Topic outline

  • General

    Learning outcomes and contents:

    After the course the student will be able to

    • understand basic algebraic structures and their key properties and differencies,
    • perform related arithmetics,
    • master and apply different proof techniques.

    The key contents of the course are:

    • groups, subgroups and quotient groups
    • group homomorphisms and isomorphisms 
    • rings, subrings, ideals and quotient rings
    • ring homomorphisms and isomorphisms
    • fields

    Organization:

    This course is an in-person course.

    • Lectures are Tuesdays and Thursdays at 10:15-12:00 in U1 (Kaie Kubjas, kaie.kubjas@aalto.fi).
    • Exercises (choose one group): 
      • H02 Thursdays 14:15-16:00 in M240 (Neehar Verma - head teaching assistant)
      • H01 Thursdays 16:15-18:00 in Y228b (Matilde Costa)
      • H03 Fridays 12:15-14:00 in U405a (Antti Haavikko)
      • H04 Fridays 14:15-16:00 in Y229a (Matilde Costa)
    • Office hours are by appointment. You can also ask your questions after the lectures.
    • Office hours before the exam: Friday, 16.2 at 10:00-12:00 in office Y237 (Otakaari 1) on Zoom

    Completing the course:

    It is possible to take the course based on either exercises and course exam (KT), or final exam only  (T0 or T01). The grade is based on the maximum of the following two options:
    • exercises 50% + course exam 50% (5 best homework grades out of 6 are taken into account)
    • final exam 100%.

    Exam:

    The exam dates for Spring 2024 are:

    • T0: February 21, 2024 (at 9:00-12:00)
    • T01: April 19, 2024 (at 13:00-16:00)
    • KT: The course exam option is available in both exams of the Spring semester 2024: February 21 and April 19. The exercise points from the period III course then constitute 50% of the total.

    Students are allowed to bring one A4 sheet handwritten on one side of the sheet to the exam.

    Please see http://math.aalto.fi/exams for 

    (a) Individual study arrangements for exams (deadline to submit the form is 1 week before the exam, but the earlier the better) 

    (b) Exam rooms (announced 1 or 2 days before the exam)

    Exercises:

    There are weekly problem sets posted under "Assignments" in MyCourses. Each problem set consists of four problems. Students who attend an exercise session need to submit solutions only to three marked problems. Students who do not attend an exercise session need to submit solutions to all problems. Solutions can be uploaded as a single PDF file to MyCourses by 23:59 on Tuesdays. Since five best homework grades out of six are taken into account, the homework submission deadlines are strict and late submissions are not accepted.

    Communication:

    Official announcements will be posted in MyCourses. Please email any questions to kaie.kubjas@aalto.fi.

    Study material:

    Lecture notes can be found under Materials. The lecture notes are from 2022 and will be updated as the course progresses. There will be no lecture recordings, however you can check the lecture recordings from 2022. We will not follow one particular source, however, all essential material is included in any standard abstract algebra book or lecture notes, for example

    • John Fraleigh, A First Course in Abstract Algebra, 7th Edition, 2003
    • Thomas W. Hungerford, Algebra, Graduate Texts in Mathematics, Springer, 2003
    • Thomas W. Judson, Abstract Algebra: Theory and Applications, Orthogonal Publishing L3C, 2020. Free online version available at http://abstract.ups.edu/
    • Tauno Metsänkylä, Marjatta Näätänen, Algebra: https://matematiikkalehtisolmu.fi/2010/algebra.pdf, 2010 (Chapters III-VI.2, in Finnish)

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