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 ...

Universality theorems occupy a central role in analytic number theory, demonstrating that families of analytic functions—including the prototypical Riemann zeta-function—can approximate an extensive ...

Inverse problems, central to modern applied mathematics, involve deducing unknown parameters or functions in differential equations from observed spectral data. This field is pivotal in understanding ...

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, ...