Ask HN: Have you been able to teach yourself advanced mathematics as an adult? | Hacker News Reader

Ask HN: Have you been able to teach yourself advanced mathematics as an adult?

29 pointsHiroshiSan21 comments

What courses and how did you do it?

Proof writing. Sat down with a textbooks and partial solutions at the back. Took a year as I had other priorities. Advice:

1.Regardless of which route you choose to go whether probability theory, algebraic geometry or optimization algorithms, do a course in proof writing. Absolutely do not skip it. It will teach the fundamentals and most importantly patience and persistence

2. If you're a programmer, prepare yourself for a much larger feedback loop. Unlike code which can just be executed and you have the satisfaction of seeing something sorta work at first try, math is a completely different beast. It will punch your expectations in the face, and the progress points you celebrate will be a joke compared to what you are used to with code

3. Screw the videos, just sit down with a hardcopyand work through the theory and most importantly work through the problems.Try to get a textbook with a partial solution set.

4. Practice Practice Practice your fundamentals

5. Have realistic goals and timelines! People trip up here big time

6. Be prepared to dive into things that at first glance may seem unrelated. Don't skip chapters just because you think you don't really need to make progress towards your topic of interest. More often than not, you'll end up coming back

7. Celebrate the small milestone

8. Expect things to get exponentially difficult as you go along.

9. Learn how to manage extreme frustration and learn to keep your promise to come back to a problem you couldn't solve again and again. Nothing ever gets done in one sitting especially if you're learning.

10. Mixup things to make sure things don't get boring!

Do you have any advice on which books to start with?

Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand Polimeni and Zhang. This was the textbook used in my intro to proofs course and it was fantastic. Worth the steep price.

Another good one that was optional reading was Book of Proof, it's free so maybe start there.

@HiroshiSan, where do you draw the line between math and advanced math? You clearly are not a beginner abd I now wonder the intent of your question

I appreciate you calling me out. I'm certainly not a beginner in the sense that I know elementary algebra very well and that I know the names of upper level courses.

That being said I'm very much a beginner. I've only come across proofs in the one course I took (where I listed the textbook above). I dropped out of Introductory Analysis due to the fact that my foundation was very very weak. I don't know know much of Calculus and so I had a lot of difficulty building intuition behind a lot of concepts and theorems.

I've been taking high school courses for the past 6 months or so in order to build my foundation because I see a lot of value in a Math degree and would like to complete it.

My intent in asking the question was just to get an idea of what people with a possibly similar background to mine did to really teach themselves upper level math, because I'm struggling at it, very very much.

Going to get into introductory analysis soon too myself! The one tip that I have been given is to build intuition by taking/relearning the computational part of calculus before diving into the rigorous part of things. Hopefully someone else can weight in on the value of the tip

I wholeheartedly recommend the book of proof! (Mostly because I went through it inch by inch)

Book of Proof by Hammack

Yes. The key is that you need to have a reason to learn it, and a can-do attitude. If you're just studying mathematics because you think it's a good thing to learn you're going to spin your wheels. Pick an interesting real world problem which requires some math, and solve it. Branch out from there to related problems requiring slightly more challenging math. When you get stuck, look at how other people have solved the problem, break the process down into chunks and start digging through wikipedia. When you see the same mathematical tools used repeatedly, or wikipedia isn't sufficient, get a textbook/solution manual and work through applicable problems.

I also advise you to explore math via programming. The notation and conventions in advanced mathematics papers are very subfield dependent. If you attempt to learn just by reading papers you're going to spend a lot of time unpacking exactly what the authors were trying to say. Computer source code is generally much clearer.

In my opinion the easiest way to get a foothold is to start with computer graphics and machine learning. Linear algebra and probability theory are super important and widely applicable, and lots of source is available for study.

Of course, if by advanced mathematics you mean some esoteric field of pure math, most of this goes out the window.

> Of course, if by advanced mathematics you mean some esoteric field of pure math, most of this goes out the window.

You hit a wall pretty quickly when the topics get more abstract. It’s inefficient at best. At this point in my own self-study path in math I ended up going to university.

No, I haven't.

I tried several books and lectures, but the lack of direct applicability and competing activities (job, gf, family, friends) drowned it out.

I know your implied question, but I consider negative responses fundamentally important to serious inquiry.

Had a similar experience. I find it fades quite quickly. If you can't triangulate with what you're already doing (or thinking of) it's going to be tough.

I think getting to a productive level would require a lot of dedication and consistency.

Honestly, what's worked best for me is buying a book on the topic I'm interested in, and just working through it methodologically. The most difficult thing has been checking my work since answer manuals are difficult to come by. If I'm really unsure, I'll try and find an appropriate group to post a question to. I'm mostly interested in algebra, category theory, and topology, so it's difficult to just ask a computer to check my work for me.

Yes. Read books and do ALL the problems. Books with answers are nice, but learning to double-check your work and convince yourself you are correct is also useful. Find others who are also learning and study with them. Find others who already know and learn from them. The key is consistent, long-term effort, but it is not easy.

If you don't know anything about vectors, start with some game programming. If you are talking things more along the lines of Hilbert Spaces or advanced physics, there's no alternative to a good book IMO.

my advanced mathematics was so poor when I was in college, even now still be. I want to learn it, and learn it well, but like all the losers, I did't make it.

I tried to learn calc to design an auto pilot system in a game designed in Unity using c#. I got frustrated and gave up =[

I tried but I just got sleepy and hungry. Does anyone have an antidote to this? Does tea work?

Keep at it. I find it mentally draining to learn a new math topic that I'm less familiar with. It knocks me out better than anything I've ever found. I accept it as a fact. After a couple weeks of this (if I'm studying more days than not), the concepts and jargon start to become internalized.

This is the source of exhaustion. When you don't know the thing you are actively exercising your brain to recall the terms, topics, definitions, etc. It's really, really hard. This is mentally draining. As the topic gets better intenalized the recall activity becomes easier. You actually know it.

Some things can help here.

One is to read a bit each day, I usually read the same chapter 2-3 times. Once rather briskly. A second time very carefully practicing each exercise and proof. And a third time where I'd only stop on the things that didn't seem familiar enough (almost as briskly as the first reading).

I've become a major proponent of spaced-repetition. Make flash cards, put them in Anki. Study them. This allows you to set the topic down for weeks or even months at a time, and still be able to pick it back up where you left off. It also motivates me to continue when my math deck review gets short (I only have 3 cards to study this whole week?!?). Anki lets you use LaTeX which means you can make some really good looking math cards.

How do you study after work.. especially when there's cooking and cleaning to be done?

I get home at about 5:30. Two days a week I go to the gym, I don't study those nights because I'm too worn out once I get home.

Monday/Wednesday I start some rice and eventually make a simple stir fry. Quick, easy dinner. But that's usually around 9pm. So I have 6-9 to study. Friday is usually a social evening. Saturday, I grab a book or whatever and head to the coffee shop down the street.

Early Saturday and Sunday are cleaning and grocery shopping times.

My girlfriend is in another country so, for now at least, my evenings before 9pm are almost always mine. After 9pm we're usually on the phone.

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