Abstract algebra

Course information

Learning outcomes

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.

Content

Groups, group homomorphisms and isomorphisms, rings, ideals, integral domains, ring homomorphisms and isomorphisms, polynomials, fields.

Teacher

Kaie Kubjas, Camilla Hollanti

Study material

See syllabus for each edition.

Workload

Typically 24+12 (4+2) contact hours plus independent work. 

Prerequisites

The student should be familiar with basic proof techniques, sets, functions, and relations, especially modular arithmetic and the congruence relation. These are covered on the course MS-A04XX Foundations of discrete mathematics, and typically in any standard book on abstract algebra. Finnish-speaking students can also looks at the lecture notes: Metsänkylä-Näätänen, Algebra, sections 0, I, II, matematiikkalehtisolmu.fi/2010/algebra.pdf ).

Evaluation

See syllabus for each edition.

Teaching time and location

The teaching time and the location of the course can be found at Sisu information system

1. The link leads to Completion methods tab of the course page
2. From the top of the page (Version drop-down menu), check that academic year 2025-2026 is selected  

3. From the blue bar, click Lecture and open the Groups and teaching times tab to see the teaching time and the location of the course. Exam times can be seen by clicking Exam.
    

   Exam instructions at the Open University

The teacher has four (4) weeks to grade the exam submissions starting from the exam date.

Further information

Substitutes the courses Mat-1.3081 Algebra I and MS-C1080 Introduction to abstract algebra.

Online learning environment for the course  

MyCourses online learning environment is a tool for both students and teachers for communication and managing everyday course work. You need an Aalto User ID to log in to the course's MyCourses workspace and participate in teaching.

Digital workspace of the course:
MyCourses

More details on completing the course will be available at MyCourses closer to the start of the course.

Registration and course fee

Registration for Open University courses is done via the link below: 
Course registration

Registration for this course starts on 8.12.2025 at 9.00  
Registration for this course ends on 12.1.2026 at 23.59

It is not possible to register before the registration period has started or after it has ended.

The number of participants is limited to 5.

This course is organized by the Aalto University School of Science.

The course fee is paid upon registration for each course at a time and it is binding. Familiarize yourself with registration and payment rules as well as other guidelines for students:
Registration, payments and rules

Activating Aalto ID and Multifactor Authentication

You can activate your Aalto User ID the day after the registration and you should activate it no later than the day before the start of the course.
Instructions for activating your Aalto user ID

Once you have activated your Aalto user ID, also enable multifactor authentication. Some of Aalto University's services require multifactor authentication.

Instructions for using Multifactor Authentication