Intereting Posts

Is a proof still valid if only the writer understands it?
Does there exist a Hamel basis $\mathcal B$ for $\mathbb R$ over $\mathbb Q$ such that $a,b \in \mathcal B \implies \dfrac ab \in \mathcal B$?
In how many ways can a teacher divide a group of seven students into two teams each containing at least one student?
Why convolution regularize functions?
Maximal ideals in $C(X)$ and Axiom of Choice
Free idempotent semigroup with 3 generators
Does $a^n \mid b^n$ imply $a\mid b$?
Book about the foundation of math?
Is it unlikely to get the same number of heads/tails?
Complex Zeros of $z^2e^z-z$
How to show that any rectangle in ellipse must be oriented parallel to axes?
The map $f:\mathbb{Z}_3 \to \mathbb{Z}_6$ given by $f(x + 3\mathbb{Z}) = x + 6\mathbb{Z}$ is not well-defined
Group containing no subgroup of index 2
Shortest method for $\displaystyle\int_{0}^{1}\dfrac{x^{4}\left(1-x\right)^{4}}{1+x^{2}}$
Prove that $\sqrt {n − 1} +\sqrt {n + 1}$ is irrational for every integer $n ≥ 1$

$$C_0 = 1,\quad C_{n+1} = C_0C_n + C_1C_{n−1}+ \cdots + C_kC_{n−k} + \cdots + C_nC_0\text{ ?}$$

Where $C_n$ denotes the number of ways of writing a valid list of open and

closed parentheses of length $2n$?

- Verifying Touchard's Identity
- Triangulations of n-gon
- Cashier has no change… catalan numbers.. probability question
- Harmonic Numbers series I
- Finding the number of monotonic paths not crossing the diagonal
- Number of ways to pair off $2n$ points such that no chords intersect

- Identity and bounding of ${ \sum\limits_{k=1}^N{ \binom{N}{k}\,\dfrac{p^k \, \left( - 1 \right)^{k} }{k} } } $ when $0<p<1$?
- Prove that a planar graph is connected if it has $p$ vertices and $3p-7$ edges
- How is $\dfrac1{(1-x)^5}=\sum_{n\geq0}{n+4\choose4}x^n$
- Prove that the maximum number of edges in a graph with no even cycles is floor(3(n-1)/2)
- Intuitively understanding $\sum_{i=1}^ni={n+1\choose2}$
- Count the number of strings containing $ac$ or $ca$ for a fixed length over ternary alphabet $A = \{a,b,c\}$ using rational series
- Combinatorial Proof: $n! = 1+\sum\limits_{r=1}^{n-1}( r\cdot r!)$
- How to calculate number of possible voting outcomes
- Find a simple formula for $\binom{n}{0}\binom{n}{1}+\binom{n}{1}\binom{n}{2}+…+\binom{n}{n-1}\binom{n}{n}$
- Coupon Collector Problem with Batched Selections

$$(1+x)^m(x+1)^m=(1+x)^{2m}$$

The coefficients of $x^m$ $$\sum_{r=0}\binom mr\binom m{m-r}=\binom{2m}m$$

- Why are maximal consistent sets essential to Henkin-proofs of Completeness?
- Show $ \frac{\cosh(a( \pi -x))}{\sinh(a \pi)} = \frac{1}{a \pi} + \frac{2}{\pi} \sum_{n = 1}^{\infty}\frac{a}{a^2+n^2}\cos(nx). $
- The Pythagorean theorem and Hilbert axioms
- If a commutative ring is semiprime and its prime ideals are maximal then it is von Neumann regular (absolutely flat).
- Iterative refinement algorithm for computing exp(x) with arbitrary precision
- Solving an infinite series containing $\arctan$
- geometric proof of $2\cos{A}\cos{B}=\cos{(A+B)}+\cos{(A-B)}$
- Show an infinite family of polynomials is irreducible
- Which non-Abelian finite groups contain the two specific centralizers? – part II
- Prove that $A^TD-C^TB=I$
- evaluating sum of limits
- Some questions about the gamma function
- Compute $\sum_{k=1}^{n} \frac 1 {k(k + 1)} $
- Non-abelian group of order $p^3$ without semidirect products
- Finite groups with exactly one maximal subgroup