Questions tagged [intuition]
The intuition tag has no usage guidance.
9
questions
15
votes
4
answers
1k
views
When should I say "nothing is as it seems"?
"Intuition" is the best friend and worse enemy of mathematicians! Sometimes using intuitive arguments could be very helpful to understand the nature of a phenomenon. Many of the deepest true ...
33
votes
12
answers
5k
views
For calculus students, what should be the intuition or motivation behind series?
I've noticed that series are one of the most difficult portions of calculus for new students to learn.
I think the level of abstraction has to do with this. Limits, derivatives, and integrals, as ...
29
votes
5
answers
1k
views
Wonder as motivation
Like all mathematicians, I have a deep appreciation of the
beauty of mathematics. Many theorems I find amazing even after
I fully understand their proofs. (Example: Euler's formula,
$V-E+F=2-2g$. That ...
20
votes
7
answers
2k
views
How can I motivate the formal definition of continuity?
In order to teach continuity of real valued functions $f:D\to\mathbb R$ one may start with the (in some sense wrong) intuition
$f$ is continuous when its graph can be drawn without lifting the pen.
...
26
votes
6
answers
1k
views
How to present $\Bbb Z/n\Bbb Z$ to highschool level audience
I have the oportunity to talk to a highschool class about mathematics, the topic I got to present are the integers modulo $n$, ie, $\Bbb Z/n\Bbb Z$ , however I don't want to be very heavy and formal, ...
18
votes
7
answers
6k
views
Lack of intuition, retention while self studying
I am a first year undergraduate student, currently in second semester.
So basically I learnt most of the first year stuff in high school, so I have a lot of free time in this year (currently in ...
5
votes
3
answers
1k
views
Determining the first digit of the Quotient using hand long division efficiently?
For instance in the following problem:
_____
48)4368
To determine an initial 9 for the first number in the Quotient, you ...
4
votes
2
answers
1k
views
Why is continuity only defined on its domain?
As mentioned in this question students sometimes struggle with the fact that continuity is only defined at points of the function's domain. For example the function $f:\mathbb R\setminus\{0\} \to \...
4
votes
1
answer
1k
views
Why is continuity defined as a local property?
The formal definition of continuity is a local property (the definition of continuity at a point is a property of the germ of the function at this point). Why is it a good decision to make the ...