UPDATE: This method of returning to the menu is currently banned.

I just finished the first Zone with no* math problems (including data capsules).

I know what you might be thinking, how is this possible???

When you return to the sign-in menu and return to the game, you will spawn either at the beginning of the sector, or the save game, depending on how far you've progressed. However, it will also save what capsules you've collected. Essentially, you no longer have to die to return to a save room.

Interestingly, data capsules can also be collected in this manner, because the game collects the capsule before you answer the question correctly (although will return it if you die by getting it wrong). This allows you to skip the entire data capsule problem and entry reading.

I haven't applied the technique to all sectors yet, but Dragon Reef 3 (V) has a notable timesave with this. Normally one enters the room with the data capsule, collects it and the other capsule, and then dies in order to warp ahead two rooms. With this method, you can collect the capsule first, then the data, and immediately "death warp" ahead.

Unfortunately, there are limitations. Not all problems are worth skipping in this manner. I merely did it as a proof-of-concept. Secondly, some problems cannot be skipped in this manner because they are in or after the save-room and cannot be skipped by any other means. Notably the radar problem in Dragon Reef 1 (V), hence the asterisk on "no"

Also, this does not apply to combo locks, since (as I have just discovered) the next sector is not triggered until you clear the outro text, and you cannot do anything during the small cutscene.

And while this works for the Windows version, it's a bit harder to execute since you cannot hit F2 and the problem triggers are not in ideal locations.

One other benefit of this however: Zoom will still reappear, if even you've already collected oxygen from her. This method can be used to very effectively stock up to full oxygen tanks. I'm not certain of a use for this yet, but it does allow for 3+ death warps in a single sector, which may be useful in the Expert game.