Mathematics Weekly Newsletter - Friday, November 28, 2014

Top new questions this week: Monty Hall Problem with Five Doors My math class went over the original Monty Hall problem a few days ago, then looked at a related question where the number of doors was increased to five. There was a struggle to figure out what the ... (probability) (discrete-mathematics) (monty-hall)   asked by Phosphatide 30 votes answered by MathIsHardNoItsNot 37 votes Checking a possible proof of Fermat's Last Theorem Theorem 1.2 of Bennett and Skinner (Canad. J. Math., 2004) asserts that the Diophantine equation $x^{p} - 4y^{p} = z^{2}$ is unsolvable for every prime $p \geq 7.$ The following is a possible proof ... (elementary-number-theory) (proof-verification)   asked by Chou 28 votes answered by TonyK 25 votes Estimate for $n$th prime A good approximation I have found for $p_{n}$ is \begin{align} \int_{2}^{n}\log (x \log (x \log (x)))\ dx\\ \end{align} and seems to be a better estimate than $n \log (n)$. The error term seems to ... (number-theory) (prime-numbers)   asked by martin 24 votes answered by daniel 3 votes Defeating Russell's paradox I am not very big in mathematics yet(will be hopefully), naive set theory has a problem with Russell's paradox, how do they defeat this sort of problem in mathematics? Is there a greater form of set ... (elementary-set-theory)   asked by beginner 19 votes answered by aes 35 votes Are there number systems corresponding to higher cardinalities than the real numbers? As most of you know, the set $\omega$ with cardinality $\aleph_0$ corresponds to what we normally know as the natural numbers $\mathbb{N}$, and the set $\mathcal{P}(\omega)$ with cardinality ... (field-theory) (cardinals) (model-theory) (infinity)   asked by mrp 18 votes answered by Asaf Karagila 23 votes % of % - Please Help Me Prove My Friend Wrong Here is the situation: My friend and I are at an impasse. I believe I'm correct, but he's so damn stubborn he won't believe me. Also, I'm not the most articulate at explaining things. Hopefully ... (probability)   asked by Trynn 15 votes answered by AAA 69 votes Nobody told me that self teaching could be so damaging... Even though I've been teaching myself math for a couple of years now I only just started (a month ago) at the university. My experience is rather mixed. For starters i'd like to mention that i'm 21 ... (self-learning) (advice)   asked by user195750 14 votes Greatest hits from previous weeks: Interview riddle On the Mathematics chat we were recently talking about the following problem @Chris'ssis had to solve during an interview : $$3\times 4=8$$ $$4\times 5=50$$ $$5\times 6=30$$ $$6\times 7=49$$ ... (problem-solving) (puzzle)   asked by Hippalectryon 41 votes answered by Denis 97 votes Maximum board position in 2048 game A game called 2048 is making rounds on social media. I am trying to determine the maximum score attainable for this game. Let's assume WLOG that only 2s are returned (if 4s are possible the max score ... (discrete-mathematics) (puzzle) (combinatorial-game-theory)   asked by Isaac 30 votes answered by DanielV 15 votes Can you answer these? $a^b+2$ or $a^b-2$ is in set Let $A$ be an infinite set of positive integers. For any two $a,b\in A$, $a\neq b$, at least one of the numbers $a^b+2$ and $a^b-2$ are also in $A$. Must $A$ contain a composite number? (elementary-number-theory)   asked by python55 7 votes How can we evaluate this tough integral? $$ \int \frac{\sqrt{\sin\sqrt x}\cos \sqrt x}{1+x^2} dx $$ I have tried combinations of $x=t^2$, integration by parts, $\tan\left(\dfrac u2\right)$ substitutions it got even more complicated. Is ... (calculus) (integration) (indefinite-integrals)   asked by reco 4 votes Is there really anything wrong with Bourbaki's Set Theory? Recently I have started reading Bourbaki's Theory of Sets on my own. Regarding one of the explanations of a concept when I went to a Professor of our college, he asked me why I was wasting my time ... (elementary-set-theory) (soft-question)   asked by user 170039 7 votes New blog post: Homology: counting holes in doughnuts and why balls and disks are radically different. by Daniel Robert-Nicoud on Nov 24 There are some questions that are really easily posed, have an obvious answer, but are in fact really, really hard to answer in a mathematically satisfactory way. Two examples are: How many holes does ...

Subscribe to more Stack Exchange newsletters Unsubscribe from this newsletter or change your email preferences by visiting your subscriptions page on stackexchange.com. Questions? Comments? Let us know on our feedback site. If you no longer want to receive mail from Stack Exchange, unsubscribe from all stackexchange.com emails. Stack Exchange, Inc. 110 William St, 28th Floor, NY NY 10038 <3