Ramified Extensions: Eisenstein Polynomials

This lecture covers the concept of ramified extensions and their relation to Eisenstein polynomials. Starting with an introduction to OneNote for Windows 10, the instructor explains the process of creating ramified and non-ramified extensions. The lecture delves into the specifics of different types of extensions, such as unramified and topologically ramified ones, and their applications in covering situations and generating covers. By examining examples and roots of Eisenstein polynomials, the lecture illustrates the significance of these extensions in various mathematical contexts.