Ask HN: How do I get good at math as a 42yo with kids?

[goshatch]

Hi HN,

I'm a 42yo software engineer (mostly working on web stuff), and back in high school I had a terrible math teacher who made me lose my interest in the subject. As a result, I lack a lot of foundations in it, and math in general scares me.

I want to become math-literate, as a first step.

Ultimately, my goal is to be able to do more ambitious things with computers; I find that my lack of confidence when it comes to math is often holding me back. For example, I want to be able to read ML papers and understand how these things work.

Grateful for any suggestions or success stories!

[sebg]

https://www.mathacademy.com/ is probably the most popular HN response.

It's expensive at $50 per month, but it seems highly thought of if you look at Algolia (https://hn.algolia.com/?q=math+academy).

I haven't used it myself, but I am evaluating it for my kids to use.

It's too early to give feedback on that front, though.

[yumraj]

I’m using it for my middle school child to accelerate math. I figured it was better than the in-class math enrichment classes that just rush through common core math curriculum, and cheaper I should add.

They are also WASC accredited if you’re in the US.

[goshatch]

Yes, I heard about Math Academy, and will likely give it a try at some point. The price tag has made me a bit reluctant, but given the near-universal praise, I might bite the bullet.

[sebg]

You could also try beast academy and aops. We are huge huge huge (did I mention huge?) huge fans of them and have worked through pretty much all of their classes (1st grade through pre-calculus thus far).

Beast academy is around 15/20 a month and apps is more but you can just buy the book and work through it. Richard (the aops co/founder) has a ton of YouTube videos as well.

A third option is aops’s alcumus - which is a free math problem database. We use that a bunch as well and you could use it to figure out what you know and don’t know

[cashsterling]

If your goal is literally to get good at math through Calculus, Differential Equations and Linear Algebra... I feel like the best approach is working through good books (reading, taking notes, and doing problems out of the book then checking answers/solutions) and hitting Youtube and Khan Academy for help with certain topics.

Fortunately, there are a lot of great older-edition, cheap used books on Pre-Algebra, Geometry, College Algebra, Pre-Calc, Calculus, DiffEq and Linear Algebra, etc.

It will take some time to master all the math you want... but if you structure your studying so that are you actual enjoy studying (i.e. enjoy the process), you will 100% get there.

I'd be happy to list out of some book recommendations.

I will echo the sentiment of others that you don't need to be a math expert to use machine learning libraries effectively in many cases. The problem is, without the math expertise you won't always be able to identify the cases when you are using the wrong approach, etc. And you'll have a harder time applying cutting edge ML to new problems.

[keepamovin]

Can you please list out some book recommendations for Vector Calculus, Differential Equations, Linear Algebra?

I also think you can ask ChatGPT to teach you, and work problems with it using math/latex.

[__rito__]

Vector Calculus: Schaum's Outline (Spiegel)

DE: Tenenbaum and Pollard (ODE) or https://tutorial.math.lamar.edu/classes/de/de.aspx

Linear Algebra: Gilbert Strang's book. There’s also an MIT-OCW course to go with that.

You could also get something like Riley, Hobson, Bence and read the relevant chapters.

[dapperdrake]

What kind of math are you interested in?

School-like math can be learned from text books, however, learning it with real people seems often more enjoyable.

University style math, where you learn how to build/make mathematics and learn how to dig into all the intricacies can be really fun and change your world view and problem solving skills forever. The tricky but is that some of the essential tribal knowledge is very difficult to find outside of good introductory university lectures. That’s a bit of a drag.

What kind of math are you interested in?

The big split (according to Grothendieck) seems to be Geometry vs. Algebra.

Algebra covers symmetries. For example, repeating patterns, scaling a business, for-loops, and double entry bookkeeping/accounting (disregarding measurement problems).

Geometry covers asymmetries, conditionals/"if"s, lengths, distances, approximation (as a concept, confer Cauchy-sequences) and things like statistics/ML/LLM, numerical optimization, computer graphics, non-standard Analysis with infinitesimals, Differential equations and dynamical systems, Fourier transforms (arguably not Algebra), compression (arguably not Algebra), and information theory (arguably not Algebra).

There is also set theory for relations (think relational databases), and graphs (with edges and vertices/nodes) (applications include register allocation in compilers via graph coloring as well as git and Merkle trees a.k.a. "Blockchain" disregarding the ledger). Then there is lambda calculus and similar fields. You can also go into formal logic (Some logicians and philosophers are unsure whether this is mathematics in the strictest sense).

Which problem domains or specific problems are you interested in?

(Interest leads to learning -- never the reverse. Paraphrasing Taleb)

[juanse]

I am in the exactly same situation than OP. I tend to think advanced calculus is key to think well: domains, limits, restrictions, functional math. Is that accurate?

[dapperdrake]

Limits are a calculus/Geometry concept. A special case are Cauchy-sequences which model approximations.

Domains (as I know the term) are more of a set theory idea. Not that that matters.

Algebra also seems to be part of thinking well, however, calculus exposed me to patterns that I hadn’t seen in programming all that much. Many of the Algebra patterns I had already been familiar with from programming.

[cweagans]

The same way you become good at anything at any point in your life: decide you want to and then put in the deliberate/consistent practice to make it happen. Set aside 15-20 minutes per day, work through Khan Academy, Math Academy, or a precalculus textbook, and then (the hard part) keep doing that.

[runjake]

I only took up to algebra and geometry in high school. My middle school kids already do trig and more advanced forms of algebra (differential equations, linear algebra, etc) that I never learned, so I make heavy use of Claude.ai to learn about and explain everything.

I try to grok what Claude explains, open Obsidian and then paraphrase it myself with the exact problem they're working on, along with 1-2 additional examples.

It helps that since graduating high school (long ago) I've developed an interest and enjoyment of math. I do some of their problems for fun.

When possible, I try to have them start by explaining what they know so far, and then we work together on filling those knowledge gaps and inaccuracies. It totally has to be a back and forth thing with me/AI or they won't grok it.

[kevinsync]

I’m a big fan of 3Blue1Brown as a visual supplement for learnin’ me some tricky number stuff [0]

There’s also an ocean of great YouTube math content, sometimes packaged in hidden ways (ex. I’m away from my bookmarks at the moment but there’s a guy who does fantastic Three.js tutorials, and to see abstract math concepts applied to real, visual projects, it’s really eureka-level shit for me personally)

0. https://www.3blue1brown.com

EDIT: found the YT channel, very solid stuff [1]

1. https://youtube.com/@waelyasmina

[_kb]

Practice.

Don't just read, binge YouTube, or click through banal tutorials with a misplaced hope of learning through osmosis. You learn math by doing math. Most likely without a computer. It's unpleasant as you will be quite bad at it, but that's a good thing as it means you can get better.

I'm a bit younger but also with kids and have been using the fracture in life that brings to fill in similar gaps in education. UoL have some courses as part of an online degree. I don't recommend it, but the references are good for fundamentals. I've been collecting them and some study notes here: https://simple.industries/notes/uol-comp-sci.html.

The Susan Rigetti guide (https://www.susanrigetti.com/math) already posted is also an incredible reference.

Also, learn with your kid(s)! There a whole set of publications around the math circles movement. I'm currently working through this with my 3yo: https://www.goodreads.com/en/book/show/12689040.

[overu589]

> holding me back

Just read the damn papers, and take notes, not because you’re going to want to review them later, because the mechanical process of writing things down burns them in.

The math will come through your persistence, I’m sure you’ll try and not finish dozens of YouTube lists and online courses. Build that store of PDFs on everything math related.

In the end it is merely making yourself do it that will make you that man.

btw, I was mathless for much of my life. Only later (also a self student of the many other things) did I have epiphanies of math that clicked it together.

A lifelong programmer, equations are like miniature procedural logic scripts or constraint definitions, one must spend the time learning every reference, and when you’ve had enough of that you will be able to “read” the math. It’s really not a large language, most people probably take years learning about sets and recursion and things that a programmer should get right away.

Like base conversion. A lot of complicated looking math is really just base conversion between different metrical scales.

[_mad_eye_]

I'd recommend Gilbert Strang's Introduction to Linear Algebra and 3B1B's calculus and linear algebra series. They focus on the intuition part of math, which makes it fun and interesting. After that do some problem sets, that should give you a solid foundation to understand ML papers with the help of things like ChatGPT.

[schappim]

As someone your age who struggled with maths, has kids, and shares your goals, I found Mathematics for Machine Learning[1] (available as a free PDF or on Amazon) and Khan Academy [2] to be great resources.

I used those along with a few exercise books and a Casio FX-82ES Plus 2nd Ed.

My advice: keep practising maths every day, or you’ll just forget it again.

You can also copy and paste complex maths problems or papers directly into an LLM - it does a decent job of explaining them. If you get stuck, try the "Explain it like I’m n" trick, decrementing n until it makes sense.

[1] https://mml-book.github.io/book/mml-book.pdf

[2] https://www.khanacademy.org/

[keepamovin]

Text books and problem sets. Sometimes the old ways are the best

[aristofun]

I'm not sure that you need math Math. As far as fundamentals go CS uses just a fraction of what The Math has to offer.

I'd focus on digging some good CS foundations course if I were in your shoes. To avoid overwhelming myself with redundant info.

[trod1234]

Its a long journey, and without someone who knows what you don't, you'll end up getting stuck because math is primarily used today to gatekeep the more advanced subjects, eschewing intuition, and describing numerical patterns instead very abstractly.

You should start with mastering the basics to the point where you are able to do the calculations in your head almost instantaneously. Start with the material from a book series called The Cosmic Calculator. Digit Sums touch on modular arithmetic and cyclic groups (in Abstract Math).

Math is all about relationships, and nearly everything is built on a shaky foundation until you reach Abstract Mathematics (Modern Algebra), where you have to go and unlearn a big portion of what you thought you knew.

In this coursework you learn how math actually works, as opposed to memorizing a bunch of skills and strategies that may or may not work depending on the circumstances.

You'll also learn how to test for the fundamental properties you will need to perform operations between two differing objects.

Most hard science uses strategies to gatekeep careers using math, and the structures of much coursework are designed so that bridges get burnt, and the student is blamed and tortured until they quit.

The NEA promoted these structures. For a concrete example, the first of several of these gates is the three course series Algebra->Geometry->Trigonometry.

What goes undisclosed is grading changes from only following the correct method to pass Algebra (not getting correct answer), to correct method and correct answer (in Trigonometry).

There is a semester between the changes of unrelated material, so you can pass 1, and 2, and then repeatedly fail 3. The student is blamed for not knowing the material, and teacher may not have the resources or time to identify and teach a class that is not their responsibility, where the student should have failed the class 2 classes prior.

This is just one of several by-design stumbling blocks. The student is made to think they just aren't good at math, and the lack of agency to correct, the isolation, and the circular nature meet all the requirements for torture. This is how students get PTSD and never learn math beyond the bare minimum that's needed.

[brudgers]

“Mathematical Preliminaries” is Chapter One, Section 2 of The Art of Computer Programming. The rest of the book is also relevant to programming. And an adequate challenge for lifetime learning.

[liontwist]

Just wanted to share an anecdote. When I first checked out this book from the library I couldn’t even get through the first math concept - mathematical induction.

It’s famously a brief intro before the rest of the book, but more math than most everyone learned.

Years later I came back after graduate school etc, and yeah chapter 0 is kind of basic material the reader should know :)

[a_tartaruga]

On top of all the great advice here make sure you do as many high quality problems as you can. Some easy ones to build your confidence, a majority that are tough but doable and then occasionally try things beyond your current abilities.

If you can make time for an in person class at a local university or community college 1-3x a week it will probably 10x your progress.

As others are saying you should focus on linear algebra which is the doorway to depth in almost all technical subjects.

[Gooblebrai]

Khan Academy until Calculus is perfect to recover the foundations

[idontwantthis]

Seconded. 10 hours per week with my stepson brought him up about 5 years in less than 6 months. Consistency is key (same as everything).

[HenryBemis]

https://www.khanacademy.org/math/

[ezekg]

Build a game or two on the side. I'm still not where I want to be i.r.t. math, but building a game in Unity, and another in Bevy, has helped me hit hard problems that have to be solved using math I don't know, which helps push me to learn. ime, 3D games require more advanced math, but could just be that I haven't done 2D enough. As far as teaching material, Khan Academy is great.

[NBJack]

I will piggy-back on this and ask similarly for how to get gud at proofs. My math is OK, by my ability to perform proofs is barely passable. I don't know what I did wrong on college in the related courses, but I would love to rectify it at some point in my life.

[bjourne]

https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...

[terrycody]

We are in same boat mostly, and I found learn from textbooks from 0 groundup is a really enjoying experience, it reminds me of the good old student era, though I didn't spend time on learning, so that I can't even find a good job now.

[bluecheese452]

Am I the only one who didn’t find math particularly helpful in their career? I did multivariable calc, linear algebra, diff equations, and a whole bunch of calc based stats courses.

I think the only thing I use is some basic algebra a few times a year.

[dapperdrake]

That might depend on the problem domains you are working in.

When I do standard CRUD in PHP, there isn’t much "math" involved. "Not even" clean category theory and/or powerful type systems.

Some other applications in number crunching and measurement are really math and stats heavy, though.

[AntoniusBlock]

This is a great resource for self-learning mathematics: https://www.susanrigetti.com/math

[goshatch]

Thank you for this!

[AntoniusBlock]

Reposting some advice I gave to someone on HN a few weeks ago:

Here's some advice I've been given by maths professors that I've put into practise. This stuff really works.

-- Make sure you can do it cold, as in make sure you can do things without looking at notes, or looking at wherever you learned it from. For example, say I give you a calculus problem, you should be able to solve it without any outside help, just you, some paper and a pen. No notes, no Google, nothing else. If you can't, then you need to study more and do more problems.

-- Build a routine. Make sure you study whatever it is you want to study every day at the same time and you'll find yourself wanting to do it after a habit is built. And if you miss a session, for whatever reason, you'll feel quite bad about it, and want to try extra hard in the next session because you know you're "behind schedule".

-- Actively recall whatever you've learnt. You can do this by quizzing yourself (make your own problem sets, or do problem sets made by others), and by using flashcards/anki for the things you have trouble memorising. This is one of the best ways to retain info.

-- Don't stress or get angry. You'll just stop the learning process. If you find yourself stressed, or angry, take a break. Remain calm, happy and curious.

You can do it. I believe in you. Start today.

[jvanderbot]

I'm about the same age / situation as OP.

What changed for me vs school days is that I don't have long blocks of time to work on a problem, so a tricky problem is likely to be skipped. I had to actively force myself to not skip hard things, meaning some days all I did was spend 10 minutes on the problem, find the wrong answer, and go to bed to try again tomorrow. Eventually I get em and move on much happier.

Unlike school days you have years to do this right.

OP, I recommend you take parent's latter points to heart. I (and likely you) need to re-learn how to learn in this phase of our lives, vs what we were used to as younguns whose entire job was just learn.

[Optimal_Persona]

I'm in a similar situation but a decade older. My "aha" moment came with Ivan Savov's "No Bullshit Guide to Math & Physics". For some reason working through this book "sticks" in a way that Khan Academy and similar online tools haven't. That, combined with randomly reading entries in "Mathematics 1001" have gotten me to where I can read through audio acoustics/DSP and information theory papers (my main area of interest) and understand what's going on.

https://minireference.com/

https://books.google.com/books/about/Mathematics_1001.html?i...

[ivansavz]

Thanks for the plug!

If anyone is interested in the "No Bullshit Guide to Math & Physics," you can check out the extended PDF preview, which includes a free chapter: https://minireference.com/static/excerpts/noBSmathphys_v5_pr...

The concept map from the book might also be of interest independently of the book, since it shows the connections between high school math topics, physics 101 (mechanics), and calculus: https://minireference.com/static/conceptmaps/math_and_physic...

[caspper69]

I have commented about this frequently on HN, about maths being my kryptonite.

But I keep at it, and I do keep learning. I am striving for better literacy (i.e. being able to read papers).

The advice I've been given, and it is helping, is to be persistent and to actually do the work. Only through doing will you start to see everything take shape. You will start to notice the way problem sets are laid out and build up your foundation.

It's like the Karate Kid. Wax on, wax off. Paint the fence. You can't just read the material and hope to keep your understanding. You have to burn it into your memory through practice.

[dustingetz]

Start here: No BS guide to Linear Algebra https://a.co/d/6em7tXE . There’s also a No BS guide to Math/Physics which goes through calculus and geometry. This is freshman level content. I read this on the couch next to my wife act age 37 for about 20-30 minutes a night, a few times per week and got through it in six months. You will need to work some of the exercises, i used a lap desk and clipboard which I store next to my spot on the couch.

[goshatch]

Thank you! I think I'm not at freshman level yet, though, so going to have to work my way up to that.

And yes - consistent practice is a must, thanks for reinforcing that.

[dustingetz]

freshman is “the beginning”, i’m pretty sure this book series is what you want

[hpaone]

Through most of my life, I believed that I was utterly incapable of doing math and mostly just kind got by in high school, didn't really think I would need it that much. Then I took a reality check the first time I attempted the equivalent of my country's SAT test. At the time, I got in my head that I wanted to be a computer engineer and that required at least above average grades in math and physics so that I could have a chance. There really isn't much I can offer in advice, besides: diligent study. That was what got me by. Sitting my ass at the desk everyday for hours on end, starting from first principles (and I mean first principles, like basic arithmetic first principles) and doing as many practice problems as I could. I probably did too many of them, but getting them right was the only thing that brought me any confidence that I was learning. I did that for about a year and, while it didn't turn me from math illiterate to math genius, it gave me enough of a foundation to get into college and have a easier time than my peers on subjects like calculus. In your case, you can take a lighter approach, since it isn't urgent by any means, and you probably won't have as much time as I did. I recommend setting a time whenever you can to study, ideally it would be around two hours, but I find it more important be consistent about it. If you are anything like I was, you may have some knowledge on math, but its akin to Swiss cheese: full of holes. That being the case, start from the earliest point it makes sense to you. I was very paranoid at the time, so I started from basic arithmetic and, although that may not have been necessary, starting from scratch gave me the confidence that I wasn't missing anything going forward. Mathematics is a cohesive structure, where the higher elements are build upon the lower foundations, you cannot get very far without having a good grasp on the basics. As to learning resources, there are many online for free (Khan Academy[1], Paul's Math Notes[2], many introductory books at the Open Textbook Library[3])

Lastly, try to have fun with it. Back when I started the journey, I was to focused on what I could get from learning math (that is, getting into college and then, hopefully, a job), that took out of the experience a bit and the only thing that kept me going, though I didn't recognize at the time, was the joy of learning something that I believed my whole life to be unapproachable, at least by me. So be patient, if you bang your head enough times against this wall, I can attest that it eventually starts to show cracks.

Good luck on your learning journey.

--

[1] https://www.khanacademy.org/ [2] https://tutorial.math.lamar.edu/ [3] https://open.umn.edu/opentextbooks/subjects

[goshatch]

Thank you for your thoughtful reply! This sounds like exactly the situation that I am in: some knowledge, but full of holes. Starting from the very basics to build confidence seems like the way to go.