Note: Q&A meeting will be held on Thursday, August 21, 16:00 (department of mathematics seminar room).

In the first course (Algebraic structures, 89-214), you were supposed to cover the following:

* Introduction to number theory: division, Euclid algorithm, gcd.

* Definition of group. subgroups. Euler group. Cyclic groups.

* Symmetric groups and dihedral groups. Cosets and Lagrange theorem.

* Normal subgroups. Quotient groups.

* Isomorphism theorems.

* Rings: definitions, division rings, fields, ideals, principal ideals, integral domain, prime and maximal ideals.

* Quotient ring and isomorphism theorems. Chinese remainder theorem.

We covered the following topics:

* Group actions

* Sylow subgroups

* p-groups

* Euclidean domains, unique factorization

* Galois theory, including the main theorem and solvability by radicals (ignoring separability issues and assuming roots of unity)

* Finite fields

You may have a look at my exercise booklet on groups (86 pp.), and my exercise booklet on rings (50 pp.). Both are more suitable for a full semester length course on the respecitve topics, but can be used here as well. Note in particular chapter 12 of the first booklet, and chapter 5 in the second. |

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