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March 22nd, 2019, 06:20 AM  #1 
Member Joined: Oct 2018 From: USA Posts: 93 Thanks: 66 Math Focus: Algebraic Geometry  What math notation do you dislike?
Hello all, I'm working on a project for a design class where I have to redesign something, and I chose to redesign some math notation. User research is an important part of the project, so I figured I'd ask you guys. Thanks. 
March 22nd, 2019, 10:43 AM  #2 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,276 Thanks: 944 Math Focus: Wibbly wobbly timeywimey stuff. 
My two least favorites: 1) Mixed fractions: $\displaystyle 1 \dfrac{1}{2}$ looks too much like 1 times 1/2. 2) Inverse trig functions: $\displaystyle \sin^{1}( \theta )$. It's too confusing for new students and they mix it up with $\displaystyle \frac{1}{\sin( \theta )}$. But how do you "redesign" a Math notation? Dan Last edited by skipjack; March 22nd, 2019 at 03:40 PM. 
March 22nd, 2019, 11:14 AM  #3 
Member Joined: Oct 2018 From: USA Posts: 93 Thanks: 66 Math Focus: Algebraic Geometry  My plan would be to change the notation so that it's more intuitive to its meaning. For example, I've seen people represent injections using an arrow that looks like ">>" which, if you don't know the notation, doesn't say "injection" when you look at it. I proposed using an arrow with a small circle at the tip to symbolize that the output is "only small enough to fit one input", and also the symbol looks like an injection in the medical sense. 
March 22nd, 2019, 12:04 PM  #4  
Senior Member Joined: Aug 2012 Posts: 2,395 Thanks: 750  Quote:
And this notation causes other confusion as well, even in math major classes. The notation $f^{1}$ may mean the functional inverse, a function that undoes the effect of $f$; or it may mean the set inverse. Students are invariably confused by this until they sort it out in their minds. But in the end, people get used to bad notation and it's not going to change.  
March 22nd, 2019, 01:04 PM  #5 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,276 Thanks: 944 Math Focus: Wibbly wobbly timeywimey stuff. 
I have a text that uses $\displaystyle sin^{\leftarrow} ( \theta )$ for arcsine (and similar for all other inverse functions) but, to say the least, the notation is not standard. Dan 
March 22nd, 2019, 02:18 PM  #6 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,838 Thanks: 653 Math Focus: Yet to find out. 
I kind of enjoy these little peculiarities though. It forces you to stay attentive and really vocalise what you’re reading, how you’re interpreting and why.

March 22nd, 2019, 02:46 PM  #7 
Member Joined: Feb 2019 From: United Kingdom Posts: 44 Thanks: 3 
When calculus was in its infancy, the difference between Leibniz and Newton’s notation was quite significant though they conveyed the same conclusions. The continental mathematicians adopted Leibniz notation while rumour has it Britain lagged behind with Newton’s.

March 23rd, 2019, 01:38 AM  #8 
Senior Member Joined: Oct 2009 Posts: 867 Thanks: 330 
The fact that the exponential notation $a^b$ has a different notation from the implication in logic $P\rightarrow Q$ really bothers me...


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