u/nzubaly

Hello, some background info first (tl;dr below this paragraph): I am a Physics student (small chance I may choose to switch to purely math, I at least want to minor in math if possible) just finishing up my first year of college. I am starting Calc 4 over the summer (It's a quarterly school, so I think the more accurate thing to say would be multivariable calculus...? For clarification: last quarter's calc course began with sequences and series and wrapped up with calculus on vector-valued functions. The first lecture of this quarter introduced functions of several variables and partial derivatives.) I have am yet to take a linear algebra or differential equations course (although we brushed on these in Calc 2 with some basics- slope fields, Euler's method, easy separable equations). I will be taking both of those next year starting in Fall. I also have not actually had a physics course in college yet, as I will be taking the ones which require calculus prereqs. I will also be starting those in the Fall.

tl;dr: I am just starting multivariable calculus, and have not (yet) learned any linear algebra.

I want to start reading published mathematics papers, but I don't even know where to start to find papers to read. I am totally open to learning new things/fields/subjects. However, I need to at least find a jumping off point that I will actually be able to understand, and sources that are free (I have access to my college's online library, though, so I may be able to read things which typically aren't free if I can access them through that). Can anyone offer recommendations/guidance for me to find what I am looking for? If more info would help, I have two main motivators - see below.

1. I think math is cool, and I like learning about it lol.

2. I have written up almost all of my projects for calculus using LaTeX. I began by going into my first document completely blind, and have learned as I went along. I have learned a lot and I am fairly comfortable with it by now, but I would like to learn how to present ideas, structure/format/edit my documents, and overall just hone my skills to write the way a real mathematician would write a paper. I want a better understanding from the little things (like when to/when not to number equations, typical conventions for page numbering/title pages/section and subsection numbering conventions, etc.) to the bigger things (like overall structure of my writing/prose, when should I be adding more detailed explanation/when is it acceptable or preferable to omit detailed explanation, etc.), and I think the best way to get a feel for these things will be by actually reading papers that hold up to the standard for publication. I know that publication standard writing is not actually necessary for these projects (I'm pretty sure I'm the only student who has even typed them up at all), but this is a personal goal of mine.

Thanks in advance for any advice!

As the sidebar of this subreddit puts it, I am just getting started with LaTeX and wondering what the fuss is about! A bit about me / my usage:

I am a first year college student pursuing a degree in physics. I am currently in Calculus 2 and Calculus 3, and I have so far used LaTeX for my projects for those classes, as well as Calculus 1. These projects are basically guided explorations of topics, with most of the work and submission usually consisting of constructing proofs. I like to have a polished final product for these, and I am aware that later in my school/career (I am hoping to go to grad school and be a research physicist) I will likely be required to use LaTeX quite often. For those reasons I have been using LaTeX to type up my projects. At the moment, as I am still new to this, that has generally been an almost painfully slow process (but so much more satisfying and polished in the end)! So here a a couple specific questions:

1. Which LaTeX editor would you recommend to me, as a beginner? I have currently only used Overleaf, but I do not know the pros/cons of Overleaf vs. others or even really what others are out there. I have done some searching independently about this query, but I am so unfamiliar with all of this that I don't even really understand most of the terms people are using in the discussions that search turned up.
2. What guides and/or resources would you recommend to learn more about LaTeX, how to use it efficiently, and how to get the most out of it? In my use so far, I have essentially just been googling as I go; things like "fractions latex; less than equal to latex; headers latex" which has worked relatively fine, albeit a bit tedious. I would like to spend some time dedicated to learning to use LaTeX outside of the context of these projects so that I can have a smoother time of it when I am doing the projects. That said, I don't know where to start with that.

Thanks in advance for any recommendations and advice!

Edit: Some additional information I just thought of - I currently do my studying on both my macbook and PC, about 50/50, so I would prefer to use a program which is available on both.