# 06-240/On The Final Exam

Our final exam is coming up. It will take place at BN3 - room 3 of the Clara Benson Building, 320 Huron Street (south west of Harbord cross Huron, home of the Faculty of Physical Education and Health) on Wednesday December 13 from 2PM until 5PM. It will consist of 5-6 questions (each may have several parts) on everything that we will have covered in class this semester:

• Fields and vector spaces.
• Spans, independence, replacement and bases.
• Linear transformation, rank, nullity, matrices.
• Row and column reduction and elementary matrices, systems of linear equations.
• Determinants.
• Change of basis and diagonalization.
• Several other "smaller" topics.

As for the style -

• You can expect to be asked to reproduce some proofs that were given in class.
• You can expect some fresh things to prove, though generally not as hard as the previous type of proofs.
• You can expect questions (or parts of questions) that will be identical or nearly identical to questions that were assigned for homework.
• You can expect some calculations (but nothing that will require a calculator).

Basic calculators (not capable of displaying text or sounding speech) will be allowed but will not be necessary. You may wish to bring one nevertheless, as under pressure ${\displaystyle 5+7}$ often comes out to be ${\displaystyle 13}$.

Remember. Neatness counts! Organization counts! Language counts! Proofs are best given as short and readable essays; without the English between the formulas one never knows how to interpret those formulas. When you write, say, "${\displaystyle v\in V}$", does it mean "choose ${\displaystyle v\in V}$", or "we've just proven that ${\displaystyle v\in V}$", or "assume by contradiction that ${\displaystyle v\in V}$", or "for every ${\displaystyle v\in V}$" or "there exists ${\displaystyle v\in V}$"? If you don't say, your reader has no way of knowing. Also remember that long and roundabout solutions of simple problems, full of detours and irrelevant facts, are often an indication that their author didn't quite get the point, even if they are entirely correct. Avoid those!

Office hours. I (Dror) will hold two sessions of extended office hours at or near my office (Bahen 6178) before the final:

• On Tuesday December 12th (the day before), 1-4PM.
• On Wednesday December 13th (the day of), 10-12, just for last minute questions.

I would have loved to give more, but long before the final was scheduled I was asked to organize a session in a Canadian Mathematical Society conference on Saturday through Monday right before our exam. So unfortunately I will be completely unreachable on these three days.

Here is a link to the exam forum: Final Exam Preparation Forum