Ask HN: I suck at math, where to start?

The problem for me is identifying where exactly in my mathematical fundamentals things fall apart (like with prime numbers, some basic arithmetic, geometry) that makes higher-level math a struggle conceptually. It's always felt like there were holes in my fundamentals. I suspect the only way to figure this out is to go back and do everything again either through Khan Academy or books. Does anyone else have this issue?

When it comes to math, I try to avoid self-diagnosing with dyscalculia or with poor working memory. Instead, I think I've gone so long with math being an anxiety-inducing subject that any time I need to solve math under the tiniest amounts of pressure, I fall apart.

Mind naming what book you used?

Agreed, I've used trig once since I left college for an image manipulation problem. Discrete mathematics, Algebra, statistics, and depending on the roles ... linear algebra are far more likely to be useful.

Any edition of "Mathematical Ideas"[0] might be a good place to start. While it may seem too basic for some, I feel that it covers a lot of concepts and material that are very useful when programming - problem solving, set theory, logic, number theory, basic algebra, etcetera - and does so in a way that is gradually cumulative and not so daunting.

Maybe this book will help you to realize you don't really suck at math, you just had some terrible teachers or whatever. It's also a great introduction to many different mathematical subfields so you can see which ones are most interesting/useful to you for future study.

[0] https://www.amazon.com/Mathematical-Ideas-14th-Charles-Mille...

I really like Jeremy Kun's writing: https://jeremykun.com/ and recommend his book, A Programmer's Introduction to Mathematics: https://pimbook.org/.

So far I've only read the first few chapters of the book, and the exercises often feel too difficult to me. But I think he does a great job of easing into mathematical notation, pausing to reflect on what a seasoned mathematician might be thinking when they come across that notation. He also makes a lot of analogies to programming, and has example programs that are easy to follow. It's helpful to have that angle to understand things from.

A related question: which part of math can be used to model object-oriented programming? AFAIK set theory deals purely with associations of objects, not how you make new ones. HS algebra is concerned with simplifying and inverting numeric equations. Meanwhile abstract algebra (and number theory) is concerned with finding talking about broad categories of numbers, relating those categories to each other, and making new, presumably interesting (read: surprising) statements about categories of numbers. Math is a study in "going meta" since each component of each activity gets a name, which are further grouped and named into other categories, limited only by what the thinker can stomach/finds useful.

But I am hard-pressed to think of any mathematical construct that reflects, even a little, the reality of OOP. This is evidence that OOP is an engineering concern, not a math concern. That is, OOP is one method to help humans deal with the complexity of a large amount of shared, mutable state (SMS), by partitioning it into smaller units of SMS. But math itself doesn't care about the scale of anything, and will happily encode any state into a single, very large integer, if you let it.

Some parts of programming are better grounded in math, like functional programming and relational algebra. Some distributed programming problems have some nice, ad hoc mathy treatment (e.g. Paxos), but don't really have a clear correspondence to anything.

Interesting the field that is closest to programming in real life, IMHO, is statistical thermodynamics. This is usually taught as part of the physics curriculum, and is pretty math intensive, and the field's remarkable job is to generally model microscopic behavior and then predict macroscopic behavior of huge aggregates. Programs always deal with huge numbers of tiny things, each having unique degrees of freedom, (alternatively, which have unique constraints), so there is some connection there. ST is also the field most closely related to certain "quant" jobs in the finance field, AFAIK, since the same tools let you model individuals in an economy and from that predict markets.