Maximize the trace of a matrix by permuting its rows

I commend to you the Hungarian method. It's an algorithm that I'm not up to writing out here, but it's available in many combinatorics, discrete math, and graph theory textbooks, also many places on the web: Wikipedia in particular will get you started.

Why pasting a finite number of commutative diagrams is commutative

Definition of predictable process

Is This a New Property I Have Found Pertaining to Mersenne Primes?

Applications of "finite mathematics" to physics

Integrals of the Bessel function $J_0(x)$ over the intervals between its zeros

Closed forms of Nielsen polylogarithms $\int_0^1\frac{(\ln t)^{n-1}(\ln(1-z\,t))^p}{t}dt$?

Show that $\prod\limits_{n=1}^\infty \frac{(1-q^{6n})(1-q^n)^2}{(1-q^{3n})(1-q^{2n})}=\sum\limits_{n=-\infty}^\infty q^{2n^2+n}-3q^{9(2n^2+n)+1}$.

Is there a closed form for $\sum_{n=1}^\infty\frac{(-4)^nH_{n-1}^3}{{2n\choose n}n^2}\ ?$

Prove that $f'(x) \to 0$ as $x \to \infty$ when $f'+f''$ is bounded abve.

Proving $\int _{-\pi }^{\pi }\int _{-\pi }^{\pi }\int _{-\pi }^{\pi }\log \left| 1+e^{i x}+e^{i y}+e^{i z}\right| dxdydz=28 \pi \zeta (3)$

how prove $\varepsilon_i \in \left \{ -1,1 \right \}$ such $\left | \sum_{i=1}^{n} \varepsilon_i z_i \right | \leqslant 1.$

Does $f$ have a critical point if $f(x, y) \to +\infty$ on all horizontal lines and $f(x, y) \to -\infty$ on all vertical lines?