Descriptif
Prerequisites: MAA101, MAA103, MAA104, MAA201, MAA206
MAA303 mainly focuses on general group theory. The first part of the course will be dedicated to the basic notions that one uses to study groups: normal subgroups, quotient group, simple groups... The second part of the course will focus on group actions. After introducing them, we will see a number of interesting applications in algebra, geometry and arithmetic, such as the so-called Sylow theorems. At the very end of the course, we will move on from groups to other usual algebraic structures, such as rings and fields. This part of the course will only be a short introduction to ring and field theory. Extra material not covered during the course itself will be provided for those students who would like to go further and understand how groups, rings and fields are deeply related through the study of algebraic equations and Galois theory.
Diplôme(s) concerné(s)
Parcours de rattachement
Pour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique
Vous devez avoir validé l'équation suivante : UE MAA203 Et UE MAA204
MAA101, MAA103, MAA104, MAA201, MAA206
Format des notes
Numérique sur 20Littérale/grade américainPour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique
Vos modalités d'acquisition :
Dear students,
Welcome to the Algebra and Arithmetic class! This short announcement is to explain you how the course will be organized. Please do not hesitate to send me an email (diego.izquierdo@polytechnique.edu) if you have any questions. Otherwise, see you on Thursday September 8th!
A. What will you find on Moodle?
1. The course notes.
2. The lecture videos.
3. Quizzes.
4. Exercise sheets.
5. Past exams.
B. How will the course be organized?
1. Face-to-face classes will take place on Thursdays at 10:15 am.
2. One week before each class, you will find the lecture videos on Moodle. You should always watch them before coming to class, since I will only do a short reminder of the content of the videos in the face-to-face class. This also applies to the first class (September 8th).
3. Also one week before each class, you will find some quizzes on Moodle. Those quizzes are compulsory and will be graded. You will always have 2 weeks to do them. You will be able to do them as many times as you want: only the highest grade will be taken into account.
C. How will the face-to-face classes be organized?
1. You should always watch the videos of the week before coming to class, since I will always assume you have done so. This also applies to the first class (September 8th).
2. At the beginning of the class, I will make a short reminder of the content of the videos, and I will answer all your questions.
3. Then we will do some exercises.
D. How will the course be graded?
There will be four grades during the semester:
-the average of the Moodle quizzes grades (MQ),
-two test grades (T1 and T2),
-the final exam grade (FE).
Your final grade (FG) will be computed through the following formula:
FG=max(FE; (3*MQ+T1+T2+5*FE)/10).
The conversion into a letter grade will be done according to the following table:
A+: 18 ≤ FG ≤ 20.
A: 16,5 ≤ FG < 18.
A-: 15 ≤ FG < 16,5.
B+: 14 ≤ FG < 15.
B: 13 ≤ FG < 14.
B-: 12 ≤ FG < 13.
C: 11 ≤ FG < 12.
D: 10 ≤ FG < 11.
E: 10 ≤ FG < 5.
F: 0 ≤ FG < 5.
I hope everything is clear.
Best regards,
Diego Izquierdo
- Crédits ECTS acquis : 3 ECTS
La note obtenue rentre dans le calcul de votre GPA.
Programme détaillé
-Groups and homomorphisms.
-Subgroups.
-Quotients and Lagrange's theorem.
-Solvable groups.
-Finite abelian groups.
-Symmetric and alternating group.
-Group actions.
-Sylow theorems.
