Let Fn be a free group of rank n with free basis x1, ⋯, xn. Let {y1, ⋯, yk} be a set of k ≤ n elements of Fn, where each yi is represented by a word Yi(x1, ⋯, xn) in the generators xj. Let ∂ yi/∂ xj ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

In the Introduction to the Derivative video we introduce the notion of the derivative of a function and explain how the derivative captures the instantaneous rate of change of a function. In the ...

Hypergeometric functions are at the heart of many analytical and applied mathematical investigations. These functions, generally defined via power series that extend the geometric series, have been ...

The GATE syllabus for Mathematics (MA) 2025 consists of questions from topics such as Calculus, Linear Algebra, Real Analysis, Complex Analysis, Differential Equations, Algebra, Functional Analysis, ...