Topic outline

  • General

    Contents:

    The goal of this course is to teach about basic algebraic structures and their properties. In particular, the following topics will be covered:

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

    In this course, an emphasis is placed on proofs. After the course, the student should be able to master and use different proof techniques.

    Organization:

    This course is currently planned as an in-person course, but might be moved online if the situation requires so.

    • Pre-recorded lectures will be made available latest by every Tuesday and Thursday 
    • Exercises (choose one group): 
      • Wednesdays 10:15-12:00 in C-sali - Y205 (offline session) and on zoom at https://aalto.zoom.us/j/69690436669 (online session).
      • Fridays 14:15-16:00 in U5 - U147 (weeks 2, 4 and 5), in U6 KONECRANES - U149 (week 3) and in T1 - C202 (week 6)
    • Office hours: Thursdays 11-12, the first half  an hour 11:00-11:30 on zoom at https://aalto.zoom.us/j/61178502532 and the second half an hour 11:30-12:00 in the office Y237

    Grading:

    50% exam + 50% homework solutions (5 best homework grades out of 6 are taken into account)

    Exam:

    The course exam will be held on 23.02 during 9-12. Students are allowed to bring one A4 sheet handwritten on one side of the sheet to the exam.

    Exercises:

    There are weekly problem sets posted under "Assignments" in MyCourses. Each problem set consists of five 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 Tuesday midnight. Since 5 best homework grades out of 6 are taken into account, the homework submission deadlines are strict and late submissions are not accepted.

    Communication:

    Official announcements will be posted in MyCourses. The rest of communication for this course takes place in Zulip. The link to Zulip is the following: https://msc1081abstractalgebra2022.zulip.aalto.fi/join/cbto52wgdav4cyvirqwcf45a/ . Please be active asking your questions!

    Study material:

    Lecture notes (possibly handwritten) are posted under "Materials" after each lecture. 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
    • Tauno Metsänkylä, Marjatta Näätänen, Algebra: https://matematiikkalehtisolmu.fi/2010/algebra.pdf, 2010 (Chapters III-VI.2, in Finnish)