 ## Top new questions this week:

Let's consider the following variant of Collatz $(3n+1) :$ If $n$ is odd then $n \to n^2-1.$ $1\to 0.$ $3\to 8\to 1\to 0.$ $5\to 24\to 3\to 0.$ $7\to 48\to 3\to 0.$ $9\to 80\to 5\to 0.$ $11\to 120\to ... number-theory recreational-mathematics collatz-conjecture asked by Adam Rubinson Score of 17 answered by Will Jagy Score of 1 ### "Multiply everything so far, plug into polynomial" - can these always yield primes? EDIT: I forgot how open number theory is! (I think that gets me put on mathematician probation or something.) For this question, I will accept any answer which assumes "standard conjectures" ... number-theory prime-numbers asked by Noah Schweber Score of 15 ### Why does it seem more natural to think of$r$as a function of$\theta$, rather than the other way around? When teaching functions in polar coordinates, the nearly universal practice is to consider functions of the form$r = f(\theta)$. I think I have never seen any examples in which$\theta$is expressed ... algebra-precalculus functions polar-coordinates asked by mweiss Score of 12 answered by user2661923 Score of 2 ### Are these equations "properly" defined differential equations? Are these equations properly defined differential equations? Modifications were made to a deleted question to re-focus it Intro Recently, in this answer I figure out that the following autonomous ... ordinary-differential-equations partial-differential-equations physics mathematical-modeling finite-duration asked by Joako Score of 12 ### The coupon collector's most collected coupon Suppose a coupon collector is collecting a set of$n$coupons that he receives one-by-one uniformly at random. If the collector stops exactly when the collection is complete, we know the expected ... probability combinatorics expected-value coupon-collector asked by Brocellous Score of 11 answered by Sangchul Lee Score of 8 ### Prove$\sum_{i,j:i<j} μ(E_{i} \cap E_{j} )=\infty$. The problem is: Assume that$(X,\mathcal{A} , μ)$is a finite measure space (i.e.,$μ(X) < \infty $) and the sequence of sets$E_{j}\in \mathcal{A}$satisfies$\sum^\infty_{j=1} μ(E_{j} )=\infty$.... real-analysis measure-theory asked by rose Score of 11 answered by Robert Israel Score of 8 ### Understanding Legendre transform (and convex conjugate) I am learning convex analysis on my own and I would appreciate some help. I know that convex conjugate is the generalization of the Legendre transform. I also know the formula known for Legendre ... real-analysis convex-analysis legendre-transformation asked by Pegi Score of 11 ## Greatest hits from previous weeks: ### A loss and gain problem This is a very simple but confusing puzzle. A customer buys goods worth$200$rupees from a shop. The shopkeeper selling these goods makes zero profit from this purchase. The lady gives him a$1000$... puzzle asked by constantlearner Score of 7 answered by fgp Score of 8 ### How many even numbers of four digits can be formed with the digits 0,1,2,3,4,5 and 6 no digit being used more? My attempt to solve this problem is: First digit cannot be zero, so the number of choices only$6 (1,2,3,4,5,6)$The last digit can be pick from$0,2,4,6$, so the number of choices only 4 Second ... combinatorics asked by akusaja Score of 4 answered by akusaja Score of 2 ### How to calculate the area of a 3D triangle? I have coordinates of 3d triangle and I need to calculate its area. I know how to do it in 2D, but don't know how to calculate area in 3d. I have developed data as follows. ... triangles 3d area asked by iamgopal Score of 51 answered by Vafa Khalighi Score of 45 ### Proof of triangle inequality I understand intuitively that this is true, but I'm embarrassed to say I'm having a hard time constructing a rigorous proof that$|a+b| \leq |a|+|b|$. Any help would be appreciated :) inequality absolute-value asked by ivan Score of 67 answered by k.stm Score of 122 ### Which way is length and which way is width? I hear people refer to the dimensions of things as "$2$by$4$" etc. and I know its length by width, but I can't tell if the length dimension is vertical (up and down) or horizontal (side to side). ... geometry terminology asked by David Score of 15 ### Inverse of the sum of matrices I have two square matrices:$A$and$B$.$A^{-1}$is known and I want to calculate$(A+B)^{-1}$. Are there theorems that help with calculating the inverse of the sum of matrices? In general case$B^{-...

linear-algebra matrices inverse asked by Tomek Tarczynski Score of 179

### Is a matrix multiplied with its transpose something special?

In my math lectures, we talked about the Gram-Determinant where a matrix times its transpose are multiplied together. Is $A A^\mathrm T$ something special for any matrix $A$?

matrices asked by Martin Ueding Score of 285 answered by Simon Markett Score of 190

## Can you answer these questions?

### Max edit distance between binary strings of length n

Given a binary string s of length $n>2$.An edit operation is a single character insert, delete or substitution. The edit distance between two strings is the minimum number of edit operations needed ...

binary dynamic-programming asked by Hosho Kana Score of 1

### Is a certain map $\mathbb{R}\to \widehat{\mathbb{R}}$ a homeomorphism?

I'm studying harmonic analysis, and I'm trying to understand the fact that $$\phi: \mathbb{R}\to \widehat{\mathbb{R}}: s \mapsto (t \mapsto \exp(2\pi i st))$$ is an isomorphism of topological groups (...

complex-analysis analysis harmonic-analysis topological-groups asked by Andromeda Score of 1 answered by QuantumSpace Score of 0

### How many ways are there to arrange $3$ men, $3$ women, $3$ children in a circle such that they alternate clockwise in this order: man, woman, child?

Problem How many ways are there to arrange $3$ men, $3$ women, $3$ children in a circle such that they alternate clockwise in this order: man, woman, child? The seats are not numbered. My Opinion I ...

combinatorics permutations asked by WS Wee Score of 1
You're receiving this message because you subscribed to the Mathematics community digest.
Unsubscribe from this community digest       Edit email settings       Leave feedback       Privacy Stack Overflow, 110 William Street, 28th floor, New York, NY 10038

 <3