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__Algebra__

**About the course**

The course provides an introduction to the basics of **Algebra** and algebraic structures such as groups, rings and fields. The goal for the end of the semester is to teach about *algebraic equations* and *solvability of polynomial by radicals *using Galois theory. In particular, the course will cover the following topics:

- elementary category theory;
- group operations, Sylow-Theorems and solvable groups;
- theory of rings and ideals;
- algebraic and transcendental field extensions, degree of a field extension, Galois theory and solvability by radicals.

**Prerequisites**

Linear algebra 1 and 2.

**Dates**

**Lectures**

There will be two classes each per week. The lecture starts in the first week of the semester, on **Wednesday, 16 October 2023 **at **14:15** in **Hörsaal IV** (building E2.4).

- Wednesdays: 14:15 - 15:45 in building E2.4, Hörsaal IV;
- Thursdays: 10:15 - 11:45 in building E2.4, Hörsaal IV.

**Problem session**

There will be one problem session per week.

**Exams**

will be announced at the beginning of the lecture period

**Assignments and exam criteria**

There will be a weekly homework assignment. Students may team up in **groups of three**.

The solutions of the weekly homework will be **corrected and graded.**

**Team**

**Lecturer **Prof. Dr. Gabriela Weitze-Schmithüsen

__Office hours__ tba

**Assistant **Pascal Kattler

__Office hours__ tba

**Tutor** tba

**Literature**

Our Library has compiled an online collection of books for your convenience.