4Fun:Worst/Best Notations in Mathematics

[CRGreathouse]

I don't know. How can the sigma notation be initimidating? Its just a nice shorthand to write the sum of a bunch of terms that have a common pattern.

Yeah, beats me. It was my favorite notation up until midway through my high school years.

 

[FrogPad]

I hate anytime that I have to use "v" and "V". I can never size them properly, so I have to write my v's with horizontal "wings" on each side, so that it looks something like a \nu. Then after awhile they start to look like check marks.

I also hate when I need to write, "0", "o", or "O".

For some reason, I really dislike the \hat i , \, \hat j , \, \hat k notation. I prefer, \hat x or \vec a_x

Oh, and for some reason I love to use \lambda anytime I need a temporary variable of some sort.

My biggest pet peeve is when professors are inconsistent with their notation (*cough* physics)

 

[mathwonk]

we once complained a professor was using confusing notation in class and he replied "yes, I intend to exploit the confusion in the proof."

 

[mathwonk]

once you begin to teach you view all notation in a new light.

it is amazing how many students fail to give any meaning at all to the simpelst looking notation. In 30 years I have never had a class in which several did not say that a derivative was something like
lim h-->0 f'(x) = f(x+h)-f(x)/h. they seem not tor ead these sequences of symbols like words in a senrtnence at all.

and sigma notation is never understood even by a fraction of my students.

these students cannot comprehend mentally that there are more than one term there just ebcause the sigma notation says so. . i.e. summation as i=1,...n, of f(n) does not speak to them at all. they have to see a strong of f(1) + f(2) +...+ f(n) wriiten out to get it.

now lately the svcholarship rpogram is bringing stronger stduents and perhaps i am hamopered by my old assumptions, but we shall see.

the following question always mows them down, even if announced in advance:

define carefully the riemann integral as a limit, explaining the meaning of any special symbols you use, such as "delta x"

 

[mathwonk]

the thing that freeaked me out as a student was when aprofessor tried to get us to understand a bit of duality by writing f(p) as p(f) and pointing out that the point could be viewed as acting on the function. i thought I was going to have an anxiety attack.

 

[Swapnil]

One more thing that I hate is that there is no good notation to denote that something is a statement other that the = sign. This causes a lot of problems. For exapmle, in induction you have to prove that P(n)\Rightarrow P(n+1) but most students forget that P(n) is a statement like "something = something" which is either true or false. It does not equal one side or the other, which is a common misconception.

 

[FrogPad]

once you begin to teach you view all notation in a new light.

it is amazing how many students fail to give any meaning at all to the simpelst looking notation. In 30 years I have never had a class in which several did not say that a derivative was something like
lim h-->0 f'(x) = f(x+h)-f(x)/h. they seem not tor ead these sequences of symbols like words in a senrtnence at all.

I think a lot of the time, it is taught this way.

If asked what a derivative is, it seems that the correct response is to regurgitate the expression you showed above.

Calc I-III was like this for me. It was a continual process of recalling a grouping of symbols to put down on the paper. It wasn't until a later math course where we used, Strang's "Introduction to Applied Mathematics" did I see that math can be an expression of the author. I really enjoyed the book, because it was less about regurgitating answers, and more about understanding the underlying idea of the topic at hand.

I've had a few professors, who when asked a question would stop, explain what needs to be done, and then write the required symbols to justify themselves. Other professors would slap symbols on the board, then explain what they are doing. The latter professors are the ones I would end up having trouble learning from them. I usually feel one step behind them, because I'm continually asking myself in the back of my mind, "why?".

 

[mathwonk]

just keep asking,
'huh?"

thats what you are paying for.

 

[Swapnil]

One of the other things that really bugs me is when they use famous notations as constants or famous constants as variables. For example, its really confusing when in some texts they use \Sigma and \Pi to stand for constants or when they use the letter \pi as a variable. I always go "Huh?," but then I realize they are just trying to play mind games.

 

[radou]

One of the other things that really bugs me is when they use famous notations as constants or famous constants as variables. For example, its really confusing when in some texts they use \Sigma and \Pi to stand for constants or when they use the letter \pi as a variable. I always go "Huh?," but then I realize they are just trying to play mind games.

I only saw \Sigma and \Pi stand for planes, while attending descriptive geometry, which I didn't find specially annoying.

 

[FrogPad]

just keep asking,
'huh?"

thats what you are paying for.

hehe.
true that

 

[cliowa]

There's another incredibly annoying thing some mathematicians do (one can see this very often in books):
They take two different things, but give them the exactly same notation (because the word begins with the same letter or because traditionally it always is n, so the author can't brake with tradition), stating that it will be clear in the context which one is meant. I hate that!

 

[mtanti]

Once I was explaining factorials to a friend in a chat room and I said 'do you know what is 3x2x1?' I said '3!'.

The reply was 'why are you shouting?'

It also gets pretty confusing when you put the factorial in a question: 'what is 3!?'

You end up having to use brackets around the number (3!)

 

[Swapnil]

Personally, I don't like the \sqrt sign, because it makes it seem that exponents are something magical. Think of the things that might go through a middle school student's mind when he is asked to take raise \sqrt 3 to the power of 3! ( BTW, I mean just the number 3, not 3 factorial!).

Plus, the squareroot sign is also long and ugly.

 

[Swapnil]

Another fact that I dislike is the use of the term "function." Sometimes, a function simply means a correspondence (a rule by which we assign each object in a set some other object(s) in some other set).

Other times it means a special TYPE of correspondence (the one which takes an object in a set and maps it to a single UNIQUE object in another set).

 

[CRGreathouse]

Another fact that I dislike is the use of the term "function." Sometimes, a function simply means a correspondence (a rule by which we assign each object in a set some other object(s) in some other set).

Other times it means a special TYPE of correspondence (the one which takes an object in a set and maps it to a single UNIQUE object in another set).

I never use it in that first sense. I use the term "relation" instead.

 

[chroot]

As CRGreathouse mentioned, the use of the word "function" is not appropriate for a relation which is multi-valued. If your teachers are using the term this way, I pity them.

- Warren

 

[0rthodontist]

Another fact that I dislike is the use of the term "function." Sometimes, a function simply means a correspondence (a rule by which we assign each object in a set some other object(s) in some other set).

Other times it means a special TYPE of correspondence (the one which takes an object in a set and maps it to a single UNIQUE object in another set).

Are you talking about the use of "function" to denote partial functions?

 

[Swapnil]

What do you mean by "partial functions"?

 

[CRGreathouse]

What do you mean by "partial functions"?

Let f:A\rightarrow B be a function. Then f':A'\rightarrow B, where A\subsetneq A' and f' is equal to f on A and undefined otherwise, is a partial function from A' to B.

Essentially, it's a function that isn't defined everywhere. Division on the integers is an example, since division by 0 is undefined.

 

[Swapnil]

As CRGreathouse mentioned, the use of the word "function" is not appropriate for a relation which is multi-valued.

Why is that?

 

[arildno]

Why is that?

Because a "function" is defined to be SINGLE-valued.
It is a fact of life.

Also note that what we might call a "multi-valued" function, can always be considered as a single-valued function from the given domain and having as its co-domain the POWER SET of of the set containing the various function values.

 

[CRGreathouse]

Division on the integers is an example, since division by 0 is undefined.

And by "integers", I mean "reals".

 

[Gelsamel Epsilon]

A person in my calculus class got upset and stormed out of class because she kept confusing imaginary numbers with vector measurements (use of i in both).

 

[Office_Shredder]

The number 3 is pretty confusing to be honest

 

[Swapnil]

I hate the prime notation for derivatives because, in physics, people often use variables like x and x' and this can be confusing sometimes. Although, I have to say that when used unambigiously, the prime notation for derivatives is pretty useful and often takes away the scary \frac{d}{dx} operator.

 

[Swapnil]

One more thing that I realized is that the function notation e^{(.)} is very limited. I mean that when the argument in the exponent gets complicated (which happens often I think), it becomes really hard to distingush what's an exponent and what's not. I would say that \exp(.) is a far better notation in the long run.