Looking for a list of what to study next

bardothello

New member
Joined
Jul 17, 2019
Messages
7
Hi,
I'm wondering if anyone can provide a list that orders learning math from beginner to advance topics.

I'm studying on my own and want to make sure I don't skip steps and miss something important. Currently I am working my way through a calculus book, but if you could provide a list that starts prior to calculus and goes past calculus I would much appreciate it.

Thanks in advance! :)
 

tkhunny

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Apr 12, 2005
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10,169
My first impression is, how good is your:

* Algebra
* Geometry
* Trigonometry
* Analytic Geometry
* Theory of Equations
* Theory of Matrices
* Maybe Discrete Mathematics
* Maybe Theory of Interest

The better you get what has gone on before, the more time you can spend learning something new. Making preliminaries "second nature" frees your mind from clutter.

Part of the Study of Mathematics is getting your brain to work in a way that is more conducive to what may be a different kind of thinking. I do recommend the usual first two calculus classes before you branch out. After that, the world is your oyster. It's not as clear that there is a particular sequence. "Direction" is not well-defined at this point.

Good places to start might be:
* Multi-Dimensional Calculus
* Linear Algebra
* Differential Equations
* Complex Variables
* Number Theory

Really, just get your hands on the graduation requirements from any reputable university and see what tracks ask you to do what path. Your interests are an important part of your travels.

My views. I welcome others'.
 
Last edited:

Otis

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Apr 22, 2015
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1,872
… I'm studying on my own and want to make sure I don't … miss something important …
Hello bardothello. What is your long-term goal? That is, why are you studying maths?

😎
 

bardothello

New member
Joined
Jul 17, 2019
Messages
7
Hello Otis,

I enjoy puzzles is the short answer.
The long answer is that I find math more rewarding than playing chess, go, or doing sudoku. Maybe because there's so much to learn.
My ultimate goal is to tackle difficult questions in mathematics, and so I want to develop the tools in order to do it; however, there is no particular branch of mathematics that I'm currently aiming at. Number Theory is the one that grabs me right now, though I'm sure that'll change over time.
 

Otis

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Joined
Apr 22, 2015
Messages
1,872
… My ultimate goal is to tackle difficult questions in mathematics … there is no particular branch of mathematics that I'm currently aiming at. Number Theory is the one that grabs me right now …
Sound great! As your motivation is recreational and not vocational, my thought is that you can start anywhere and go in any direction. Whenever you come across an unfamiliar topic or scenario, you can ask about the situation here (if you sense that you might be missing something obvious) or you can put the matter on hold and move onto a side track for discovery (then return to the main line, once you've filled in the missing pieces).

It takes experience to tackle difficult question in mathematics, so, when pursuing maths for fun, I'm in the camp that says, "Do what you enjoy in the moment, and learn as you go." (If you have a decent calculus text, then it contains a number of difficult questions.) Basically, for you, I'm saying that doing math is a very good way to find not only what you need but also where you'd currently like to spend your time.

We look forward to helping you navigate the journey. Cheers

😎
 
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