Mathematics Weekly Newsletter
Mathematics Weekly Newsletter

Top new questions this week:

Does the string of prime numbers contain all natural numbers?

Does the string of prime numbers $$2357111317\ldots$$ contain every natural number as its sub-string?

(elementary-number-theory) (prime-numbers)  
asked by Buddha 34 votes
answered by Rebecca J. Stones 45 votes

Self-learning mathematics - help needed!

First, I apologise for the nebulous nature of my title but I can't adequately explain myself concisely. I am about to start an MSc in pure maths after a fairly shaky undergraduate degree. I am very …

(self-learning) (learning)  
asked by Elliptic2005 30 votes
answered by Newb 22 votes

When does L' Hopital's rule fail?

This thought jumped out of me during my calculus teaching seminar. It is well known that the classical L'Hospital rule claims that for the $\frac{0}{0}$ indeterminate case, we have: $$ …

(calculus) (teaching)  
asked by Bombyx mori 30 votes
answered by JimmyK4542 28 votes

how to get $ f(x) $ if we know $ f(f(x))=x^2+x $

how to get $ f(x) $ if we know $ f(f(x))=x^2+x $ Is there elementary function of $f(x)$ satisfy the equation?

(functions) (functional-equations)  
asked by user694345 23 votes
answered by lhf 18 votes

Math symbol in German thesis from 1963

I have the following math symbol in a German thesis written in 1963. Is it anything more than just a function name? It is used in the following context and then goes on to state that "If the …

(notation) (math-history)  
asked by user2235373 18 votes
answered by Frunobulax 22 votes

What is the motivation for quaternions?

I know imaginary numbers solve $x^2 +1=0$, but what is the motivation for quaternions?

(soft-question) (math-history) (quaternions)  
asked by zerosofthezeta 17 votes
answered by Frunobulax 22 votes

Why is an image called an "image"?

Given a function $f : A \to B$, the image, denoted by $\operatorname{Im}f$ is the set of all $f(x)$ where $x \in A$. Why do we call this set the image? When was it first used, and what motivated its …

(functions) (elementary-set-theory) (soft-question) (terminology) (math-history)  
asked by William 16 votes
answered by Frunobulax 10 votes

Greatest hits from previous weeks:

What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)

I'm a children's book writer and illustrator, and I want to to create a book for young readers that exposes the beauty of Mathematics. I recently read Paul Lockhart's essay "The Mathematician's …

(soft-question) (recreational-mathematics) (education) (big-list) (teaching)  
asked by Liz 444 votes
answered by Will 213 votes

What is the practical difference between a differential and a derivative?

I ask because, as a first-year calculus student, I am running into the fact that I didn't quite get this down when understanding the derivative: So, a derivative is the rate of change of a function …

(calculus)  
asked by Faqa 78 votes
answered by Arturo Magidin 49 votes

Can you answer these?

Fractional Part of $ a^n $

Prove that there exists a real number $ a>1 $, such that $ \{a^n\} $ belongs to $[\frac{1}{3},\frac{2}{3}]$ for all positive integers $n$ and $\lfloor a^n\rfloor$ is even iff $n$ is a prime. …

(real-analysis) (contest-math)  
asked by john 10 votes

How many hamilton paths can a non-hamiltonian graph have?

What is the maximum number of hamilton paths a graph with $n$ vertices can have without having a hamiton cycle ? If my turbo pascal program works well, the first few values for $3,4,...$ vertices …

(graph-theory) (hamiltonian-path)  
asked by Peter 5 votes

Is there a name for graphs with the following property?

The property of the graph is the following: For any vertex, there is a hamiltonian path starting with this vertex, but the graph is not hamiltonian. The following graph is a small example: …

(graph-theory) (terminology) (hamiltonian-path) (knight-tours)  
asked by Peter 4 votes
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