left and right from there. One analogy makes the idea of "opposite of there" make sense.

Most of math is like that. Arithmetic is impossibly tedious when thinking about numbers as individual lines (III), or in the Roman Numeral system. Move to decimals (sets of 10) and you've just unlocked a superpower. Not a lot more work, but you have 3rd graders with better math skills than Roman emperors. That's how learning should be done baby.

Nice, maths.

Dude, I minored in math as an undergrad and I didn't fully understand some of this shit until just now. I got good marks too, but I just took a lot of stuff as a given. Square root of a negative number? Eh, fuck it, throw a little i in that bitch. That's just what you do. Thinking of it as a rotation never occurred to me. And when you think of it that way, the applied stuff makes a lot more sense.

Thanks for this, dude! Definitely going to binge watch your vids at some point this week.

I really like your teaching style. I'll definitely be checking out the site when it goes back online. I've always struggled with math myself because I find it to be very difficult to get those aha moments where something suddenly makes intuitive sense. I feel like its a waste of time to simply memorize a bunch of equations to pass a math exam, and for some reason its hard to find courses that focus on fundamental understanding. Thanks for putting these together.

Awesome site, good job! Keep up the good work :)

I really love how you use history of math as part of your explanations! I have used the big History of Mathematics, and Geometry Civilized. What resources do you use to find history of math? Thanks!

Upboat4u

it took me far too long to realize that your username was not, in fact, "peanut butter zeppelin"

Thank you so much for this. I went through a period of not being able to concentrate in school around 15 and it really hampered my progress, I still passed exams and stuff, but that was just luck. I'm trying to relearn some stuff so I can move on to more advanced stuff, this is very helpful, thanks

I'm just saying we have way better ways to think now! That's how math expands your brain.

When I read this, it made me think of the metric system. It's a sussinct way to describe how I feel about it. It's made with science in mind and is constantly improved in that regard. It's a less-obtuse and more-useful system that doesn't waste as much of your thinking on the plethora of conversion constants. It also avoids (you could probably argue "discourages") snapping to the closest fraction; fractions being well-established as generally unintuitive to the masses.

But it's an important thing to learn; how to temporarily forget what you "know" so you can entertain a new perspective. Makes learning paradigm-shifting discoveries a lot easier

I'm looking forward to giving these a look through, and checking out your website when it's back up.

But I just wanted to say that this amazing! Although I didn't have a very difficult time understanding math concepts in school, MANY of my friends did, and although I was generally able to help them, I always felt that there had to be a better way to explain these concepts!

Such a shame I didn't know about this 5 years ago! I'll definitely recommend it to my little brother though. Would there be any scope to add other subjects? Maybe some biology/chemistry etc at college I'd have killed for a site that tells me advanced concepts in plain English.

neat. i'm looking into getting further into math and computer science, so i fully plan to check this all out. i saw a comment or two praising the calc. subbed to the subreddit as well!

I went to your site.. Copy this all into a book. I will buy it and I'm sure others will too.

Nice job

How do I give your site gold rather than Reddit gold?

Hey man I was a math tutor for 4 years. Thanks for teaching me how to teach people what e is in an intuitive way

Thank you. You've explained imaginary numbers in a way I finally get. I could use them but never really understood how it worked.

Awesome site! Any plans to do one on lagrange multipliers?

Hey, Kalid. Thank you for the work! I ended up on your explanation of Log N over the weekend, and it was very in depth. It really helped with the excel course I am trying to take on Coursera.

As someone trying to learn the math needed to develop my own synthesizers, this is amazing.

Holy crap, dude. I know what "e" means now. I mean, I knew how to use it, but now I know what it is.

I could not for the life of me find any of these links actually on the website....

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This will definitely help a lot of people. Thanks.

You're getting so many responses that I'm sure you've already answered this and I can't find it, so no pressure if you can't get to this question.

How is reddit's hug of death affecting you personally? Is this going to cost you a lot of money?

Thank you, thank you, thank you. I dropped out of maths at high school aged about 15 because I didn't "get" calculus etc - it was too abstract, I didn't understand how it related to anything "real". I enjoyed stuff like chemistry & biology, but dropped them eventually because you couldn't do them at university level without maths. As an adult I had a go at learning maths a few times - I kept an interest in science & got into computers in the 80s. I dated a mathematician for a while & got him to try teaching me. Bad idea!! Ha ha, he had no idea how little I knew. I tried self-teaching from books, but still no joy. I started to think maybe I had a kind of dyslexia but with numbers.

Five minutes on BetterExplained and I think maybe this is it. At the age of 63 I might finally learn some maths. The analogy approach is like a magic trick! You have showed me the light switch and I could not be more grateful. Brilliant.

Hey, do you accept submissions? I think we all have some subject we can explain and maybe after a bit of cleanup (so they have a consistent style) you could add those to your site.

I mean, at least I feel I owe you one for this image, I always try to remember those relations or going to Wikipedia, now that is in my favourites ready to save me lots of time.

Wish you would do more updates !

You're the math teacher we all wished for but never had. Thank you so much.

I wish this could be in Spanish too. I have a lot of friends who would love this, but they live in a place where learning another language is kind of difficult because they don't "need" it there.

I cannot say thank you enough for this!

I somehow made it through calculus into differentials without ever fully understanding trig! Now after reviewing your site it's like a light has been shined down from heaven. Thank you!

I always thought I sucked at math and so did my math teachers, so I just stopped trying and accepted my fate. Then I got a teacher who explained everything slowly and systematically and if you didn't understand she was glad to do everything over again. After her I got a math teacher who went faster but taught us things in different ways, taught us more than just the formulas, made us think outside of the box.

Without those 2, math would've never been my best subject in high school in the end. I really believe that there are tons of people right now who think they suck at math who just haven't been told the concepts correctly.

So THANK YOU for doing what you're doing!

Your /u took me a second, but is likewise awesome.

Dk if this will get buried or not, but as a physician, if you could explain biostatistics (the clinical sort we see in journal papers, not the basic science stuff), I know for a fact it's a need we have.

Starting with specificity/sensitivity/absolute risk reduction, etc.

Here's something I lifted from a Stanford syllabus:

Week 1 - Descriptive statistics and looking at data

Week 2 - Review of study designs; measures of disease risk and association

Week 3 - Probability, Bayes' Rule, Diagnostic Testing

Week 4 - Probability distributions

Week 5 - Statistical inference (confidence intervals and hypothesis testing)

Week 6 - P-value pitfalls; types I and type II error; statistical power; overview of statistical tests

Week 7 - Tests for comparing groups (unadjusted); introduction to survival analysis

Week 8 - Regression analysis; linear correlation and regression

Week 9 - Logistic regression and Cox regression

Thanks!

The extreme responses are pretty disappointing.

1) The guy owes us nothing, and I don't see him as being manipulative, a jerk, or trying to sell us something (did I see a print book? - that costs money). If looking at his website for a few minutes gave you no benefit, move on.

2) Many others and I found much of what he said helpful.

3) Lastly, I found some of his explanations not so helpful or not really different than I've seen elsewhere. So what?! Should I roast him for that? I gave him some suggestions when I thought I had some.

He's sure helping the world a lot more than most of these angry people who sit at home and do nothing.

As a giant failure who basically skipped college out of an irrational fear of math caused by dumbass public schools, I would like you to know that YOU'RE TOO LATE :(

For reals though, those articles are awesome. Can't wait to see the rest.

Just kidding, I still have no idea what any of this means.

Now works...

Had to recalibrate the phase inhibitors but it's back online :).

Still down for me

Down for me but even the Error 544 is explained very well!

Literally had no idea what "e" was til I watched that video. I remember punching it into formulas in college but had no idea what it actually meant. Interesting stuff.

We killed it again

Holy crap. All.fucking.semester during my tutoring sessions, I'd see e and start to mildly hyperventilate. (I saved the heavier hyperventilation for exams.) My tutor would tell me calm down and reassure me that it was only a number - but that didn't make it any easier for me to comprehend. So then I'd start mumbling to myself, "It's only a number, it's only a number." That didn't work either.

Thank you for this site!

Awesome, glad it's helping! e is one of my favorite topics.

I thought so too!

What's cloudfare?

Look at the top comment. Many usefull math links.

It's still a better textbook than others. The main problem with STEM textbooks, and textbooks in general, is that they are written by experts, not by writers. An expert knows the information, but they often don't know how to convey it to someone unfamiliar with the concepts. A writer's job is to understand the perspective of the readers and make them understand and enjoy what they are reading, or else s/he's a bad writer. This is where the success of the For Dummies collection comes from: the authors are writers who care about the people without basic knowledge.

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Kahn is a great all around resource. The single best lecturer I've even seen anywhere is Professor Leonard on Youtube. Best Calc. teacher I've ever seen.

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This is pretty much how they explained it at my uni.

Thanks! Yeah, the cross and dot products are two parts of the complete picture. When you have vectors (a, b, c) and (d, e, f) there are 9 interactions. The 3 symmetric ones are the dot, the asymmetric ones are the cross. So simple! And never shown to me this way.

I didn't try cross products. I'll give it a look. I checked limits and derivatives, and both were more complicated than my classes or textbooks...

This was the one for me. I've been studying vector calc this year and I could do it, but I didn't really understand a lot of the underlying stuff. That article really helped

The part of calculus that students struggle the most with is the algebra. The actual calculus part of it is pretty straightforward.

I think it is better understood in the context of physics, as that was what calculus was made to originally solve.

Taking first year physics and Calc at the same time can help with understanding the math intuitively.

Have you taken calculus at a university level before? They tell you calculus is the study of change. Hence why the derivative is such a big deal for it. Also, there's a whole section called applications that give real world applications of calculus. I'm not the best at math, but I was able to pick that up.

Yes, by a process called "spending time and practice learning it."

....huh?

Hey Lucas! Thanks for the mention. I love your work and have been meaning to reach out about working together :). For anyone who doesn't know, /u/lucasvb makes some of the best math animations I've ever seen.

Go back to your room, we have visitors!

Thanks for putting this out there. People are chiming in with "meh", or "it's so much simpler to think of it this way". That's the problem with learning/teaching. Everybody learns and thinks differently. With concepts, I think it is critical to have many, many different descriptions or view points. Take a box in an empty room with a single light source. The box is the concept, and it should be described from many different angles. One persons perspective might offer a better explanation that makes sense to a given group of people. Once the understanding sticks, then it's "ohhh, it's just a fucking box!", and how we reached that understanding is a moot point.

I myself really like looking at trig functions in the expanded circle/wall thing. I think wikip. does it also.
But I think it may be too complicated for most stduents.

I think trig really needs only two basic concepts. 1) sine and cosine are your vertical and horizontal components of angular movement. There are so many examples it's ridiculous. Rarely do things move exactly at right angles or along a certain scale/measurement 2) abstract this only a little. draw a triangle, show what sine and cosine were, noting they are ratios of two sides. Then mention that instead of making any other ratio complicated in terms of sin and cos (ohh, that will come soon enough), we simply call all the other ratios a new name (function).

The trig function diagram is definitely a really good one. However, I think your explanations of logarithm/exponentiation and cross product are actually really confusing, and this is coming from someone who completely groks these concepts and uses them all the time. The explanation of "grower's perspective" is just really making the issue harder than it needs to be. Most people can get what exponentiation is, they understand taking something to a power and how it relates to multiplication. It seems to me the easiest way to explain the logarithm is to make them understand that it's simply the inverse operator of exponentiation.

I certainly agree with your assertion that teaching understanding is miles better than teaching by rote, and if your site is useful for some people (as the rest of the comments suggest it is) then that's great. I just don't think it would help out the students I teach particularly for the reasons I mentioned.

With regards to trigonometry: part of the problem is that it is expected (in this country) to be learnt by some students who don't have a solid grasp of the concept of ratio. The language and concepts of your trigonometry post are likely to go over the heads of the students in my classes who most struggle with trig. They may of course not be your audience: what reader age did you have in mind when you wrote of these posts?

typical trig class... without painful memorization

Ask some high school math teachers whether they think "memorization" is the right way to learn trigonometry. 99% of the time they try like hell to teach the concepts, then fall back on mnemonics when the STUDENTS complain they don't get it and don't have any grasp of the difference between tangent and sine.

And from a basic business perspective, insulting your competition isn't smart.

Take pi and circles for example: I've much more success with lower ability groups when approaching this as an investigation (draw circle, measure their circumferences etc.) than instructing or giving notes or the like.

Because you haven't taken the time to think about what they're teaching, and the teachers themselves probably don't fully understand it. Common core is considerably more effective if it's taught well.

A website that teaches you how to visualise textbook information to try and help people learn from books who struggle with it would be amazing.

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Random person here: I'm gonna say something needlessly aggressive

None of my students have put me on it. :(

Thanks, just left a comment. And really appreciate the reddit submission, it means a lot!

Derivative.

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No kidding! I'm 29 and back in college, taking math. I have had this feeling all semester like there would be a way to pack a TON more information and understanding into the education than has been the case in my class. I like the multidimensional approach you're taking and that ADEPT acronym sounds great!

Thank you! :( unfortunately (I just finished the final) I think it is possible I will fail!!!! Will have been the first class ever I've failed. I think that's positive in a way, I wanted to challenge myself. Just another milestone in life. It is interesting being a bit older than these kids. I feel like I would learn the material better in a different way because of the way in which I've discovered I like to think about things. What are you studying?

We dont add extra letters to shit. It is more efficient that way.

Yeah right. We have live more exciting and action packed lives; we don't have time for extra letters (maths, colour). Shit even autocorrect is telling me I got those wrong :P

Or you mean we're actually consistent with how we abbreviate things.

Yeah, and they could care less.

Do you abbreviate "economics" as "econs"? Do you abbreviate "politics" as "pols"?

It's fine if you prefer "maths" because that's what you grew up with. But how we abbreviate things is ultimately arbitrary. The fact is that "maths" isn't inherently any more logical than "math". It's just that one abbreviation happened to catch on in Britain and the other happened to catch on in the US.

But math is an abbreviation and mathematics isn't plural.

The word mathematics is generally accepted as a SINGULAR word. The 's' at the end is somewhat deceptive. So you should leave it off when abbreviating.

I didn't look at the more elementary topics, but I can say that the article on Fourier transforms definitely helped my understanding.

Every resource has its pros and cons, and different students will respond better to different materials and presentations. I do appreciate the craftsmanship you put into your content.

The resources that many other people in this thread have already mentioned are good. I push Khan Academy in my classes, and I tend to send my students links to Khan Academy videos, but there are a couple of places in the calc sequence where I send them a video of a complete lecture so they can digest the material at their leisure. I have only used online videos as a completely optional resource for my students. I have not used free online stuff that isn't video based in my classes, because my experience has been that students will never ever read. They'll look at their notes perhaps, and if they can't get the homework then they'll find a classmate or a tutor to explain it. At my institution we have a very available and accessible tutoring center.

Son is 12; we are working a mixture of 7th through 12th grade curriculum. This bright kid really keeps me on my toes. :)

Sure! I have a gifted child who learns faster than the schools can teach him. He is 12 and doing advanced maths, which really keeps me on my toes even though I am quite proficient. He also studies Spanish, Latin, robotics, computer programming, grammar, composition, science, history, and literature. He is an athlete; we run, do yoga, indoor and outdoor soccer, and soccer-specific sports training, so that covers P.E.. We homeschool for academic rigor rather than religious reasons, which I think is important to point out because the stereotypical homeschooler is extremely religious.

has almost 3 million points on Kahn Academy. I was an awful student in a school where the math teachers were horrible. All of them were tenured burn outs. Now I love the maths. One of the GREAT things about KA is that you can watch and rematch the videos until you figure out what you missed or what parts of an equation you simply do not understand.

People are getting gunned down like COD out here and you wonder why a mom would want to home school? jk There's like a million reasons, sometimes the kid is involved in an activity that requires homeschool for a better fit, like gymnastics, a lot of times the parent might be a former teacher or just an involved parent and believe they can do a better job, and thinking through it they probably could in most cases because they care more than any teacher could.

http://i.imgur.com/eDGeC7W.png

Like this?

Well, that actually makes more sense than us just calling it "math."

English is weird.

The ol' hug of death.

I accept it, and know how to cipher it, but it makes no sense in practical application.

If I have two apples three times, it's six apples. If I do not have two apples not three times, I suddenly have six apples?"

I do like "bad at being bad", though. Something in that seems a key.

Thanks for that offer. I work my way through things now with help from Google University. Thankfully I've taught myself how to use Excel and I use it to get myself out of tough spots. :-)

My sincerest apologies, this isn't my main account so I'm not on it often. Yes, Graspable Math does indeed work on an iPad.

Ahhh it makes sense now.

"In a very intuitive" rather than In very intuitive". The "a" is attached to "way" (n.) but gives way to descriptors "very" and "intuitive".

You can also use "the" in place of "a", or a number "two ways" but it wouldn't make sense in this context as it is just one of a variety of unnamed and unknown ways.

And hello! You have an excuse, usually it's just people that don't know how to write in their own language which is sad. This is actually a really cool site, I'll probably be using it as I go back to school to study up for my masters.

https://www.youtube.com/watch?v=j2zlPNGuPbw

I know what it comes from. Its still sounds corny as shit.

Mathematics is not plural.

Wow, I never knew we were so on top of things :D

Keep in mind that not all countries in this world speak English, so math vs maths isn't even an issue in most countries.

Also, since you seem to think mathematics is plural, how often does one say

Mathematics are my favorite subject!

Linguistically, mathematics isn't plural.

Technically, it's more grammatically correct, as "mathematics" is plural.

It's arbitrary, not technically correct in any way at all.

Edit: How do English speaking European folks abbreviate economics or politics? Yea, it's completely arbitrary. Also, fun fact, "math" is the older form than "maths."

It's fun watching Brits try to defend their illogical word usage.