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Mistakes in the exersice Sheet 5

Geschrieben am 20.11.24 von Pascal Kattler

Dear participants,

ther had been a few mistakes on the exersice Sheet.

-In 1c) it holds F_2 = <<[x,y]>>, instead of F_2=<[x,y]>

- In 2a) j shell be a injective map, instead of a homomorphism.

-In2b) \phi(s_i) = h_i, instead of \phi(s_1)= h_i

Best,

Pascal Kattler

Outlook

Geschrieben am 19.11.24 von Gabriela Weitze-Schmithuesen

For those who want to look ahead: We will learn basic notions in category theory, as "functors" , especially the hom-functor, and "natural transformations".

You can find these topics e.g. in "Skript Lineare Algebra I und II von 2018/19" (see materials in this cms-course) or in Chapter I of… Weiterlesen

For those who want to look ahead: We will learn basic notions in category theory, as "functors" , especially the hom-functor, and "natural transformations".

You can find these topics e.g. in "Skript Lineare Algebra I und II von 2018/19" (see materials in this cms-course) or in Chapter I of "Categories for the Working Mathematician (Springer 1978) by Saunders Mac Lane: https://link.springer.com/book/10.1007/978-1-4757-4721-8

Best,

Gabriela Weitze-Schmithüsen

Lecture tomorrow: online

Geschrieben am 19.11.24 von Gabriela Weitze-Schmithuesen

Dear participants,

unfortunately I am ill. Therefore the lecture tomorrow will be online in… Weiterlesen

Dear participants,

unfortunately I am ill. Therefore the lecture tomorrow will be online in teams.:

https://teams.microsoft.com/l/meetup-join/19%3ameeting_MjRiMjRkMjQtNzUwMi00MmFkLWJiNjQtYmNmMTJmYjA3YmMy%40thread.v2/0?context=%7b%22Tid%22%3a%2267610027-1ac3-49b6-8641-ccd83ce1b01f%22%2c%22Oid%22%3a%226551f036-dc5b-44f7-9e78-ba9b49d5d892%22%7d

Meeting ID: 325 519 013 063

Passcode: om7t2Pr9

If someone has technical problems, please let me know today. Maybe these students can meet in the usual lecture hall and watch the lecture together on a laptop that we provide.

Gabriela Weitze-Schmithüsen

Small Mistake on Sheet 4

Geschrieben am 13.11.24 von Pascal Kattler

There had been a mistake in Exercise 1b of Sheet 4. The Intersection of N and H shall be {1}.

Seminar Anwendungen der Linearen Algebra

Geschrieben am 06.11.24 von Gabriela Weitze-Schmithuesen

As promised today here are some further information: In this seminar (unfortunately in German) we are presenting some topics, where you directly how linear algebra is applied. Some of them are applications in the "real world", as for example cryptography, the page rank algorithm used in Google's search or error correcting codes. Others are application within the mathematics, e.g. in differential geometry, Hilbert spaces and the theory of presentations of finite groups. Talk 9 ab out Hilbert spaces is still free. Please let me know, if you are interested.

Exam

Geschrieben am 06.11.24 von Gabriela Weitze-Schmithuesen

Dear participants,

here is as promised the decision about the type of the exams: They will be written exams. The dates are 17-02-2025 and 26-03-2025.

Gabriela Weitze-Schmithüsen

Show all

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: Wednesday, 4:15 - 5:00

Assistant Pascal Kattler

Office hours: Wednesday, 13:00 - 14:00

Literature

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

Additional Literature

Ebbinghaus: "Einführung in die Mengenlehre", Springer 2021: https://link.springer.com/book/10.1007/978-3-662-63866-8
Jech: "Set theory", Springer 2003: https://link.springer.com/book/10.1007/3-540-44761-X