Ask HN: How did you learn math notation?

Now, of course, you have the internet and it can tell you what the square root of 217 is. Consequently, the value of these used CRC handbooks is low and many are available on eBay for a few dollars. Pick up a cheap one and in it you will find many useless pages of tables covering square roots and trigonometry, but you will also find pages of formulas and explanations of mathematical terms and symbols.

Don't pay too much for these books because the internet and handheld calculators have pretty much removed the need from them, but that is how I first learned the meanings of many mathematical symbols and formulas.

You might also look for books of "mathematical formulas" in you local bookstores. Math is an old field and the notations you are stumbling over have likely been used for 100 years, like the triangle you were wondering about. (Actually the triangle is the upper case greek letter delta. Delta T refers to an amount of time, usually called an interval of time.)

Unfortunately, because math is an old subject it is a big subject. So big that no one person is expert in every part of math. The math covered in high school is kind of the starting point. All branches of mathematics basically start from there and spread out. If you feel you are rusty on your high school math, start there and look for a review book or study guide in those subjects, usually called Algebra 1 and Algebra 2. If you recall your Algebra 1 and 2, take a look at the books on pre-calculus. The normal progression is one year for each of the following courses in order, Algebra 1, Geometry, Algebra 2, Pre-Calculus, and Calculus. This is just the beginning of math proficiency, but by the time you get through Calculus you will be able to read the paper you referenced.

Is it really a year for each of those subjects? It can be done faster but math proficiency is a lot of work. Like learning to be a good golfer, it would be unusual to become a 10 handicap in less than 5 years of doing hours of golf each and every week.

Calculus is kind of the dividing line between high-school math and college level math. Calculus is the prerequisite for almost all other higher level math. With an understanding of Calculus one can go on to look into a wide range of mathematical subjects.

Some math is focused on its use to solve problems in specific areas; this is called applied math. In applied math there are subjects like Differential Equations, Linear Algebra, Probability and Statistics, Theory of Computation, Information & Coding Theory, and Operations Research.

Alternatively, there are areas of math that are studied because they have wider implications but not because they are trying to solve a specific kind of problem; this is called pure math. In pure math there are subjects like Number Theory, Abstract Algebra, Analysis, Topology & Geometry, Logic, and Combinatorics.

All of these areas start off easy and keep getting harder and harder. So you can take a peek at any of them, once you are through Calculus, and decide what to study next.

I was filled with crushing disappointment when I learned mathematical notation is "shorthand" and there isn't a formal grammar. Same goes for learning writers take "shortcuts" with the expectation the reader will "fill in the gaps". Ostensibly this is so the writer can do "less writing" and the reader can do "less reading".

There's so much "pure" and "universal" about math, but the humans who write about it are too lazy to write about it in a rigorous manner.

I can't write software w/ the expectation the computer "just knows" or that it will "fill in the gaps". Sure-- I can call libraries, write in a higher-level language to let the compiler make machine language for me, etc. I can inspect and understand the underlying implementations if I want to, though. Nothing relies on the machine "just knowing".

It's feels like the same goddamn laziness that plagues every other human endeavor outside of programming. People can't be bothered to be exact about things because being exact is hard and people avoid hard work.

"We'll have a face-to-face to discuss this there's too much here to put in an email."

When you get down to the microcode of the CPU that implements the ISA you might have an issue if it's ill-specified. You might be talking about an ISA like RISC-V, though, specified at a level sufficient to go down to the gates. You might be talking about an ISA like 6502 where the gate-level implementations have been reverse-engineered.

You can take programming all the way down boolean logic if you need to and the tools are readily available. They don't rely on you "just knowing" something.

I see this a lot from programmers, but in essence, you seem to be complaining that maths notation isn't what you want it to be, but is instead something else that mathematicians (and physicists and engineers) find useful.

If programmers would write code like that (even fortran programmers use 3 characters), noone would be able to understand the code...