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The language of physics is mathematics. In order to study physics seriously, one needs to learn mathematics that took generations of brilliant people centuries to work out. Algebra, for example, was cutting-edge mathematics when it was being developed in Baghdad in the 9th century. But today it's just the first step along the journey.
Here are some of the topics in mathematics that a person who wants to learn advanced topics in theoretical physics, especially string theory, should become familiar with. Real analysis In real analysis, students learn abstract properties of real functions as mappings, isomorphism, fixed points, and basic topology such as sets, neighborhoods, invariants and homeomorphisms.