Mathematics is the science of: numbers, quantities, structures, space and change, and the relationships between them.

  • Foundations of Mathematics
  • Arithmetic
  • Algebra
  • Geometry
  • Calculus
  • Applied Mathematics
  • Statistics
  • Computational Mathematics

Foundations of Mathematics

Foundations of Mathematics is the study of the philosophical, logical, and algorithmic basis of mathematics. It can be viewed as the study of the basic mathematical concepts and how they form hierarchies of more complex structures and concepts.


Arithmetic is a branch of mathematics that consists of the study of numbers (quantities), especially properties of the operations: additions, subtractions, multiplications, division, exponentiation and extraction of roots.


Algebra is one of the main branches of mathematics, covering the study of structure, relation and quantity. It is the branch of mathematics in which arithmetical operations and formal manipulations are applied to abstract symbols rather than specific numbers. Algebra studies the effects of structures: adding and multiplying numbers, variables, and polynomials, along with their factorization and determining their roots.


Geometry is the branch of mathematics concerned with properties and relations of: points, lines, surfaces and solids. Euclidean geometry combines space and numbers, and includes using the Pythagorean Theorem. Trigonometry is the study of angles and their relationships of: planar and three-dimensional figures (space). It deals with relationships between: the sides, the angles of triangles, and with trigonometric functions.


Applied Mathematics


Computational Mathematics