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https://betterexplained.com/articles/developing-your-intuition-for-math/ https://betterexplained.com/articles/developing-your-intuiti... This website does a re

by laddng 10y ago

https://betterexplained.com/articles/developing-your-intuition-for-math/ https://betterexplained.com/articles/developing-your-intuiti... This website does a really good job explaining complex calculus ideas to me. One of which is 'e', where the history and its origins will help you understand why it behaves the way it does. Without this context, 'e' is just some arbitrary number that you have to memorize. This is solely why I believe that history of math should definitely be taught. Finance is also another area where history should be taught since ideas like continuously compounded interest was a recent development, and it's history explains why anyone wanted to compound continously.

kalid 10y ago
Kalid from BetterExplained here, glad you're enjoying it! I often go to the history of a concept for both historical appreciation and, practically, to understand it better. We often study Calculus without looking at what Archimedes was able to do -- break shapes into smaller parts -- and without really seeing how the notion of infinitesimals come into play. (Epsilon/delta definitions don't give the same insight.) The natural log was discovered before e -- why would that be? Sine, cosine, trig functions -- they started as measurements of triangles, evolved into analytic definitions of their own -- why does this progression make sense? In my mind, truly understanding a concept means you understood the path it took to the current state.
- laddng 10y ago
  Oh wow, this is why I love Hacker News - thank you for helping me overcome my mathematical anxieties in college as I was working on my Computer Science major. Your site really helped me gain an appreciation for math since I had terrible teachers as a kid and led me to believe that I could never 'get it'. Would love to see some more linear algebra materials as well
  - kalid 10y ago
    That's awesome to hear, thanks (I started the site to help other students). Yeah, my only linear algebra content is: General Overview: https://betterexplained.com/articles/linear-algebra-guide/ https://betterexplained.com/articles/linear-algebra-guide/ Matrix Multiplication for Programmers: https://betterexplained.com/articles/matrix-multiplication/ https://betterexplained.com/articles/matrix-multiplication/ Hoping to flesh it out over time.
    - chillee 10y ago
      Out of curiosity, how is the content generated? Do you write it all yourself, or are there other contributors? I've always thought that betterexplained was a great resource, and was wondering whether there was any way I could contribute.
      - kalid 10y ago
        Just saw this now :). I write it all myself, but sometimes get pointed at resources by others. https://aha.betterexplained.com https://aha.betterexplained.com - forum to discuss ideas. It's in the background currently but I'd like to make it into more of a public place. If you like, shoot me an email, I'm putting together a list of people who might want to be contributors. Thanks! https://betterexplained.com/contact https://betterexplained.com/contact
repsilat 10y ago
> One of which is 'e', where the history and its origins will help you understand why it behaves the way it does. Without this context, 'e' is just some arbitrary number that you have to memorize. What? I have no idea about the history of `e` (though I have a good idea who "found" it) but it is incredibly important and it's pretty easy to explain why -- if you have a dollar in the bank, earning interest at an instantaneous rate of 100% per annum, but continuously compounded, `e` is the amount of money you'd have at the end of one year. Very, very simple. When the rate of change is equal to the quantity itself, `e` is the thing you exponentiate.

by laddng 10y ago

kalid 10y ago

Kalid from BetterExplained here, glad you're enjoying it! I often go to the history of a concept for both historical appreciation and, practically, to understand it better. We often study Calculus without looking at what Archimedes was able to do -- break shapes into smaller parts -- and without really seeing how the notion of infinitesimals come into play. (Epsilon/delta definitions don't give the same insight.) The natural log was discovered before e -- why would that be? Sine, cosine, trig functions -- they started as measurements of triangles, evolved into analytic definitions of their own -- why does this progression make sense? In my mind, truly understanding a concept means you understood the path it took to the current state.

laddng 10y ago
Oh wow, this is why I love Hacker News - thank you for helping me overcome my mathematical anxieties in college as I was working on my Computer Science major. Your site really helped me gain an appreciation for math since I had terrible teachers as a kid and led me to believe that I could never 'get it'. Would love to see some more linear algebra materials as well
- kalid 10y ago
  That's awesome to hear, thanks (I started the site to help other students). Yeah, my only linear algebra content is: General Overview: https://betterexplained.com/articles/linear-algebra-guide/ https://betterexplained.com/articles/linear-algebra-guide/ Matrix Multiplication for Programmers: https://betterexplained.com/articles/matrix-multiplication/ https://betterexplained.com/articles/matrix-multiplication/ Hoping to flesh it out over time.
  - chillee 10y ago
    Out of curiosity, how is the content generated? Do you write it all yourself, or are there other contributors? I've always thought that betterexplained was a great resource, and was wondering whether there was any way I could contribute.
    - kalid 10y ago
      Just saw this now :). I write it all myself, but sometimes get pointed at resources by others. https://aha.betterexplained.com https://aha.betterexplained.com - forum to discuss ideas. It's in the background currently but I'd like to make it into more of a public place. If you like, shoot me an email, I'm putting together a list of people who might want to be contributors. Thanks! https://betterexplained.com/contact https://betterexplained.com/contact

repsilat 10y ago

> One of which is 'e', where the history and its origins will help you understand why it behaves the way it does. Without this context, 'e' is just some arbitrary number that you have to memorize. What? I have no idea about the history of `e` (though I have a good idea who "found" it) but it is incredibly important and it's pretty easy to explain why -- if you have a dollar in the bank, earning interest at an instantaneous rate of 100% per annum, but continuously compounded, `e` is the amount of money you'd have at the end of one year. Very, very simple. When the rate of change is equal to the quantity itself, `e` is the thing you exponentiate.