Search Results

Let $\pi(p,n)$ be the probability that the favorite wins the tournament. Fact. For any fixed $p>1/2$, $\lim_{n\to\infty} \pi(p,n) = 1$. … a more important effect than the fact that the increase in the number of games is giving the favorite an opportunity to demonstrate a skill edge. …

(Related: your favorite surprising connections in mathematics. But this question is looking for more concrete examples, particularly those that illustrate the power of the idea.) …

The only branch where I think this is explicitly recognized in the literature is topology, where for example Munkres is careful to point out and discuss his favorite counterexamples in his book, and Counterexamples … So: what are your favorite examples of counterexamples that really illuminate something about some aspect of a subject? …

Possible Duplicate: ADE type Dynkin diagrams What is your favorite ADE-style classification? Here ADE style is to be understood in a very broad sense. …

What's your favorite equation, formula, identity or inequality? …

One of my favorite papers. Stallings shows how to apply covering spaces to finite graphs in order to prove several non-trivial properties of free groups. …

Christmas is almost here, so imagine you want to buy a good popular math book for your aunt (or whoever you want). Which book would you buy or recommend? It would be nice if you could answer in the f …

There are certain things in mathematics that have caused me a pleasant surprise -- when some part of mathematics is brought to bear in a fundamental way on another, where the connection between the tw …

There are many "strange" functions to choose from and the deeper you get involved with math the more you encounter. I consciously don't mention any for reasons of bias. I am just curious what you cons …

(The title was initially "What are your favorite concrete examples that you would compute on the table during lunch to convince a working mathematician that the notions of limits and colimits are not as …

When you are checking a conjecture or working through a proof, it is nice to have a collection of examples on hand. There are many convenient examples of commutative rings, both finite and infinite, …

Here is mine. It's taken from page 11 of "An Introduction To Abstract Harmonic Analysis", 1953, by Loomis: https://archive.org/details/introductiontoab031610mbp https://ia800309.us.archive.org/10/item …

What value on P gives an ellipse with 768 lattice Points? x^2 + 3y^2 = P P= 4*7*13*19*31*37*43 gives 384 lattice points

The equation of the ellipse interpolating the six lattice points $(0,0)$, $(1,0)$, $(0,1)$, $(d-1,d)$, $(d,d)$, $(d,d-1)$ in the plane for a fixed $d$ (at least 3) is $$ x^2+y^2 - \frac{2(d-1)}{d}xy-x …

Let's say I have my favorite finite dimensional algebra $A$, and favorite module $T$. … Now assume that the reason $T$ is my favorite module is that it has a cool property: there is an injection $A\to T$ which is a $\mathrm{add}(T)$-approximation (that is, any map of $A$ to a summand of …