As an engineer, calculations are performed which involves math. When pursuing a Masters degree in engineering, most courses are heavily math.
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# observation of phenomena and development & making a quantitative measurement whenever possible
No, it's not true, lots of engineers are very good with mathematics, physics and their engineering but they cannot write a good paper for their life.
Tools are important to engineers because they need it to help build, repair or make things if they didn't have it. If they didn't have tools, it would be impossible for them to make a repair or build so it is very important for them to have tools.
Because engineers have to understand and use natural things to achieve advantages for people, and physics helps by telling us a lot about the natural world in a logical and systematic way. Engineers and physicists use mathematics to give structure to the knowledge discovered.
It is important to technical people like Marine Engineers because it is the ability to form ideas and designs, and turn these into realities is always never -ending task to the engineers.