I made progress on khanacademy with basic algebra and geometry.
1 hour on pre-algebra
More khanacademy. I'm still brushing up on math I knew how to do 20 years ago.
I'm still working through pre-algebra from khanacademy.
It's been a long time since I've made any progress in math. njwildberger's videos have been helpful.
The main thing I did today was watch the Wildberger video--below, and then thought about how to prove the communitive law to someone who doesn't understand modern language or numbers. I'm not sure the way I came up with works without the explanations around it.
I don't really understand the distrubutive law or why we are using k, m, or n. I'll have to read an explanation of it before I can try to prove it in the same way I did the communitive law.
I'm not really sure how to structure these daily updates, but for now they will probably take the form of a small end of day update--above, and then random thoughts and stuff I'm encountering during the day--below.
To get better at doing tests the reccomendation is to do the test twice and then compare answers. Being able to solve the problems quickly will allow answering them twice rather than just looking over the answers.
Give reasons why these rules are true:
Prove them true in a way that a 10 year old 100 thousand years ago would understand. Up until this point Wildberger has used lines for counting and has introduced the notation of a succesor function. I should be able to essentially create drawings that I could show to someone who doesn't understand the concept of numbers or speaks a language I understand.
Here is my attempt at the communitive property:
I'm going to show that nm=mn using 4 and 3.
first we show that m(4) groups of n(3) is equal to 12
Then we show that n(3) groups of m(4) is equal to 12
Finally, we show that m(4) groups of n(3) is equal to n(3) groups of m(5) using the method of drawing connections between our lines that represent a unit of 1.
someone who doesn't know the number 12 should be able to compare m groups of n compared to n groups of m and determine it's the same.
This looks interesting
"
3:22
you should stick to your simple toolbox initially
Start with simple problems, and then work your way up to very hard problems
using these exact same simple tools
You would be very surprised how advanced problems can be solved
using just a hammer and a screwdriver of mathematics
The third step, after you have really exhausted all the tools in your toolbox
is going on and adding a new tool to your toolbox
The problem with most education systems in the world is
that this step happens way too early!
Typically, you've just barely learned how to solve like three or five
different types of problems using a given tool
And then you move on to learning the next one
And the word "learn" may be an overstatement here
because many students just memorize the steps to solving a problem
"
Art of Problem Solving - good introductory content for different competency levels.
In the back of Thomas’s book he had supplementary problems, the teacher didn’t assign the supplementary problems; I worked the supplementary problems. I was, you know, I was scared I wouldn’t learn calculus, so I worked hard on it, and it turned out that of course it took me longer to solve all these problems than the kids who were only working on what was assigned, at first. But after a year, I could do all of those problems in the same time as my classmates were doing the assigned problems, and after that I could just coast in mathematics, because I’d learned how to solve problems. So it was good that I was scared, in a way that I, you know, that made me start strong, and then I could coast afterwards, rather than always climbing and being on a lower part of the learning curve.
Stand-up Maths wrote code that ran in 31 days, and then his viewers wrote code to solve the problem faster using both math and computer programmer techniques. It seems like the fastest improvements came from switching from python sets to binary, and other improvements that were programming details and not maths.
Today I made some progress on KhanAcademy. I'm almost ready to start the integrated math track that combines algebra 1,2, geometry, and some statistics.
I listened to John McWhorter on the Evolution of Language and Words on the Move - EconTalk. I'm going to add his book to my to-read list.
I started Cathy O'Neil on Weapons of Math Destruction - EconTalk. O'Neil talks about recidivism rates being associated with sentencing. She makes good points for algorithmic and data transparency. I'm going to finish the podcast at some point and add the book to my to-read list.
I created weekly streaks for Information Security, Computer Science, Math, non-fiction reading, and fiction reading. I don't have a plan on how much time I'll put into each, but I think it might be helpful to track each individually.
the main point of creating these streaks is to try to prevent constantly shifting my focus from topic to topic. I heard David Brady say on a Ruby Rogues podcast something along the lines of "some programmers have 10 years of experience and some have 1 year of experience 10 times". I think my inability to stay focused on one or a few topics at once has lead to having 1 year of experience 10 times.
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