Abhishek

If you are aiming to study mathematics at college/university to degree level, or further, then your mathematical study will need to be sufficiently broad to cover the sorts of topics you are likely to meet in a typical undergraduate mathematics course. The mathematics curricula of different universities will differ in their choice of topics and the depth to which they are developed in a degree course, these differences being dictated to a certain extent by the interests of the lecturers, the research activities of the mathematics (and physics) faculty, and whether the course is more geared towards pure or applied mathematics. But all mathematics curricula will have certain broad subject areas in common. The easiest way to discover what these are would be to visit the websites of various university maths faculties and look at the subjects they teach. These are likely to include the following topics (many of which overlap each other) as a minimum (listed in no particular order, though some topics are more advanced than others, and have certain prerequisites):Set Theory Group Theory Algebra (linear, abstract, etc.)Differential and integral calculus of a single variable differential and integral calculus of several variables Ordinary differential equations Partial differential equations Real Analysis Complex AnalysisTopologyDiscrete mathematics (combinatorics, graph theory, etc.)Number Theory Geometry (projectile, differential, etc.)Probability theory Statistics (statistics is often taught.