Algebra

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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;
• Rings and ideals, factorial rings, polynomial rings and the lemma of Gauß;
• Algebraic and transcendental field extensions, degree of a field extension, Galois theory and solvability by radicals.

The course and the problem sessions will be held in English.

Prerequisites

Linear algebra 1 and 2.

Dates

Lectures

There will be two classes of 1h30 each per week. The lecture starts in the first week of the semester, on Wednesday, 25 October 2023 at 10:15 in Hörsaal IV (building E2.4).

• Wednesdays: 10:15 - 11:45 in building E2.4, Hörsaal IV;
• Thursdays: 10:15 - 11:45 in building E2.4, Seminarraum 6.

Problem session

There will be one problem session of 2h per week. The first problem session will take place in the third week of the semester, on Tuesday, 7 November 2023 at 10:00 in Seminarraum 6 (building E2.4)

• Tuesdays: 10:00 - 12:00 in building E2.4, Seminarraum 6.

Exams

the first exam will be on February 19.  from  9 am to 1 pm  Building E2.4 Seminar Room 6
the second exam will be on April 10.  from 9 am  to 1 pm  Building E2.4 Zeichensaal U.39

Assignments and exam criteria

Starting from the second week of the semester (31.10.2023), students will have as weekly homework to solve 4 exercises to be handed in before the start of the next problem session. Students should team up in a group of two, solve the exercises and hand them in together. The solutions can be either

• written digitally (exported in .pdf format) and submitted online on CMS before the deadline;
• handwritten and delivered directly to the tutor at the beginning of the next problem session.

NOTE: for online submission, please remember to submit as a team.

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

Each student should present the solution to one exercise during the semester. The choice of the week and of the exercise from the exercise sheets is up to them, as long as there are no other students with the same choices. Each student presenting a solution to an exercise should meet the teaching assistant for this lecture prior the next problem session to discuss their solution.

The final exam will be a written exam. In order to register for the final exam, the students must:

• obtain at least 50% of the total points of the exercise sheets;
• present the solution of one exercise during the semester.

Team

Lecturer    Jun. Prof. Dr. Simon Brandhorst

Office hours Fridays: 11:30 - 12:30 in building E2.4, office 2.22.

Assistant  Stevell Muller

Office hours Mondays: 11:00 - 12:00 in building E2.4, office 2.21.

Tutor         Bastian Heinen

Office hours Mondays: 13:00 - 14:00 in building E2.4, third floor, Gruppenarbeitsraum

To enter in contact with a member of the team, you can meet them during office hours or write on the Forum. Alternatively, the email addresses are available in the tab Information>Team.

Literature

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