Comment by jahbrewski
6 years ago
For another great source of open source textbooks I highly recommend OpenStax (https://openstax.org/). I am currently re-learning calculus and their Calculus text is great. As an aside, I'm currently working through mathematics I wish I had taken in college (I was a biology major), starting with Calculus, and would love to connect with anyone else on a similar mathematical journey!
And for even more open source textbooks: https://open.umn.edu/opentextbooks/
I've been doing Khan academy most days (like, 28 of 30) for the last year. It's been super friendly and I've moved through the algebra, geometry, trig, precalc, and differential material... I'm currently working through some integral calc stuff. I'm planning on doing the stats and linear parts of kahn before trying to take some of the online college-level courses; Sal Kahn is super great as a teacher but I am starting to feel like I can now benefit from some more difficult to digest material.
My hope is to generally increase my math abilities so I can do some electronics design classes and some study about how to start applying ML/ AI tools.
But I've found studying math to be quite fun and useful in its own right. It's fun and I feel like it's helped my general intellectual abilities.
Khan Academy is great, the only issue I have with it is it's too long-winded sometimes. Taking much longer than necessary at the cost of maintaining that comfort level of a beginner student. There is something to be said about struggling just enough according to your proficiency level (the idea of Flow in psychology).
I too would like to work my way up to calculus and beyond.
What sequence of courses do I take on the site to get to calculus, starting from the beginning with the basics?
How familiar are you with algebra? The stronger you are with algebra, the easier you will find Calculus. You will also need a relatively strong understanding of trigonometry, but I've mostly been able to review the trig I need as it comes up. That being said, don't feel like you need to be an expert at all prior math before jumping into Calc. In fact, Calculus might be the class you finally grok algebra since you'll use it so much!
Here is a good review of the algebra you'll use in a Calc I course: http://tutorial.math.lamar.edu/Extras/AlgebraTrigReview/Alge...
I had a humbling experience last year when I browsed the available courses until I found one that only contained math I'm already familiar with and I had to go all the way back to fourth year elementary school. :/
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What was your math background before you started Khan?
20 years ago I flunked out of a Calc 2 class in college and (unrelated) never got back to it because I changed my major to Philosophy.
I program for a living, but was having trouble, like, with multiplying fractions and that basic level. But it's not hard to learn if you do it every day.
I mean, it's slow going, and I am certain that there are folks who think that integrals are pretty basic math, but its fun and interesting to me, and derivatives have helped me understand quite a few things I never quite groked already.
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I had a look at their pre-algebra chapter. They differentiate between "counting" number and whole numbers.
Why not use the correct terminology and call "counting" numbers "natural" numbers, it's what we've been taught in schools for tens of years, if not hundreds now.
Sure, explain that naturals are "countable" at the beginning, but this redefinition is verging on dumbing down.
edit:
reading further:
"Counting numbers are also called natural numbers."
But they seem to keep calling them "counting" numbers. Just call them their proper name and re-enforce this.
And then in this first intro... below a terrible graphic.:
"The point labeled 0 is called the origin. The points are equally spaced to the right of 0 and labeled with the counting numbers. When a number is paired with a point, it is called the coordinate of the point."
WTF?
I was taught that whole numbers is a wider set of numbers than natural numbers. While "counting numbers" is a good name for natural numbers, because they are used for counting, the idea of countable set is all about our ability to count elements of this set. We can of course talk about countable set in terms of finding a bijection between the set and natural numbers, but it doesn't matter really. It is just different words to spell the same idea, while (we cannot deny it) counting elements is easier to a beginner. Maybe counting numbers is easier to grasp then natural, maybe it is just authors of textbook thinks so. I cannot understand why are you so bothered with it.
> Just call them their proper name and re-enforce this.
I'll tell you a story. When I learned math in college I was stuck by a Galois theory, I just was unable to understand it. So I decided to look different authors, to find some other approaches to explaining things. I found at least one textbook which I was forced to read from a very beginning, because it used a very different notation which I couldn't understand at all.
It was not the first time I have meet a new (for me) notations for things I already knew. I spent two more years learning math, and finally I understood one thing: there are no such a thing as "proper name" in a math. If you need to refer to a some thing, you need to define it. Math is all about your ability to name and to define things, to invent a math notation to write this things down, and to stick your mind to live inside universe which was built by your definitions, names and notations. It is doesn't matter then how original your notation is. All that matter is what results you can achieve.
From all the branches of math algebra is the most about different notations for the same thing. Just take a look at multiplicative and additive notations for groups. You can use either with any group, nothing matter just your convenience. If you like to use a plus sign and write "a+b" then use additive notation. It you prefer to use no sign and write "ab" then use multiplicative one. In algebra it is your respected right to use notation you like. But it comes with a cost: you need to respect other's right to use any notation they like.
You can do better in your own textbooks :)
I've been reviewing the calculus I've forgotten years ago, by taking pictures of my old Schaum's study guide with my iPad, and doing the problems while sitting on public transportation.
I find the badly kerned math typography of the Open Stax offering, and the PDF version of the modern Schaum's study guide, to be distractingly jarring.
It's impressive that they managed to mess that up. They didn't use LaTex for math?
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Your product sounds interesting but promoting it more than once per thread might turn some people off, especially around here.
Understood. Thanks. Will remove the comment above.
Your scrolling enhancement makes the site hard to navigate. I scroll down and the page keeps sliding, as if I'm skidding on ice.
Yes. I apologise for that. I will remove that in a week or two when I launch Primer.
Front end is not my forte. Clearly. :(
Similar journey here! It's an exciting journey personally.