High School Does anybody write any operations differently?

[Thinkaholic]

For example, Richard Feynman used his own symbols for trigonometric functions and their inverses.
I write logarithms differently. I make a symbol which is like a radical, but instead of a √-shape at the end, it is the Greek letter lambda (λ). Under the radical shape is the argument, and below the triangle shape in λ is the base.
Does anybody have different notation for operations?

 

[mathman]

Advisory: use standard notation - communication is easier.

 

[fresh_42]

Simple question: Why? I sometimes abbreviate $\sin$ and $\cos$ by $s$ and $c$, especially when used in matrix multiplications to save time, but I would never do so if I wrote down my results. I just do this on scraps of paper. So again: Why? Don't you have enough to learn yet, that you need an extra vocabulary? Well, I could give you some ...

 

[jedishrfu]

The programming language APL was founded on a principle like that where Greek letters represented operators that worked on values, vectors and array of any dimensions. Wikipedia has an article on the language

 

[FactChecker]

Until your reputation matches Feynman's you should try to make your writing as standard and universally understood as possible. Rather than try to learn a new symbology, people might just get aggravated and ignore your work. If there is some very good reason that a new symbology will make your work much easier to understand, you might consider it. But not till then.

 

[Thinkaholic]

I don't use this notation on actual results. I just use it on scraps, chalkboards, etc.
I just use it because I think it looks better than 'log'. Sorry for not mentioning that.

 

[fresh_42]

In these cases I use $\operatorname{ln}$ as the basis is usually not of interest and without basis $\log$ is the natural logarithm anyway. And $\operatorname{ln}$ is easy to write in hand writing. (I haven't really understood why this is "old fashioned" and people switched to use $\log$ instead. Doesn't make sense to me.)

 

[jedishrfu]

They ln was used because Euler spoke French and so referred to it as "log naturel"

http://www.purplemath.com/modules/logs3.htm

 

[fresh_42]

They ln was used because Euler spoke French and so referred to it as "log naturel"

http://www.purplemath.com/modules/logs3.htm

I thought ln was the Latin logarithmus naturalis. Anyway, it is convenient, as it is shorter, and Euler isn't the worst reference. I still see no reason not to use it. It would be interesting to know, when and by whom the log became stylish.

 

[UsableThought]

For example, Richard Feynman used his own symbols for trigonometric functions and their inverses.

Since you're citing the case of Feynman, you're almost certainly aware of the following - but I will mention it just in case. I first read it a book somewhere but found it repeated on the web in a short biography of Feynman at this page: http://www-history.mcs.st-andrews.ac.uk/Biographies/Feynman.html - it's an amusing anecdote (like about 983,001 other anecdotes about him); I have bolded the part that seems most relevant:

At school Feynman approached mathematics in a highly unconventional way. Basically he enjoyed recreational mathematics from which he derived a large amount of pleasure. He studied a lot of mathematics in his own time including trigonometry, differential and integral calculus, and complex numbers long before he met these topics in his formal education. Realising the importance of mathematical notation, he invented his own notation for sin, cos, tan, f (x) etc. which he thought was much better than the standard notation. However, when a friend asked him to explain a piece of mathematics, he suddenly realized that notation could not be a personal matter since one needed it to communicate.​

Which is what other folks have already said.

On the other hand, if it gives you pleasure to invent a notation, there can't be any harm in that; and if you find it enjoyable to do so, whether for looks or any other reason, then why not? Feynman's experiences growing up serve as a good example of someone getting great fun out of learning in many ways - one of these being his reliance on finding original ways of doing things. And of course that served him well later on.

 

[jedishrfu]

Your own shorthand be an effective mnemonic device especially when prepping for a test. I used to make little stick triangles to represent the various triangle ratios that I'd write at the top of my test for reference.

They helped me setup problems much faster and eliminated the monkey nature of the brain to doubt what you remember which affects your confidence and slows you down as you attempt to reprove it...

My high school geometry teacher would create tests that took 45 mins to complete i.e. The whole class period. He said he'd take the test himself in 5 mins and then figured we could complete it in 45 mins. It was his personal heuristic for designing a test. We would really struggle through it, they were really tough. One time, the whole class failed to complete all the problems or got many wrong on Athena various line equations so he taught us how to take his tests.

The key was not waste time with pretty XY plots with each axis numbered from -10 to +10 like what was shown in our book. He said he accepted simple plots where a point was simply to place three marks on the X and then draw a vertical and place four marks upward and draw a big dot to represent the point (3,4). It told him everything he needed about the point. For me it was quite a revelation and changed my view of math greatly.

 

[fresh_42]

Another example is a debate I once had about matrix notations. Usually $A_{ij}$ denotes a matrix and $A_{ji}$ its transpose. Of course there is no rule to do it this way, it could as well be the other way around. But nobody wants to waste time on a discussing whether the first index numbers the rows or the columns or whether $i$ should be used first. It's simply not worth it. And even more: people are used to read $A_{ij}$ as the matrix eases reading a lot.