
Ask HN: Have you been able to teach yourself advanced mathematics as an adult? - HiroshiSan
What courses and how did you do it?
======
oggyhead
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!

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

~~~
HiroshiSan
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.

~~~
oggyhead
@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

~~~
HiroshiSan
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.

~~~
oggyhead
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

------
CuriouslyC
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.

~~~
decasteve
> 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.

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kleer001
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.

~~~
auganov
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.

------
acomar
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.

------
cottonseed
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.

------
jacob9706
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.

------
CoMList
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.

------
nubb
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 =[

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

~~~
Jtsummers
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.

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

~~~
Jtsummers
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.

