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Results tagged with big-list
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user 8435
Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
2
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1
answer
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Examples of new results found via exams [closed]
I suspect that there have been many instances throughout history where a new proof of an existing result has been discovered by a student while taking an exam. Does anyone have an example of this?
3
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Examples of common false beliefs in mathematics
A set is compact iff it is closed and bounded.
106
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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 …
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 …
6
votes
Old books still used
Barry Simon and Michael Reed's classic volume on Functional Analysis (1981) is my one of my favorites.
Ayoub, "An Introduction to the Analytic Theory of Numbers," (1963) is out of print but one of th …
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
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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 …
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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.