I have read some old discussions about this topic and would like to get some up-to-date advice, if possible.
How can I take math notes, write formulas and draw graphs on my pc (win 7), the easiest and quickest way?
Thanks for your consideration.
[Math] Best software to take math notes
educationgraphing-functionsmath-software
Related Solutions
GeoGebra is easy to use, free, and the graphs look good.
TL;DR: Learn by reading, doing, following online courses. Join groups/clubs. Work on projects. Find the area you really enjoy. Eventually you'll contribute to helping people out especially if you believe in whatever field you end up joining.
I love your awesome attitude about math and I wish there were more people like you. Well, there is a lot you can do to help people with math. A LOT! It really boils down to what do you want the world to be like and help it be more like that.
Do you want a greener/cleaner world? Go into environmental engineering.
Do you want a healthier world? Go into the biomedical sector.
Do you want a more technological advanced world? Go into computer science or some technology related engineering field.
Do you want people to be more educated? Go into teaching.
Do you want to do either of these or more but the current environment won't let you? Start a startup company.
I could go on and on and on with these recommendations. The thing is that mathematics is a very flexible subject. You can do with it whatever you want. Heck, there are even Simpsons and Futurama writers who are mathematicians: http://en.wikipedia.org/wiki/Jeff_Westbrook
Don't worry too much about helping people out. It kinda comes as a side effect of doing math. For example, studying graph theory back in the days of Euler may have sounded niche and a waste of time but if it were not for graph theory, no internet. (and certainly no facebook... although... i know people who think that wouldn't be such a bad thing)
Focus on finding something you really like and just roll with it. My recommendation... read, read, read. If you have difficulties taking those courses, read the books. A trick I used to do is that I looked at the syllabi of the courses I wish I could take and just got the textbooks and went through them chapter by chapter.
Learn as much as you can: set theory, graph theory, game theory, optimization, cryptography, differential equations, algebra... whatever you can. And try not to limit yourself to mathematics. We live in a complex interconnected world. Many ideas in math today come from economics and biology and physics and all sorts of places.
When you say you'd like something like taking classes... you know, there just isn't enough time and it is not always possible. But youtube exists. And all those MOOCs (Massive Online Open Courses) like Coursera, EDX, or Udacity. They have loads of courses, some more mathy than others. Even all those computer science Udacity courses are interesting because computer science in the end is all about math.
But learning is not enough, actually working on projects is way more helpful. If you have access to clubs or can get friends to work on some project, you'll learn so much more. Just a simple project like getting a little robot to follow a line on the floor or making a video game will challenge you mathematically and thus you'll get to see how you can apply math in the real world.
So, don't worry too much. Just by your attitude I can tell that you'll manage to do good in the world with math. Just learn, practice, and make awesome.
Best Answer
I recommend using Mathematica. The student edition was around $130 the last time I checked, and it's well worth it (if you're not a student, the home edition runs around twice that). Formulas are easier to write than in LaTeX, and you have the option of saving as LaTeX, as well as HTML, postscript, plaintext, rich text, and a few other formats. You also have the option of easily being able to play around with the math and see how it works, which you usually can't do outside of math programs very easily.
Mathematica is designed for notes, and there are already many (Mathematica) notebooks out there that allow you to play around with the math, very easily. I also recommend using a paint program running alongside Mathematica, such as Windows Paint Shop or something similar. This allows you to quickly draw a complicated diagram with all kinds of options, such as colors and effects, that are usually hard to do on paper. You can quickly add in pictures into your Mathematica notes, and their are additional options allowing further manipulations of the pictures in Mathematica.
It's easy to quickly make copies of your notebooks and play around with specific things in each copy. It's generally how I take notes, ESPECIALLY IF I'M IN A HURRY.
If you're planning on sharing you notes, you may prefer to use LaTeX if you feel that you're comfortable with enough time to use it. Generally I convert my Mathematica notebooks in LaTeX and then PDF when I'm sharing something with someone that doesn't have Mathematica. This, however, is generally reserved for when I'm going to make an important presentation, and I have enough time to really make the notes look pretty. However, simply converting Mathematica notebooks into another format is usually good enough, or even preferred if the presentation doesn't have to be spectacular.