First of all a man had to have a good basic education and if he were adept at math and/or logic, he would learn the basics of his trade, as most Romans did, by being an apprentice to a master of whatever craft he wanted. He would most likely join a guild and be considered for jobs through the guild. (Just about all Roman professions from Flute players to funeral directors had guilds)
Chat with our AI personalities
The Roman engineers built aqueducts to transport water to where it was needed.
Romans enineers built roads, bridges, aqueducts, sewers, fortifications and ports.
What Roman slaves wore depended on whether they were educated or not. Regular slaves wore clothing of the cheapest material while educated slaves wore clothes made of better material. Though slave's clothing did not even compare to a patrician's (wealthy person's) clothing. Slaves working in the mines and quarries went naked.
Your question is a little vague. The Roman army had specialists in all areas. Some of them were engineers, architects, bookkeepers, accountants, armorers, blacksmiths, instructors in the various types of combat and the use of weapons, artillerymen, bowmen and slingers. Each division or compartment of a legion had its compliment of specialists in certain areas.
A Roman legion (army corps) had 5,320 infantrymen and 120 cavalrymen. In addition there were support men, such as catering men, supply men, engineers and the like. This was an ideal number. The actual numbers varied according to the requirements of a given military campaign. Sometimes the legions were undermanned