There is no mention of any other continents anywhere in the episode. There is no mention of foreign relations involving anyone from any other continent. No other continents appear on any maps. Small islands near the coast of this continent appear on one map. Information on other polities is limited, there's only any detail on two larger ones, Anavel Sani and Thervigenia, the former now a state and the latter totally lost, and one tiny island one, the Sovereign Republic of Anemone Bay.
There's a sample of North Essi with a Hari translation. It isn't completely obvious that it's not produced by a vocal apparatus that could also pronounce Hari, but it might seem likely just from that sample. It's also mentioned that illusion mages can pronounce Ereli even if they're agerah or caralendri.
The math is all explained verbally, not written.
The existence of regular flights is illustrated with a map and a video of an airport in Mar Geru.
...and he's Mahan and he'll be teaching you Hari, today's lesson is about common materials! This is coal, coal is the sixth element, this is wood, wood's not an element, this is a candle, the candle is on fire, the fire is using vital air, vital air is the eighth element. This is steel, steel can't be made by a sun mage but can be made by a structure mage. This is silver, silver is the forty-seventh element, it can be made by sun mages. Silver's a common material for door handles, taps, things a lot of different people have to touch. This is gold, it's number seventy-nine. This is titanium. This is adamantite, three parts titanium to one part gold. This is platinum, very useful for a few very specific applications that Mahan doesn't go into detail on. This is glass, this is graphite, this is cement. Try to avoid lead. It's not safe to use lead for things people might eat or drink from. It's not safe to make elements that might be radioactive. Don't assume a compound is safe just because the elements it's made of are.
Mahan seems to have no trouble at all getting examples of precious metals to show people and "adamantite" is clearly an everyday word.