**Mathematics** includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (calculus and analysis).

Mathematics is widely used in science for modeling phenomena. This enables the extraction of quantitative predictions from experimental laws. The independence of mathematical truth from any experimentation implies that the accuracy of such predictions depends only on the adequacy of the model for describing the reality. So when some inaccurate predictions arise, it means that the model must be improved or changed, not that the mathematics is wrong.

#### Number Theory Books

Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German ...

#### General Mathematics Publications Books

mathematics, the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of ...

#### Mathematics Differential Geometry

Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds, using ...

#### Mathematics Complex Functions Theory Books

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates ...

#### Mathematics Complex Analysis Books

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates ...

#### Calculus Books

Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way ...

#### Algebra Books

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. In elementary algebra, those ...