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• Algebraic structures I & II
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# Algebraic structures I & II

## Algebra I

Lecturer: Johanna Rämö, email: firstname.surname 'at' helsinki.fi

These courses are taught in Finnish. The course assignments, course material and lectures are all in Finnish. However, you can submit your coursework in English. The exams are provided in English if needed. If you would like to take the exam in English, please contact the lecturer.

#### Literature

John B. Fraleigh's book "A First Course in Abstract Algebra" covers quite well the topics of the courses. If you wish, you can also have a look at the Finnish course material that is Häsä J. and Rämö J., Johdatus abstraktiin algebraan.

#### Topics

The courses cover the following topics. The numbers after each topic show where the topic can be found in Fraleigh's book (sixth edition). You can use any edition of the book.

##### Algebraic structures I
• Binary operations (1.1)
• Group and subgroups (1.3-1.4)
• Permutations (2.1, 2.2, exluding Even and Odd Permutations and The Alternating Groups)
• Group isomorphism (1.2)
• Generating a subgroup (1.4, 1.5)
• Cyclic groups (1.5)
• Equivalence relation (7)
• Cosets and the Theorem of Langrange (2.3)
##### Algebraic structures II
• Rings (5.1)
• Fields (5.1)
• Integral domains (5.2)
• Quotient groups / Factor groups (3.2, 3.3, excluding Simple Groups and The Centre and Commutator Subgroups)
• Quotient rings / Factor groups (6.1)
• Ideals (6.1)
• Group homomorphisms (3.1)
• Ring homomorphisms (6.1)
• First isomorphism theorem (3.2)
• Polynomials (5.5, 5.6, excluding Uniqueness of Factorization in F[X])

#### Course assignments

Even though the problem sheets are in Finnish, you can probably understand many of the questions. The problem sheets can be found under the title "Harjoitustehtävät" on the Finnish Website.

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