91–100 of 102 posts
It’s awesome to see more & more devs getting interested in math & stats as machine learning, optimization & sequential testing (what you folks call a/b test) becomes more mainstream. The obvious benefits are, much of math literature is currently written for consumption by math grad students & profs, so all of this will get a much needed rewrite. I foresee a surge in material like Jeremy Kun’s popular “math for progra…
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I agree with this comment and would supplement as follows: whatever you intend to learn, consider how you're going to retain it. I'm quite sure that I've forgotten a lot more maths than I know. I'm not sure about the utility of forgotten maths. You may think it rehydrates well, but it doesn't. It won't be as hard to relearn but it'll be hard. So consider, for whatever you learn, are you going to be using it? Are you…
I think most of us are highly invested in the value of easily-rehydratable knowledge, because an incredible amount of the first third of our lives is spent learning facts that we'll forget. If we admitted there might be a better way, we'd have to do the hard and thankless work of institutional overhaul in our schools.
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This guy did something similar: completing a 4-year MIT undergrad CS degree in just one year! https://www.scotthyoung.com/blog/myprojects/mit-challenge-2/
Scott Young is a publicist - his goal is to sell, sell, sell. Completing a world-renowned 4-year curriculum in 1 years time is impossible. (He also admitted to reading the solutions instead of doing the problem sets)
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it’s a good undergrad book. also on that page he says lights out game is a “linear algebra problem”. It’s actually not. incidentally I worked on Lights out for my thesis, and my advisor made a whole career out of lights out! That game relates to Fibonacci polynomials, studied in Combinatorics - https://www.unf.edu/~wkloster/fib.html
How would you compare coding the matrix to strang ? I'm going to be starting out on one of these and coding-the-matrix is very python centric (which is super helpful and practical) versus MATLAB in Strang's book.
whether the code is in python or matlab matters little. the code is just a supplement to the main material which is still math. trying to understand that math by reading code is actively counterproductive and actually quite foolish. my professor gave a symposium talk on this topic, so i will use one of his examples -
At 0 minutes you have 0 dollars. suppose each minute you toss a coin. if it’s heads you make a dollar. if it’s tails you pay a dollar out of your pocket. What are the chances you’ll have $30 in an hour ?
This is the sort of classic problem that can be coded up in python or matlab under 5 minutes. it’s just a for loop & an if statement. It won’t tell you much about the actual probability because that number is so small your code will have to run for a long time to get a meaningful answer. Whereas it’s trivial if you just do the math by hand.
One question for all the self-learners here (I have immense admiration). Do these courses inform your day to day job in some way? Or is this for personal knowledge (even more impressive)? How do you find the damn time? Need some suggestions. My goals are infinite and my time is so short.
EDIT: Brain health also derives from a healthy social life, I forgot to add that to the list involved. Having friends that are interested in learning the same things as you, and discussing it with them, help you to develop self-checking techniques.
Also, Alan Kay pointed out in a speech in the last few years that our economy is doing really poorly right now producing researchers, and people who understand research, and you really can't get there without a good education.
I'll go one further and suggest that 'Transfer', which is the application of understanding of one topic to another, is one of the prime sources of what we consider 'innovation' or 'paradigm shifts'.
I feel as if that should be enough proof that education is an end to itself, but I need to be really clear: continuing education doesn't need to have a goal, and I would strongly discourage you from adding one. I go to the gym all the time without goals. I go for walks everyday, without goals. Each of these items are basic maintenance. Learning new things _well_ is basic maintenance for your brain. If you want to do continuous learning then you should install Anki, get a notebook and learn Cornell notes, then go out and take a quick class, lecture, or study material.
If you are learning something new, the fastest way to learn and retain the material is to move to self-testing as quickly as possible. I can go over this in more detail, but perhaps the first class I would recommend would be "Learning How To Learn" (Coursera), which produced a serious attitude shift in me about learning and what I am capable of as a human.
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I think most of us are highly invested in the value of easily-rehydratable knowledge, because an incredible amount of the first third of our lives is spent learning facts that we'll forget. If we admitted there might be a better way, we'd have to do the hard and thankless work of institutional overhaul in our schools.
This mistakes the purpose of school. It’s less learning than childcare for primary school, socialisation and teaching children to do apparently boring and meaningless work as directed by superiors, and ranking and proof of intelligence and conscientiousness at higher levels. We’ve known most people forget almost everything they learn at school for a very long time and spaced repetition and the forgetting curve date f…
It’s awesome to see more & more devs getting interested in math & stats as machine learning, optimization & sequential testing (what you folks call a/b test) becomes more mainstream. The obvious benefits are, much of math literature is currently written for consumption by math grad students & profs, so all of this will get a much needed rewrite. I foresee a surge in material like Jeremy Kun’s popular “math for progra…
The Coding The Matrix textbook is exactly the type of book you've described that is tailored for programmers. I've read only the first few chapters and found it a joy even if a little wordy in some parts. https://codingthematrix.com/
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How would you compare coding the matrix to strang ? I'm going to be starting out on one of these and coding-the-matrix is very python centric (which is super helpful and practical) versus MATLAB in Strang's book.
this is classic “mistaking the map for the territory”. whether the code is in python or matlab matters little. the code is just a supplement to the main material which is still math. trying to understand that math by reading code is actively counterproductive and actually quite foolish. my professor gave a symposium talk on this topic, so i will use one of his examples - At 0 minutes you have 0 dollars. suppose each…
not what you thought though.
Suggestion: Set aside complex variables and do measure theory instead. For the Fourier and Laplace transforms, cover those via measure theory. For measure theory, H. Royden, Real Analysis and the first half of W. Rudin, Real and Complex Analysis. Then take a course in graduate probability which is based on measure theory. Good authors are Loeve, Neveu, Breiman, Chung, among others. So, learn about the cases of conver…
Personally, I think complex analysis is important. I really like Serge Lang's book "Complex Analysis." It is supposedly a graduate level text, but the first half of it covers the basics at a level suitable for upper division undergrad class. Ahlfor's book is also really really good, but a little harder to read in my opinion. I didn't like either Royden or Rudin. I really like Folland's book "Real analysis: modern tec…
I just never could see much utility in complex variables: Complex valued functions of real variables. Sure. Complex valued measures? Sure. Fourier theory making a lot of use of complex numbers? Of course. A vector space where the field is the complex numbers? Certainly. Hermitian and unitary matrices with complex numbers? About have to like those due to the fundamental theorem of algebra, that is, roots of polynomials and, thus, complex eigenvalues. Functions of a complex variable? Never could see the utility.
One question for all the self-learners here (I have immense admiration). Do these courses inform your day to day job in some way? Or is this for personal knowledge (even more impressive)? How do you find the damn time? Need some suggestions. My goals are infinite and my time is so short.
If learning is part of a well-rounded set of activities that you are doing in your life, then it will lead to several positive effects. One, learning new things, by itself, with nothing else, reduces cognitive decline and increase brain health. But optimal learning and brain health also derives from physical activity and sleep, so it's a small part of the puzzle. EDIT: Brain health also derives from a healthy social…