For questions that don't admit a definitive answer. Please do not ask too many of these.
2
votes
2answers
72 views
Big Topics in Mathematics [closed]
My question is as follows: It is now the year 2013 as we know it, and I'm wondering what the "big topics" in mathematics are. What fields are of utmost interest and foundation in the modern era? How ...
1
vote
2answers
46 views
The maths required for an economics degree
I have a degree in computer science and I wanted to do another degree in economics.
However, my maths have been weak since high school always scoring slightly above passing rate. During my course of ...
7
votes
3answers
234 views
Why is 1 raised to infinity Not defined and not “1” [duplicate]
$1$ square is $1$, so is raised $1$ to $123434234$.
My maths teacher claims that $1$ raised to infinity is not $1$, but not defined. Is there any reason for this?
I know that any number raised to ...
1
vote
2answers
28 views
How do I find the residue of a function with a huge exponent?
How would I find the remainder of a function that has a huge exponent that would take ages to work out?
Say I have something like this:
$\frac{5x^{110} + x^4 - 7x^2 - 6}{x-1}$
I honestly don't know ...
0
votes
1answer
32 views
I think I solved it, but can someone check my solutions please? - Instantaneous Rate of Change
It's been awhile since I've done anything with rates of change and I'm struggling with deriving a formula in terms of 'x.'
From what I can recall.. the average rate of change and instantaneous rate ...
-5
votes
0answers
29 views
Mathematics and Language: An Outlet For Opinion [closed]
Why does mathematics exist as such a liquid language of thought? Is it really the universal language? Is this a naive question?
\begin{eqnarray}
0
\end{eqnarray}
4
votes
1answer
46 views
Why are germs of functions important?
Why is it necessary to define germs of functions (in my case, for foliations, but my question is in general)? does any inconsistency arises if instead of using a germ in some context, I use ...
6
votes
1answer
104 views
Which languages are preferable to study for a mathematician?
I am already fluent in portuguese and english, and I can also read spanish well. I have to read a text which is in french, and I'm having some difficulties. Knowing that there are a lot of people out ...
2
votes
2answers
57 views
Pascal's triangle and combinatorial proofs
This recent question got me thinking, if a textbook (or an exam) tells a student to give a combinatorial proof of something involving (sums of) binomial coefficients, would it be enough to show that ...
10
votes
4answers
204 views
What does it mean for a set to exist?
Is there a precise meaning of the word 'exist', what does it mean for a set to exist?
And what does it mean for a set to 'not exist' ?
And what is a set, what is the precise definition of a set?
1
vote
1answer
28 views
Extreme Value Theorem proof help
Extreme Value Theorem: If $f$ is a continuous function on an interval [a,b],
then $f$ attains its maximum and minimum values on [a,b].
Proof from my book: Since $f$ is continuous, then $f$ has the ...
5
votes
3answers
57 views
Analogy between Integration and Summation
There are many analogies between definite integral and Summation: $$\int_a^b \leftrightarrow \sum_a^b$$, This makes me wonder if there is analogous concept of indefinite integral, derivative and ...
0
votes
0answers
73 views
Math is a young man's game? [closed]
Do you agree with this quote from Hardy? Supposedly someone is in their prime between ages 18-25.I don't think I agree with this, since most of the people doing research and advancing math are ...
0
votes
1answer
31 views
How to get to these steps?
I found this question here (I reccomend that you read the question and the highest-voted answer there) How to solve for $x$ in $x(x^3+\sin x \cos x)-\sin^2 x =0$? and the math below is an answer. I ...
10
votes
2answers
184 views
Working habits in mathematics
Short version of my question: What are good and motivating working habits for a mathematician?
Note that, there are similar questions to mine: see this (reading books) or this or this. But none of ...
