News
Additional exercise session on ThursdayGeschrieben am 11.02.25 von Gabriela Weitze-Schmithuesen As promised Pascal Kattler will do an extra session do give you the option to ask questions about the solutions of the additional Exercise Sheet 14. It will take place in Seminar room SR 6 on Thursday (13.2.) at 2:15 pm . |
First version of Sheet 14 uploadedGeschrieben am 10.02.25 von Gabriela Weitze-Schmithuesen As promised we have uploaded already some mixed exercises as "Sheet 14" to help you to prepare the exam. We will add more exercises to the sheet soon. |
Registeration for the examGeschrieben am 10.02.25 von Gabriela Weitze-Schmithuesen Dear Participants, IMPORTANT: if you want to write the exam next week please do not hesitate to register TODAY (one week before the exam). Sincerely, Gabriela Weitze-Schmithüsen |
ExamGeschrieben am 10.02.25 von Gabriela Weitze-Schmithuesen The exam next Monday (17.2.2025) takes place from 9 to 12 at Hörsaal III.
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Additional office hour today from 12:45 - 13.45Geschrieben am 31.01.25 von Gabriela Weitze-Schmithuesen Dear participants, unfortunately I am not that free today as I thought. Directly at 12 does not work, but you are very welcome to come between 12:45 and 13:45 to ask questions. Best, Gabriela Weitze-Schmithüsen |
Evaluation Link now availableGeschrieben am 30.01.25 von Gabriela Weitze-Schmithuesen Dear participants, you can now fill in the evaluation for the lecture. You find the link under Informationen --> Materialien --> Others (almost at the end of the page). Unfortunately, the evaluation is only in German. Sorry about this! It is great if you fill in the evaluation and give us… Weiterlesen Dear participants, you can now fill in the evaluation for the lecture. You find the link under Informationen --> Materialien --> Others (almost at the end of the page). Unfortunately, the evaluation is only in German. Sorry about this! It is great if you fill in the evaluation and give us your feed back! The link is open until next Tuesday. Gabriela Weitze-Schmithüsen |
Additional office hour today form 11:45 - 12.25Geschrieben am 24.01.25 (letzte Änderung am 24.01.25) von Gabriela Weitze-Schmithuesen As said in the lecture, please feel free to come today at 11:45 if you have questions. I have to leave around 12:30. Gabriela Weitze-Schmithüsen |
Exersice 3 on sheet 12Geschrieben am 21.01.25 von Pascal Kattler Dear participants,
We changed Exersice 3. You can now assume that K is infinite in Exersice 3. The statement is also true for finite K, but hard to show with our current knowledge. Best Pascal Kattler |
Exercise 1b) on Sheet 11Geschrieben am 17.01.25 von Gabriela Weitze-Schmithuesen Dear participants of the lecture, Exercise 1b) on the current sheet seems to be more difficult then we intended it to be. Hence it will not count to the regular pointing system. If someone solves it she or he will obtain 2 extra points for it. We also corrected some small typos in it. In… Weiterlesen Dear participants of the lecture, Exercise 1b) on the current sheet seems to be more difficult then we intended it to be. Hence it will not count to the regular pointing system. If someone solves it she or he will obtain 2 extra points for it. We also corrected some small typos in it. In particular the module should again be finitely generated. I apologize for the inconvenience! Gabriela Weitze-Schmithüsen
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Office hour has to be postponedGeschrieben am 15.01.25 (letzte Änderung am 15.01.25) von Gabriela Weitze-Schmithuesen Dear participants, as announced today: the office hour this week will be on Friday (17-01-2025) from 12:00 to 13:00. Best, Gabriela Weitze-Schmithüsen |
Correction + Tip to Sheet 10Geschrieben am 09.01.25 (letzte Änderung am 09.01.25) von Gabriela Weitze-Schmithuesen Motivated by a question of a student here comes a correction and a tip for Exercise 3 a) on Sheet 10: M should be finitely generated here. As hint for the proof: 1) Recall for this that M/M_tor is free (Look it up in the lecture :-) ) 2) This helps you to find a homomorphism from M/M_tor… Weiterlesen Motivated by a question of a student here comes a correction and a tip for Exercise 3 a) on Sheet 10: M should be finitely generated here. As hint for the proof: 1) Recall for this that M/M_tor is free (Look it up in the lecture :-) ) 2) This helps you to find a homomorphism from M/M_tor to M which embeds M/M_tor as submodule in M. Thanks for the question!
Aufgrund einer Nachfrage eine kleine Korrektur und ein Tipp für Aufgabe 3 auf Blatt 10: M soll hier endlich erzeugt sein. Zeigen Sie für a): 1) Erinneren Sie sich daran, dass M/M_tor frei ist (Schauen Sie dazu nochmal in die Vorlesung :-)). 2) Nun können Sie einen Homomorphismus von M/M_tor --> M definieren, der M/M_tor als Untermodul einbettet. Vielen Dank für die Nachfrage! |
Heute keine SprechstundeGeschrieben am 08.01.25 (letzte Änderung am 08.01.25) von Gabriela Weitze-Schmithuesen Heute findet keine Sprechstunde statt. Dafür ist die Sprechstunde morgen (Donnerstag) 12 Uhr - 13 Uhr. |
Inquiry of a student from our lecture: Interested in a seminar on topology next summer?Geschrieben am 17.12.24 von Gabriela Weitze-Schmithuesen Inquiry regarding a possible seminar in the upcoming summer semester: Who would be interested in a seminar on Algebraic Topology in the summer semester? There is a possibility that Professor Lazić will offer this again if there is sufficient interest. I have put the list of topics of the… Weiterlesen Inquiry regarding a possible seminar in the upcoming summer semester: Who would be interested in a seminar on Algebraic Topology in the summer semester? There is a possibility that Professor Lazić will offer this again if there is sufficient interest. I have put the list of topics of the seminar held in 2023/24 here in the cms into materials/others. If you are interested, please send an email to Mr. Philipp Weisang (email: philipp.weisang1@gmail.com). He can also provide you with more information about it.
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Anfrage zu einem möglichen Seminar im kommenden Sommersemester:
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Exercise SessionGeschrieben am 07.12.24 (letzte Änderung am 17.12.24) von Pascal Kattler Dear participants,
unfortunately there is no other time for the exercise session. So the exercise session will remain at monday 8:30.
Best, Pascal Kattler |
Seminar Anwendungen der Linearen AlgebraGeschrieben 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… Weiterlesen 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. |
ExamGeschrieben 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 |
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