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diff --git a/docs/random/latex_handwriting.md b/docs/random/latex_handwriting.md new file mode 100644 index 0000000..f02bddf --- /dev/null +++ b/docs/random/latex_handwriting.md @@ -0,0 +1,78 @@ +# Better Handwritten Math with LaTeX + +2022-09-04 + +Argument: LaTeX improves your handwritten math. + +Put more precisely: If you are a first-year undergrad in science or +engineering, practicing LaTeX is beneficial for your handwritten math. + +I began learning LaTeX in high school for mostly trivial tasks. In +university however, my calculus professor awarded a 10% bonus to whichever +group submitted their assignment in LaTeX. Unless circumstances forbid, +I would be responsible for formatting my own and my teammates' handwriting +into LaTeX, and secure the bonus even if I was ignorant math-wise. + +In the summer semester the same professor taught us linear algebra and +multivariable calculus, and the bonus remained in effect. Meanwhile, as an +experiment, I kept my linear algebra notes in LaTeX. + + + +Any LaTeX user knows there are two styles for math script: inline and +display. To use these two options wisely is part of what makes a document +"beautiful". For example, if I had an equation that looks like `x += expression = another expression`, I will consider: + +- How many equal signs are in there? +- If I wrote it inline, how wide will it be? + +and, most importantly, + +- Will I need to label individual steps? + +This is a case where display is way better than inline: + + + +LaTeX is helpful here because you can always try again if you messed up. +I learned to avoid overfull hboxes, and formed many other typesetting +habits this way. I underwent the transition from quick & dirty scribbling +to structured logical statements (compared to whatever shit math I was +doing before). + +The magical thing is, __these habits aren't constrained to the keyboard; +they will flow from your pentip also.__ + +Later this semester we had a midterm exam, where we had to write on paper. +I knew, with a little conscious thought, where or how large something +should be even without LaTeX. It was as if I was compiling a LaTeX +document from my head, except it was more like JIT interpreting. I would +remember to: + +- Leave a margin +- Align equations by equal sign +- Label equations +- Make parentheses large enough +- Draw a tombstone after a finished proof +- Write the real set in `mathbb` style + +Most of these are trivial, yes, but I believe they contributed to an +answer sheet that at least went easier on the eye. There were +significantly fewer scribbles and awkward linebreaks than I usually had in +high school. + +Why is it so? + +Hypothesis: Donald Knuth, Leslie Lamport, and the folks who made amsmath +were all virtually swimming in academia. They expected a math paper to +look a certain way, and when they designed the (La)TeX ecosystem they made +it the default. As such, when you are using LaTeX, you are basically +reusing a template made by top scholars. And when you write LaTeX, you go +their way by default. The error messages are super unintuitive, but if you +don't get any, you can be pretty sure you're doing things right. + +Conclusion: LaTeX is not only a typesetting program for digital documents; +it helps you preprocess your mathemetical thoughts before you commit it to +any medium. If you practice LaTeX as a first-year undergrad, you will find +handwriting math easier and prettier on the first try. |