Foundational concepts involving numbers, operations, fractions, and simple equations.br br Algebra: The study of symbols and the rules for manipulating those symbols; it includes solving equations and understanding structures like groups and rings.br br Geometry: Focuses on shapes, sizes, properties of space, and spatial relationships. It ranges from basic Euclidean geometry to advanced fields like differential geometry.br br Calculus: Involves the study of rates of change (differentiation) and accumulation (integration), with applications in various fields like physics and engineering.br br Number Theory: The study of properties and relationships of numbers, particularly integers, and includes topics like primes, divisibility, and modular arithmetic.br br Probability and Statistics: Deals with data analysis, randomness, and the likelihood of events, used in fields like science, economics, and actuarial studies.br br Linear Algebra: The branch of mathematics concerning vector spaces, linear equations, and transformations, essential in areas like computer science, engineering, and physics.br br Topology: The study of properties of space that are preserved under continuous transformations, concerned with concepts like continuity and boundary.br br Set Theory and Logic: These are the foundations of modern mathematics, dealing with the structure of sets and formal logic systems.