The lecture provides basic ideas on mathematical analysis including functions of one real variable, sequences, series and power series. It also covers notions of limits of a function, continuity of a ...

In this page, we introduce a differential based method for vector and matrix derivatives (matrix calculus), which only needs a few simple rules to derive most matrix derivatives. This method is useful ...

Faltings’ Theorem ️ It explains why certain algebraic equations have only a limited number of solutions, even though numbers themselves go on forever. Imagine a curve drawn by a polynomial ...

In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

Prerequisites: Credit for MATH 2312 with a grade of C- or higher, or a satisfactory score on a placement examination. Course Description: Calculus of single variable functions, limits, continuity, ...

Limit and Continuity: These ideas gained clarity and rigor in the 17th century with the independent development of calculus by Isaac Newton and Gottfried Wilhelm Leibniz. Later, Augustin-Louis Cauchy ...