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Ask HN: How do I re-learn maths as a middle-age person?

33 points by noneeeed ↗ HN
I'm in my early 40s. Recenlty I was looking at one of my old CS textbooks (Mitchell's Machine Learning), and I quickly realised I have forgotten most of my maths, I found much of it impenitrable, despite having no problem with it when I was at university.

It's been 18 years since I've had to do any maths beyond the basics, that was just some trig to do coordinate conversions. Most of the code I've written since uni has been information systems, not mathmatical in nature. I'd love to try my hand at interesting problems, a bit of ML, stats, probability, perhaps simulation or signal processing, and some electronics. But I feel like a carpenter who's forgotten how to use his saw.

I'd really like to regain what I've lost, and perhaps advance a bit more from A-level (that's the 16-18 qualification in the UK). I know I can learn it, I did before.

What are good resources for re-learning maths? I have two small kids so I'd like to find something structured that I can do a little at a time in the evenings, a good book with exercises or an online course would be great.

25 comments

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mindcrime
I can relate. I'm 47 and also working on learning/re-learning previous maths, and extending my knowledge as well.

One of my favorite resources: Professor Leonard. He has videos of him teaching everything from pre-algebra through calc III, statistics, and differential equations. He's planning a linear algebra sequence soon'ish as well.

https://www.youtube.com/channel/UCoHhuummRZaIVX7bD4t2czg

Then there is Gilbert Strang:

linear algebra - https://www.youtube.com/playlist?list=PL221E2BBF13BECF6C

calculus - https://www.youtube.com/playlist?list=PLBE9407EA64E2C318

Others:

ProfRobBob - https://www.youtube.com/user/profrobbob

3blue1brown - https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw

Organic Chemistry Tutor (not just "organic chemistry"!) - https://www.youtube.com/channel/UCEWpbFLzoYGPfuWUMFPSaoA

(could also be useful if you actually did mean "meths" and not "maths")

And, of course, there is always Khan Academy.

nabla9
You also need to do exercises.

Schaum's Outline Series is good for that.

mindcrime
Agreed. There are also several series of "problem books" out there, that are nothing but hundreds and hundreds of problems (and solutions) for a given subject. They tend to have titles like "The Humongous Book of Calculus Problems" or "The Humongous Book of Algebra Problems", or "1001 Solved Problems in Linear Algebra", etc.

I also buy cheap used copies of older editions of various text-books to supplement the video stuff. When you don't have to worry about using the latest version because it's required for a class, you can find some really cheap deals.

noneeeed
That looks great, thanks so much for that. The professor Leonard channel looks perfect, especially as it starts at pre-algebra. I'm not sure what that covers, that was a long time ago, but it would be good to cover that again just to ease myself into it.
jjgreen
meths -> maths :-)
noneeeed
Doh! And of course I had the no-procrastination turned on and couldn't get back in until now.
jjgreen
With respect to your question, I did something similar, getting decent A-level results but then, er, having other things to do for 10 years. I went back and worked through my A-level textbooks again at 28, I found it quite helpful knowing "that I had done this before" and I think it got me back up to speed quite quickly (a summer).
noneeeed
Yeah, I definitely think that will help. I've had the same experience when trying to get back into running. Knowing I used to run a lot makes it a lot easier getting started all over again.
dang
That was a good one but we'll fix it now :)
noneeeed
Thank you!

Btw, just thought I'd hijack this moment to say how much I appreciate the moderation work you do here, it's fine art, and HN seems to get it about right most of the time, which is all we can really ask.

bushi_do
The thing about math(s) is that it's cumulative--it builds on all the previous math(s) you learned or should have learned.

I would literally go back as far as necessary (2nd grade/form even) until you find math that isn't challenging, but still takes mental effort to remember. For example, do you remember fractions? exponents? If not completely, go back and re-learn them.

Then progress grade by grade will go much much quicker than the first time you learned them. Khan Academy is a good help.

Someone else mentioned drills and Schaum's. I second that. Drilling is even more necessary as one gets older (I say this as an oldster.)

Once you've exhausted grade-school math, you would be ready for some of the other suggestions listed by others.

mindcrime
I literally went all the way back to "pre algebra" when I started down this path. It bruises the ego a little bit, but as you say, it goes faster the nth time around. And it really is important to have the prereq stuff down, or you'll start flailing with the later material, not because it's conceptually difficult, but because of not remembering how to do the "easy" stuff.

In one of his videos Professor Leonard says "Calculus is the class you take to finally fail Algebra". I think there is some merit to that.

noneeeed
Yeah, I'm definitely up for doing that. I don't need to go back to fractions, but I think I'd like to start from the beginning of basic algebra. I figure that even if I know the material, the practice will help before I move on.
st1x7
Khan Academy

Two main reasons why it's better than other resources for your use case:

- it covers everything from pre-school arithmetic all the way up to multivariable calculus. This means that you can pick up from the level that you're comfortable at and build up from there

- Sal (who delivers most of the tutorials) teaches in a very approachable way and doesn't mind overexplaining basic things that university lectures tend to skim over

Once you're past Khan Academy, you can get some undergraduate/postgraduate lectures from MIT or just textbooks if you're interested in more rigorous treatment of mathematics or more advanced subfields.

psyklic
The key is to do lots of problems. Toward this, I highly recommend "The Art of Problem Solving" which is packed full of neat insights and interesting problems from math competitions (at an "advanced high school" level).

https://www.amazon.com/Art-Problem-Solving-Vol-Basics/dp/097...

noneeeed
That looks great, thanks. One of the things that will help me re-learning is that I now have a much better understanding of how maths can help you answer questions and solve problems, rather than just working through rote exercises. I always found that maths made more sense in physics lessons than in some maths lessons.
trilinearnz
I've been through this experience myself, so I know what you mean! The best resource I found was something provided by my local university called "Mathercize" (may just be something specific to them), which gave you a range of problems you could complete online, with a brief run-down of the theory on how to solve them. It was positioned as a "refresher" on maths for those doing college-level study, and in my case the problem sets were designed for MBA students.

Maybe looking around for these kinds of refreshers rather than discrete textbooks in their own right is your best bet? I know that I encountered analysis paralysis when trying to re-learn "everything" from the ground up, and got nowhere as the information wasn't curated enough for my needs.

Barring this, I found the "MathIsFun" to be the best all-round resource for grokking foreign math concepts.

OnACoffeeBreak
I'm only a few chapters in, but so far this book has struck a balance of being dense enough to not be boring:

"No Bullshit Guide to Math and Physics"

https://minireference.com/

noneeeed
Cool, thanks for the recommendation, those look great.
nextos
If you think you are roughly at A-level, get a quick refresher:

* Basic Mathematics by Serge Lang

* Calculus Made Easy by Silvanus Thompson

Then try a DIY bootcamp in the spirit of Harvard Math 55. If you are interested in continuous math:

* Vector Calculus by Hubbard & Hubbard

If you are interested in discrete mathematics and computation:

* Logic in Computer Science by Huth & Ryan

stakkur
Before you dive into the inevitable recommendations of websites and YouTube channels, I strongly recommend A Mind for Numbers by Barbara Oakley. I can almost guarantee you'll find it worthwhile. Don't dive into doing hours of exercises first.
mindcrime
I second this recommendation. I read that book a few months ago, and think very highly of it.
vram22
MathWorld may or not be what you are looking for, but it looks like a good reference site, for short takes on a large number of math topics. Good graphics too.

Caveat: only viewed it briefly until now.

Last I saw, it was part of Wolfram, though maybe independent earlier.

Check the About page for a good overview.

https://mathworld.wolfram.com/

https://mathworld.wolfram.com/about/

dirktheman
Slightly related, but my daughter's junior high school offers a special course 'Maths for parents'. It's awesome since a lot of parents have forgotten even the most basic maths principles since they last sat in the school benches. Myself included, if you don't calculate the circumference of a circle on a daily basis you tend to forget how to do it, for instance...

One thing that stuck out to me is that there are so many great YouTube videos on virtually any subject. Back in the day you were stuck with your textbook and if you, like me, were stuck with a less than stellar teacher, a lot of things didn't stick. I have an identical twin brother, but we had different teachers and took different classes from middle school on. My brother was excelling at maths, I was faltering. My brother flunked french, it was my favorite subject. The only variable here is the teacher: my maths teacher was widely regarded as a boring, old and uninspiring man. My brother's maths teacher actually cared about you grasping the subject. Same way around with our french teachers.

rtdrury
Keyword is enjoy. Kids learn fast because they enjoy. Are you enjoying the math lesson? If not, pause, try again later. Investigate for yourself, whether enjoyment makes a difference. Don't assume it does not just because nobody is emphasizing it.