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I have an embarrassing question... math has always interested me but by luck and circumstance I have had a pretty successful career without needing anything bey

I have an embarrassing question... math has always interested me but by luck and circumstance I have had a pretty successful career without needing anything beyond college Algebra. Can anyone recommend a curriculum that a busy adult may be able to follow in their spare time? I just want to fill in blanks and explore what is possible.

jerkstate 1y ago
mathacademy.com is pretty awesome IMO. one hint: don't take notes/allow yourself to refer to notes during quizzes and reviews, the point is to be able to recall using just your brain, even if your progress is much slower that way, you'll learn a lot better.
- kstrauser 1y ago
  Many studies concur that the act of taking notes dramatically improves your ability to remember what you wrote, even if you never look at the notes again. You generally don't have time to transcribe a lecture like a stenographer would, so note taking requires you to understand the material enough to summarize it and describe it in your own words. Don't rely on your notes come quiz time, if you can get away with it, but by all means do take them during the learning process. And in the real world, you're allowed to refer back to your notes as often as you want to.
pavel_lishin 1y ago
I don't think that's embarassing. I like solving math puzzles, and I'm often realizing that I'm missing something I've forgotten since middle school or high school - some formula that I know exists that would make a problem trivial. I'd like to re-learn that stuff, especially as my kiddo starts advancing in math classes.
JKCalhoun 1y ago
For me, I set out to write a flight simulator from scratch following a book [1]. I learned a lot of linear algebra that way. Such that when I later took Calculus III in college (it was linear algebra) I aced the class. (Also, reinforced what I remembered from Trig, I finally fully grokked it. Except for trig identities, ha ha.) The book was targeting DOS and C++. I wrote it in C for the Macintosh. (That required that I figured out what was going on.) Go write one in JavaScript using an HTML5 canvas as your buffer. (I made a quick pass at doing something similar [2] — but do it on your own, don't follow my link below or look for the sources for Phosphor3D on GitHub.) [1] https://archive.org/details/build-your-own-flight-sim-in-c-dos-game-dev-michael-radtke-chris-lampton https://archive.org/details/build-your-own-flight-sim-in-c-d... [2] https://engineersneedart.com/Phosphor3DTest/ https://engineersneedart.com/Phosphor3DTest/
- glimshe 1y ago
  Did you finish your flight simulator?
harshreality 1y ago
College algebra is just rehashed high school algebra. Math is a broad subject. This is something LLMs are actually reasonably good at: ask them for textbook recommendations, and get into a dialogue about which sub-areas of math you're interested in and what level you're currently at, whether you want pure math (more theorem-proof focused) or applied math (more practice solving concrete problems, e.g. finding lots of derivatives and integrals). Toss in names of books that have been recommended and ask where they fit in to the LLM's other recommendations. LLMs don't understand the math, but they're trained on a lot of discussions and recommendations for math books, and have a reasonably good sense of what level different books are at. Download multiple recommendations in each area and try them all out. Seeing how different authors start out approaching largely the same material will help you conceptualize it better than just relying on a single approach. There's no universal "right" book to learn from. I wouldn't buy non-free textbooks without trying them out first. Youtube has a lot of math lecture series, which can help if you're stuck on a particular point, but they're not the same as doing problem sets yourself.
- rerdavies 1y ago
  LLMs DO understand the math. At least Claude does. Seems to be able to solve linear systems, invert matrices, and do a significant amount calculus, and handle some seriously advanced math problems. I haven't probed the outer limits, but, so far, Claude has handled all the math problems I've given it so far.
  - harshreality 11mo ago
    Even if a deep thinking LLM like Opus can get some math questions right when that depends on identifying the type of problem and applying a learned procedure, it's not going to be able to evaluate the pedagogy of math books it's never encountered, or at most was fringe material in its training set. I'm also referring to the faster models, not the slow and expensive deep thinking ones which I have little experience with. I don't see how reasoning would enable deep thinking models to meaningfully evaluate textbook pedagogy, either.
    - 11mo ago
fouc 1y ago
I've heard of adults going through Khan Academy's math curriculum for fun to refresh their math skills. It goes from K to 12 and up to 2nd or 3rd year university math, including calculus and such.
fainpul 1y ago
I wanted to brush up on my mostly forgotten high school math and found a free online course which used this ALEKS [1] tool. It was perfect for my situation. It was some course on edx [2]. Can't find it right now, but you might find another course which uses it. [1] https://www.aleks.com https://www.aleks.com [2] https://www.edx.org https://www.edx.org

jerkstate 1y ago

mathacademy.com is pretty awesome IMO. one hint: don't take notes/allow yourself to refer to notes during quizzes and reviews, the point is to be able to recall using just your brain, even if your progress is much slower that way, you'll learn a lot better.

kstrauser 1y ago
Many studies concur that the act of taking notes dramatically improves your ability to remember what you wrote, even if you never look at the notes again. You generally don't have time to transcribe a lecture like a stenographer would, so note taking requires you to understand the material enough to summarize it and describe it in your own words. Don't rely on your notes come quiz time, if you can get away with it, but by all means do take them during the learning process. And in the real world, you're allowed to refer back to your notes as often as you want to.

pavel_lishin 1y ago

I don't think that's embarassing. I like solving math puzzles, and I'm often realizing that I'm missing something I've forgotten since middle school or high school - some formula that I know exists that would make a problem trivial. I'd like to re-learn that stuff, especially as my kiddo starts advancing in math classes.

JKCalhoun 1y ago

For me, I set out to write a flight simulator from scratch following a book [1]. I learned a lot of linear algebra that way. Such that when I later took Calculus III in college (it was linear algebra) I aced the class. (Also, reinforced what I remembered from Trig, I finally fully grokked it. Except for trig identities, ha ha.) The book was targeting DOS and C++. I wrote it in C for the Macintosh. (That required that I figured out what was going on.) Go write one in JavaScript using an HTML5 canvas as your buffer. (I made a quick pass at doing something similar [2] — but do it on your own, don't follow my link below or look for the sources for Phosphor3D on GitHub.) [1] https://archive.org/details/build-your-own-flight-sim-in-c-dos-game-dev-michael-radtke-chris-lampton https://archive.org/details/build-your-own-flight-sim-in-c-d... [2] https://engineersneedart.com/Phosphor3DTest/ https://engineersneedart.com/Phosphor3DTest/

glimshe 1y ago
Did you finish your flight simulator?

harshreality 1y ago

College algebra is just rehashed high school algebra. Math is a broad subject. This is something LLMs are actually reasonably good at: ask them for textbook recommendations, and get into a dialogue about which sub-areas of math you're interested in and what level you're currently at, whether you want pure math (more theorem-proof focused) or applied math (more practice solving concrete problems, e.g. finding lots of derivatives and integrals). Toss in names of books that have been recommended and ask where they fit in to the LLM's other recommendations. LLMs don't understand the math, but they're trained on a lot of discussions and recommendations for math books, and have a reasonably good sense of what level different books are at. Download multiple recommendations in each area and try them all out. Seeing how different authors start out approaching largely the same material will help you conceptualize it better than just relying on a single approach. There's no universal "right" book to learn from. I wouldn't buy non-free textbooks without trying them out first. Youtube has a lot of math lecture series, which can help if you're stuck on a particular point, but they're not the same as doing problem sets yourself.

rerdavies 1y ago
LLMs DO understand the math. At least Claude does. Seems to be able to solve linear systems, invert matrices, and do a significant amount calculus, and handle some seriously advanced math problems. I haven't probed the outer limits, but, so far, Claude has handled all the math problems I've given it so far.
- harshreality 11mo ago
  Even if a deep thinking LLM like Opus can get some math questions right when that depends on identifying the type of problem and applying a learned procedure, it's not going to be able to evaluate the pedagogy of math books it's never encountered, or at most was fringe material in its training set. I'm also referring to the faster models, not the slow and expensive deep thinking ones which I have little experience with. I don't see how reasoning would enable deep thinking models to meaningfully evaluate textbook pedagogy, either.
  - 11mo ago

fouc 1y ago

I've heard of adults going through Khan Academy's math curriculum for fun to refresh their math skills. It goes from K to 12 and up to 2nd or 3rd year university math, including calculus and such.

fainpul 1y ago

I wanted to brush up on my mostly forgotten high school math and found a free online course which used this ALEKS [1] tool. It was perfect for my situation. It was some course on edx [2]. Can't find it right now, but you might find another course which uses it. [1] https://www.aleks.com https://www.aleks.com [2] https://www.edx.org https://www.edx.org