Abstract Algebra

Tutorial Schedule

• Tuesdays 11:30 – 12:20
  

See Avenue or Mosaic for the location.

Office Hours

• Thursdays 12:30 – 1:20
• Fridays 1:30 – 2:20

See Avenue for the location. Other ways to get help include by email and the discussion board on Avenue. The discussion board is preferred as the whole class will benefit from questions asked and answered in this public forum.

Tutorial Information

We will use the tutorial time to go through practice problems that have a similar flavour to the assignment problems. Participation is encouraged by way of asking questions about practice problems or lecture content, or by suggesting next steps in the current exercise.

At the bottom of the page there is a list of all problems covered in tutorial this term.

Resources

Math 3GR3 is a course that involves proof writing. Prof. Van Tuyl wrote the short guide Creating and Writing Proofs for a course in 2010 that outlines several good practices in proof writing.

Tutorial Problems

Find below the tutorial problems for each week. We did not necessarily cover each problem in tutorial, but they are all good practice. You can also find here all the tutorial problems condensed into one file.

Topics	Problems
Equivalence relations, partitions. Euclidean algorithm, greatest common divisor.	Tutorial 1 Problems
SageMath. Groups, Cayley tables, commutativity.	Tutorial 2 Problems
Integers mod n. Group of units. Subgroups. Cyclic groups.	Tutorial 3 Problems
Cyclic groups. Cycles. Permutation groups.	Tutorial 4 Problems
Test 1 review. We did not get to any of the prepared problems on: Alternating groups, dihedral groups.	Tutorial 5 Problems
Subgroups of symmetry groups. Cosets. Lagrange's Theorem.	Tutorial 6 Problems
Cosets partition a group. Isomorphisms.	Tutorial 7 Problems
Internal direct products. Normal subgroups.	Tutorial 8 Problems
Test 2 review. No problems prepared.
First isomorphism theorem for groups, applications.	Tutorial 10 Problems
Rings. Integral domains, etc. Isomorphisms.	Tutorial 11 Problems
Mini-lecture on 4th year algebra topics (mostly algebraic geometry).	Tutorial 12 Slides