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Results tagged with soft-question
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user 8435
Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
1
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0
answers
268
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Recreating the wheel [closed]
I recently finished my Phd in pure maths and I am looking for open problems in my research area, functional analysis. Without going into the details, I stumbled onto an interesting problem and I shar …
- 3,699
106
votes
12
answers
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What is entropy, really?
I first saw the term "entropy" in a chemistry course while studying thermodynamics.
During my graduate studies I encountered the term in many different areas of mathematics.
Can anyone explain why thi …
4
votes
Real analysis has no applications?
I have a good undergraduate analysis book, "Real Analysis with Real Applications," by Kenneth R. Davidson and Allan P. Donsig. The book is divided into two parts. Part A deals with "Abstract Analysi …
15
votes
Examples of great mathematical writing
Riemann's paper, "On the number of primes less than a given magnitude," is the reason why I decided to study mathematics (at the graduate level and beyond). I read the paper as an undergraduate and …
1
vote
Understanding/Mastering Analysis in Topology, necessary?
I was working with some fellow grad students (studying algebraic topology) a few years ago and they were having trouble computing some integrals. This was not unusual, but then they asked me if one e …
- 3,699
6
votes
Interesting Calculus Questions/Exercises
The following problem is often found in introductory Real Analysis courses but can be solved by IVT:
Let $f :[0,1] \to [0,1]$ be continuous. Show that f(x) has a fixed point. In other words, there …
6
votes
What are your favorite instructional counterexamples?
My favorite counter-example is given in the short paper, "Almost Commuting Unitaries," by R. Exel and T. Loring.
Here is a little background. Two $n \times n$ matrices $A$ and $B$ are said to be "alm …
1
vote
What are your favorite instructional counterexamples?
Another one of my favorite counter examples is $2\mathbb{Z}$ which is a RNG, or a ring without identity.
0
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Nontrivial question about Fibonacci numbers?
Ask them to prove that the ratios of the Fibonacci sequence tends to the golden ratio. That is $\frac{F_n}{F_{n-1}} \to \phi$. This can be done with basic calculus.