 Functionally separated sets and partition of unity
 Conley index as a subset of an isolated invariant set
 Proving Equivalence Relations, Constructing and Defining Operations on Equivalence Classes
 Exercise on Counting rules
 Tail bounds for partial coupon collector process
 Sum of a series in $\mathbb{Z}^d$
 The augmented ideal of a commutative group ring $R\left< \sigma \right>$ is generated by $\sigma1$.
 Distribution of the sum of conditional Bernoulli random variables
 Find Matrix T with respect to the basis beta
 Constructing a 2periodic extension of the absolute value function using floor and ceiling functions
 Dividing two generating functions and finding the resulting polynomial
 spectral properties of the shift operator
 Why $\mathbb E\left[\sup\frac{Y_tY_s}{ts^\alpha }\right]<\infty$ imply $(Y_t)_t$ continuous?
 Graph theory — the number of verticies of graph G
 Costbenefit analysis
 limits of integration & joint pdf calculations
 Extension of a nonnegative and symmetric real valued function to a psudometric
 Show or disprove $f[\cap\chi]=\cap\{f[X]:X\in\chi\}\forall\chi\subseteq\mathcal{P}(A)$ with $\chi\neq\emptyset$
 How to find image, preimage, domain and range of function?
 Finite etale covers and Grothendieck groups
How did Superman reverse the destruction of the Great Wall of China?
Everyone knows that Superman doesn't have magical abilities. He can't simply construct something just by thinking about it.
In the movie Superman IV: The Quest for Peace, Nuclear Man destroyed the Great Wall of China in many places. Moments later, Superman reversed this just by seeing those places (meaning that the wall was rebuilt in opposite fashion of its destruction). How did he do this? Is there a science behind it?
There is no science behind it. It was common practice with Superman, Flash and Green Lantern comic stories to show the hero repairing the damage, often at superspeed. In the movies, particularly with budgetary issues being what they are, running the film backward, and undoing the event would be the movie versions of superrepair and replace.
And yes, it is cheesy, but no cheesier than having superheroes being able to repair anything they destroy in the first place.
In the movie, Superman uses an apparently new power to repair the Great Wall

There is no science behind it. It was common practice with Superman, Flash and Green Lantern comic stories to show the hero repairing the damage, often at superspeed. In the movies, particularly with budgetary issues being what they are, running the film backward, and undoing the event would be the movie versions of superrepair and replace.
And yes, it is cheesy, but no cheesier than having superheroes being able to repair anything they destroy in the first place.
20181019 06:04:19 
In the movie, Superman uses an apparently new power to repair the Great Wall. Specifically, he seems to have developed some form of telekenesis, which permits him to move objects at high speed using just his vision.
He uses a similar power later in the movie, to catch a pair of falling police officers and lower them safely to the ground from a distance.
Although this is a brand new power for Superman, it is vaguely similar to a power Zod displays (this time, a beam of energy from his fingers) in Superman II.
Note that the graphic novel adaptation of this movie does not include the same power; in that scene, Superman repairs the Great Wall by physically moving all of the blocks into their proper place, obviously at super speed.
20181019 06:17:31 
I recall one instance in the old black and white tv series (The Adventures of Superman) in which Superman (at that point dressed as Clark Kent) reassembled a torn up piece of paper in a trash can only by looking at it. So it's not a really new display of a not so well known power. Though there is not much reference to him ever having this ability.
20181019 06:28:49 
In the original script he did it by physically putting each brick back in place
Scene 313:
SUPERMAN Flies toward the scene. The NUCLEAR MAN sees him and starts a
barrage of stones and bricks in the direction of SUPERMAN. He hurls
hundreds of them, at superspeed, into SUPERMAN'S path. SUPERMAN
knocks them aside and heads for the WALL.
Scene 314:
A TOURIST Running from the scene, slips and falls off the edge of the
WALL. SUPERMAN flies in, catches her, and returns her safely to her
husband.
Scene 315:
A BLUR OF MOTION As SUPERMAN, reassembles the WALL. In a moment,
every brick and stone is back in place. He looks up to see NUCLEAR MAN
flying away. He takes off to follow.
20181019 06:35:28