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It is great you like Math but also working with others because many scientists and engineers are introverted and afraid of collaboration.
Regarding management it is very had to become a manager without first having done "something" as an individual contributor. Its a bit like sports where managers come from former players so they learn the game by doing.
Example: engineer for a while --> engineering manager
Programmer for a while --> software manager
Don't forget a manager is someone that their direct reports (employees) comes to get help and the best way to give help is having "done it"!
As for design marketing manager It may exist in advertising? As for engineering fields there are marketing people who are very technical who started as an engineer then became a marketing person.
Marketing is understanding how to meet the current and FUTURE needs of customers. Good marketing in technical fields deeply understand products and their customers.
Hope this helps!!