# Kelvin Soh

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 8 integer $a$ for which $x^3-3x+a = 0$ has $3$ distinct real roots in $x\in (0,1)$ 5 $Ax=v$, $Ax=w$ consistent; what about $Ax=v+w$? 4 What is difference between cycle, path and circuit in Graph Theory 4 Deal or No Deal: Monty Hall? 3 Show that a regular, connected bipartite graph does not have a bridge.

# 974 Reputation

 +10 Proof verification: (Pretty pictures :) )Showing two graphs are not isomorphic. Bondy/Murty - Graph theory Page 5 +5 Euler-Mascheroni constant: understanding why $\lim_{m\rightarrow \infty} \sum_{n=1}^{m} (\ln (1 + \frac{1}{n})-\frac{1}{n+1})= 1 - \gamma$ +20 Determine the convergence of infinite series $1-1+\frac{1}{2}-\frac{1}{2}+\frac{1}{3}-\frac{1}{3} +\cdots$ +5 If $u(z) = \frac{az+b}{cz+d}$ is bijective on the upper half complex plane, show that $a,b,c,d$ are real.

# 3 Questions

 2 If $u(z) = \frac{az+b}{cz+d}$ is bijective on the upper half complex plane, show that $a,b,c,d$ are real. 2 Euler-Mascheroni constant: understanding why $\lim_{m\rightarrow \infty} \sum_{n=1}^{m} (\ln (1 + \frac{1}{n})-\frac{1}{n+1})= 1 - \gamma$ 1 Limsup of intervals $(-\infty, - n \sin(1/n))$

# 41 Tags

 19 graph-theory × 12 6 discrete-mathematics × 7 11 algebra-precalculus × 3 6 sequences-and-series × 3 8 probability × 8 5 calculus × 4 7 linear-algebra × 2 5 vector-spaces 7 matrices × 2 4 trigonometry × 2

# 4 Accounts

 Mathematics 974 rep 112 MathOverflow 101 rep Mathematics Educators 101 rep 1 Area 51 101 rep 2