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Ask HN: How to learn math from zero for adults?

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Re: Ask HN: How to learn math from zero for adults?

#141

Post by jay3ss »

Tempest1981 wrote: post #92
chongli wrote: post #82

Earlier quoted context omitted.

It depends where you study and what courses you take / who teaches you. Sometimes the professor will drive a ferocious pace of instruction and assessment and you will simply not be able to meaningfully keep up unless you sacrifice the depth of your learning in exchange for getting everything done. I have been in that position and watched my grades tank. Then, a year later, I watched my peers struggle with follow-up m…

I was always pushing to take 16-18 units (5-6 classes), so never any extra time to "savor" the details, or deep dive into areas of interest. If I did it again, I would take the minimum of 12 units (3-4 classes)... assuming I could afford to stay in school for 6 years. At the time, I was racing to graduate and get a job.

12 units was the sweet spot for me. I was able to digest and master the material because I had the chance to put in the necessary work to truly understand the material and still have a life outside of school. I decided to take more classes (21 units or 7 or 8 classes) and although I was still able to get very good grades (graduated with about 3.8/4.0), I wasn't able to master the material and I had no life outside of school.

> I was racing to graduate and get a job

This is also why I increased the number of units that I was taking.

Re: Ask HN: How to learn math from zero for adults?

#142

Post by rg111 »

Perez418 wrote: post #136
rg111 wrote: post #56

Earlier quoted context omitted.

I was an A+ student up to Sophomore year in HS. I downgraded to A or B+ student after I knew how much fun actual learning is. Before that, all I was doing was memorizing and practising heuristics to get A+. I actually started learning Science since 11th grade. I grew and grew. And my scores tanked. Got only 6.xx/10 in college as well. But no regrets. Learning Math properly gave me a super solid foundation to learn De…

I would love to chat sometime if you’re available. I’ve been teaching middle school math for the past 6 years. I’m now trying to transition into tech.

Send me something, like a Discord username, or an email.

Best would be Libera.chat, though.

Update your profile, and I will check back after 24 hours.

Re: Ask HN: How to learn math from zero for adults?

#143

Post by freedomben »

Perez418 wrote: post #136
rg111 wrote: post #56

Earlier quoted context omitted.

I was an A+ student up to Sophomore year in HS. I downgraded to A or B+ student after I knew how much fun actual learning is. Before that, all I was doing was memorizing and practising heuristics to get A+. I actually started learning Science since 11th grade. I grew and grew. And my scores tanked. Got only 6.xx/10 in college as well. But no regrets. Learning Math properly gave me a super solid foundation to learn De…

I would love to chat sometime if you’re available. I’ve been teaching middle school math for the past 6 years. I’m now trying to transition into tech.

What do you want to do in tech? You want to do software development (like building apps, websites, etc) or something else? I pivoted into software after starting somewhere different and happy to give advice.

Re: Ask HN: How to learn math from zero for adults?

#144

Post by jostylr »

This won't help in a practical sense, but Norm Wildberger has a very different take on mathematics and maybe this could be a way of coming to peace with what you hated: https://cosmolearning.org/courses/math-foundations-with-norm...

For a more practical direction, you should start with Guesstimation if you are not already versed with it. It is an indispensable tool for getting people to think you know some math as well as helping you detect really bad ideas in addition to helping you get playful with mathematics, which is the only way to really master it as a tool.

Re: Ask HN: How to learn math from zero for adults?

#145

Post by astrange »

DantesKite wrote: post #6

I always recommend courses on Udemy, Coursera, etc. Anywhere you have to pay for the knowledge. The money seems to be an important filter for quality. Not always, and there are certainly exceptions, but in my experience, it's highly predictive of useful knowledge.

This is subject to Goodhart’s Law. I’m not sure how to avoid that except by deleting this comment so nobody knows what measure you use.

Re: Ask HN: How to learn math from zero for adults?

#146

Post by blagie »

Viliam1234 wrote: post #124
blagie wrote: post #70

Earlier quoted context omitted.

I'll just mention: From a scientific perspective, this is absolutely the wrong advice. If you couldn't understand something yesterday, that's very good evidence you won't make sense of it today. You should work hard, go deep, and try hard problems, but if you fail to understand something after putting in the effort, just move onto something else. Learn a few unrelated things, and come back. Much of the time, if you c…

> From a scientific perspective, this is absolutely the wrong advice. Those are unnecessarily harsh words. You and elliekelly are not contradicting each other, but talking about different things. If you didn't understand chapters 1 and 2 from a textbook, reading chapter 3 from the same book is usually a BAD idea. Sadly, this is what formal education often tells you to do, because it follows a predetermined schedule.…

This also, while common sense, is unfortunately often incorrect -- at least the part about avoiding chapter 3 (a different book is a good idea).

If you didn't understand chapters 1 and 2 in a textbook, reading -- or at least skimming -- chapters 3 and 4 is usually helpful. It doesn't make sense to read them for mastery, but you'll see context where material from chapters 1 and 2 is applied, or concepts that build on them. You have to be comfortable with confusion, since most of it will go over your head. You will pick out some parts.

Once you've done that, go back to chapters 1 and 2.

Think of calculus: limits -> derivatives -> integrals.

However, you can understand a Reimann sum without derivatives or limits. It helps understand and motivate both.

This is called a whole math approach. You make successive passes with increasing depth. I've explained calculus concepts to kids under 10 with no problems, as have many others. Over time, you want to develop:

- Mechanics of integration, differentiation, and other computation

- Applications (e.g. debt versus deficit)

- Intuition

- Formalism

- And so on...

All of those support each other.

You see this in how you read research papers too. Novices read them linearly, and experts absorb them nonlinearly.

As a footnote, Vygotsky (in the original, e.g. 1978 translation) is probably the first person to discover that doing things beyond your level of ability accelerates learning. Not aiming for mastery means you're free to fail, free to try harder things, and learn faster (if more painfully).

85% of American textbooks about Vygotsky, though, always say exactly what he was trying to debunk. He pushed very hard for learning being harder and more abstract than most thought possible.

Re: Ask HN: How to learn math from zero for adults?

#147

Post by wly_cdgr »

I've been in a similar boat. Khan Academy has been helpful, as have some other resources:

* Gelfand (et al.)'s HS math book series: System of Coordinates, Functions And Graphs, Algebra, Geometry, Trigonometry

* The problem collections Challenging Problems in Geometry and Challenging Problems in Algebra, available from Dover

* The math and logic courses on Brilliant.org

* Smullyan's Introduction to Logic

* Balakrishnan's Introduction to Discrete Mathematics

* For a bracingly irreverent "skip the bullshit" perspective, George Simmons' Precalculus Mathematics In A Nutshell

* The A-Levels A* prep sequence from Imperial College London, available on edX (this is actually roughly equivalent to a first year undergrad curriculum at US unis)

General advice:

* Practice, practice, practice - solve lots of problems & push yourself to repeatedly prove and reprove things. 'Getting it' once is not enough, math is like basketball. Something all the resources above have in common: tons of exercises, with solutions

* Keep mixing up difficulty so that you get some easy wins for confidence and motivation but also challenge yourself and keep yourself humble. Occasionally dip way down to remind yourself how far you've come, and on the other hand sometimes dip into something like Concrete Mathematics to remind yourself how far you still need to climb

* Go over the same material many times from different authors/teachers/sources

* Take your time. As long as you keep challenging yourself, and keep putting in those 10-20 hours a week, every week, you'll get to a good place and then keep going

Re: Ask HN: How to learn math from zero for adults?

#148

Post by ImaCake »

methusala8 wrote: post #43
ImaCake wrote: post #35

Earlier quoted context omitted.

>It seems silly looking back that I was solving problems on the number line as an adult. I study biostatistics and dabble in population genetics research. I still resort to number lines and venn diagrams frequently. There is a reason we teach number lines - they are very useful!

Where exactly do you use number line? Thanks.

Usually just when I am having trouble with an idosyncratic number scale. So usually when I need to make sense of dates and the time between them. It's often got nothing to do with work, but I do use them in my personal life.

Re: Ask HN: How to learn math from zero for adults?

#149

Post by saminjerseycity »

zerohp wrote: post #28

I was a C student in high school. I never took a math class beyond basic algebra. I started from Khan Academy's first exercise when I was 33 years old. It seems silly looking back that I was solving problems on the number line as an adult. At that time, around 10 years ago, Khan Academy had excellent coverage through trigonometry and single variable calculus. Once I reached that point I went to my local community col…

Almost same thing. Khan Academy is amazing.

Re: Ask HN: How to learn math from zero for adults?

#150

Post by joeld42 »

I recommend this book:

https://www.glassner.com/portfolio/deep-learning-a-visual-ap...

It goes over the basics in the first half to make sure you have a foundation to understand the deep learning stuff.

And don't feel bad if there are gaps in your math. Go to khan academy or youtube and fill in the gaps. The most important thing is to find exercises and do them yourself, watching videos and lectures help understand the big picture but you'll never internalize them without doing the work.

I think in any kind of knowledge, math, music, art, etc... the biggest limitations come from people not knowing the basics deeply. Don't just work on stuff until you get it, or it clicks, keep going until it's so boring it's automatic. It will feel slower but you'll ultimately learn faster as you won't eventually hit walls.

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