Similar to the OP, I had a lot of anxiety around math and academic performance. I dropped out of college at 18 and the highest math class I took was in high school (pre-calc), which I almost failed.
At age 33, I enrolled in community college and took Calc I-III, Linear Algebra, and Differential Equations. The community college hosts weekly "math jams" and offers free 1:1 tutoring.
I'm currently taking a Discrete Math and Probability class at UC Berkeley for fun this summer (CS70), which would have seemed absurd just a few years ago. The community college system in California is extraordinary; I'm glad I got to experience it first-hand.
Seconding Cal JC hype. I sandwiched a JC in between two stints at traditional 4-year schools. All of the instructors at the JC seemed miles more interested in teaching than their university counterparts. They were almost universally more approachable and invested in your education.
The core of math, as GP mentioned, is learning proofs.
I would go as far as to say that most high school “math” and “math” taught in many college courses is borderline irrelevant.
It’s like learning how to paint by memorizing names of colors. Learning to fix a car by reading parts list.
Painters can tell you about colors and mechanics parts but you don’t become like them by making those things your goal.
The only way to learn math is to learn proofs rigorously.
Calculus isn’t math, it’s just calculus. Algebra, linear algebra, they’re not math. Any “math” without rigorous definitions and theorems with proofs for each one isn’t math. (memorizing names of colors isn’t being a painter)
I think there's a problem in American english in particular. We call the subject 'math', but I think the british 'maths' is more appropriate. There's multiple different kinds of mathematics. Not just one. The American misnomer makes a lot of people falsely believe that grade-school/high-school math is the 'path' into higher math. It's not.
That's not to dismiss the importance of arithmetic (and this is what I believe we should call grade school math operations): everyone should know how to add, subtract, multiply, divide, etc. But the core of mathematics is logical thinking and reason, not numbers
> The core of math, as GP mentioned, is learning proofs.
Well it may be the core but it's not the purpose. As an engineer and later quant I actually use math for practical purposes in everyday life. It wasn't like this in the beginning, I remember primary school was a torment of being fed math olympiad-style problems and hating it. Then somewhere in gymnasium I discovered electronics and everything changed. Math became not just useful but inevitable and from then on learning of math for my own purposes went hand in hand with practical applications in electronics, from simple equations to matrices to differential equations, numeric calculus etc.
Of course there's also always the "standard math" (for passing the SAT/baccalauréat) and entering the good schools, that's inevitable. One can say that "Learning Math Ahead of (the vast majority of) Others" is the way to get ahead :)
> The core of math, as GP mentioned, is learning proofs.
That is the midpoint, the core goal of math is getting enough intuition that facts are obvious, the proofs are just a guide to get you there.
This means you shouldn't study proofs, you should study facts, the proofs are just an example of how to support that fact, you can prove things in many different ways and also many things can be constructed in many different ways and still have the same properties. All of that is much easier when you think in terms of facts instead of proofs.
If you struggle with proving something then you don't understand it. If you memorize a proof for it, then you still don't understand it. The right path to take is to build understanding and then the proofs comes on their on.
Math it's way easier than you think it is, it greatly depends on how you approach it. I really like the style of Robert Ghrist videos on YouTube.
A great tutor/video goes a long way. I wish I could share some resources but am a bit outdated on that.
The overall idea is that some people can explain math concepts in a very clear and straightforward way, while some others will write up a bunch of symbols and let you figure them out. Avoid the latter. As a note, those are usually the lowest performers in academia, lol.
math is just formalizing ideas into symbols and creating rules to manipulate and understand the ideas further. It is really the "ideas" that are important but all school really teaches is the manipulation aspect of it which is a bit boring without understanding the ideas. Most of early mathematical education is of the form "assume we have so and so arcane formulation - here is what we can do with it by applying these rules whose truths you just have to memorize"
You learn math best by doing math. Sure, good explanations help, but sometimes dry rigorous ones are preferable since it asks you to grapple with the subject.
My experience with the comments in this thread, the overwhelming majority of people I know IRL and the widespread sentiment that "Math is hard" does not seem to reflect that.
You can start simple. Read Basic Mathematics by Serge Lang and do all exercises. Solutions are included. That book basically covers all mathematics up to junior high in a rigorous but approachable fashion. Serge Lang was a great mathematician. Then you move to logic, calculus, linear algebra and probability. Afterwards, focus on more specific areas that interest you.
Springer Undergraduate Texts in Mathematics and Dover have lots of elegant and concise textbooks that can help you. At the beginning, the key is to move slowly and build some solid foundations.
It would be a good idea to investigate the belief you have that you are "terrible at math". What does that mean, exactly? Are you bad at computation? Do you forget rules? Are there gaps in your knowledge which are preventing you from accumulating more advanced concepts?
Learning math is like learning any natural language. For example, I'm "bad at Russian" because I have devoted all of 6 hours in my life to learning Russian and there are profound gaps in my understanding of Russian writing and grammar.
But I don't believe I am intrinsically incapable of learning Russian. The reality is that I've simply not put the effort into it.
It's truly the same with math. I am personally quite bad at computation by hand. It's exhausting, I often make careless errors, and I find computational problems by hand to be very boring. But that doesn't mean I'm bad at math! I've simply not invested much effort into improving my skill at computation by hand. I'm not terrible at proofs, for example; and the reason for this is that I find them interesting, and have devoted extra time and effort into learning how to write them. The heart of math isn't computation (which I'm not strong at), but proof and abstraction (which I am strong at, only because abstraction is interesting to me).
So really investigate your belief system regarding your capacity for mathematics. It's unlikely you are innately bad at it. Maybe you have knowledge gaps or you, like me, are not innately skilled at computation. But there are strategies you can employ to improve both.
I burnt my maths books at 16 and didn't do any math after that until I was 30. Then I took Real Analysis as part of a PhD course. I was more mature, and I discovered I enjoyed the different approach. So (a) don't assume you haven't changed and (b) find the parts of math you like best, and start there.
I went back to university. I wouldn't have had the motivation to do this outside of the structured environment of academia and, critically, the pressure of exams and grades that come with school. A huge amount of my motivation comes from the fear of "getting a bad grade". Without the fear of a bad grade, I definitely would have given up learning math as soon as I got bored.
