Master of Memory: Accelerated learning, education, memorization - MMem 0477: How to learn Calculus, part 1

Episode Date: January 5, 2016

John asks about learning calculus. Although I have never taken any calculus classes myself, I give my best suggestions for starting to learn the subject from an accelerated learning perspective. What do you want to learn? Leave your question at http://MasterOfMemory.com/. Music credit: Maurice Ravel’s String Quartet, 2nd movement, performed by the US Army Band.

Master of Memory 477. Welcome to Master of Memory. I'm Timothy, and I'm here to answer your accelerated learning questions every day and to inspire and empower you to learn anything you want to learn faster than ever. John submitted a written question at masterofmemory.com slash question. John says, Hi Timothy, I was wondering how you would go about learning calculus in an accelerated manner, especially if you wanted to learn it on your own. Thanks for the podcast. I've particularly enjoyed

seeing the principles applied across a broad range of disciplines. I don't see one on calculus though, so I'd very much appreciate one. So based on that last thing that John said, I've decided to take on this question, even though I've never taken calculus and I really don't know calculus. So my response here is going to be based on how I would approach calculus and how I would approach it similar to other things that I would approach, you know, in similar manners, as John mentioned, across a variety of disciplines. So basically the principle that I'm going to talk about is the idea of oscillating between the most basic definition of something and the details. So as an analogy, let's imagine that you wanted to get to know a little town that you've just moved to, and this town has a main street that runs through the downtown, and then it has a bunch of other streets that run off along in different directions. Now, you might go ahead

and try to memorize all the streets, but that's not going to work very well. Instead, you might just learn the main street and always walk up and down that street each day. Then on other days, once you've learned that street really well and know where things are along that street, you might choose a couple of other streets to go down and learn those, a couple of other main streets that branch off of the single main street of the town. So now you know Main Street and you know the other branches of the main avenues of the town as well, but they all point back to Main Street. As often as you go down those other tracks,

you're going to walk along Main Street again. And then eventually your forays will go along those avenues and then down smaller and smaller streets, but then always go back to Main Street as you continue to learn the town. your forays will go along those avenues and then down smaller and smaller streets, but then always go back to Main Street as you continue to learn the town. Then you'll know the town as well as anybody. You'll know it perfectly by heart, the whole town, just simply based on the fact that you've

always returned to that main avenue and learned everything else in relation to that. So that's what I'm going to do with calculus and with any other subject that I approach is basically start with the most basic definition of calculus and then always go back to that as I learn deeper and deeper things. So it's like starting at the surface, digging deep, then coming back up to the surface, then digging deeper, and then coming back up to the surface. So as long as you keep returning to the main definition, everything is going to be easier to learn and going to have a context that makes sense. Plus, hey, you're learning the most important thing,

which is what calculus is, and you can explain that to other people, which is very important. So applying this to calculus, what I'd like to do is start with the basic definition of calculus, then find the most frequent terms or concepts that are used when people refer to calculus and kind of learn what those mean and how they work, and then go into more detailed

learning from there. So the basic definition of calculus that I've found is basically that calculus is the mathematical study of change in the same way that geometry is the study of shape, and algebra is the study of operations and their application to solving equations. Now I'm gonna keep going back to the basic definition of calculus as the study of change, while digging deeper into how that works out mathematically and in all the concepts that we study in calculus. So calculus is the study of change, and what that means mathematically. The next step here is I've found the most frequent unfamiliar terms on the Wikipedia page. I actually have a tool that lets

me do this and I can give people access to that. I can't really make it public at this point, but basically, you know, whether you're studying a language or studying something in English, you submit a text and then it'll sort all the words that you don't know by frequency, which is pretty handy. But the words that came up for me were on the, and what I did was I just took the text from the Wikipedia page on calculus. So about as basic as you can get, defining calculus and the various aspects of it. But the terms that we have are function, which, you know, I know what that means algebraically. I work with it all the time, but I don't know what it means for calculus. Derivative, integral, analysis in its various uses, differential, and limit. Now here's the thing. Instead of going through a textbook one topic at a time, I'm going to look up these,

I guess, six different terms and concepts as they relate to calculus and figure out exactly what they mean and how they're used and, you know, what is a limit in the calculus sense and just figure out as deeply as I can based on those sort of avenues in the town of calculus that I'm trying to learn. But then each time that I study each of those, I'm going to go back to the main definition of calculus as the mathematical study of change. And so those things will make sense in that context. And I'm going to keep going back to studying why a limit has to do with the study of change or why a differential has to do with the study of change. Now, the way that I'm going to do this is I'll study these terms through Wikipedia and beyond,

probably with some work from Khan Academy, just as far as giving myself some examples that I can see and hear and work with. So Wikipedia and Khan Academy will give me pretty much what I need to study these terms that I've chosen. The final step is to go from there and start digging deeper into a thorough study of calculus, maybe with some sort of curriculum, like the entire Khan Academy curriculum.

But now I have a context to fit everything into. So John, thanks for the question. This episode was fun to do. And yeah, that's how I'd study calculus. Now for everyone listening, if you want more on accelerated learning and how to learn any subject faster than ever, go to masterofmemory.com slash start for a completely free starter guide on how to use mnemonics and accelerated learning.

Meanwhile, what do you want to learn? The world's knowledge can be yours. Leave your learning request at masterofmemory.com slash question and I'll talk to you again soon.