# 189-235A: Algebra 1

## Assignments

The bi-weekly assignments are an essential part of the course. You should plan to devote at least ten hours a week (and quite possibly more) to the assignments.
If you are stuck on a problem, you may seek out the help of a TA, the professor, or one of your classmates. It is OK to work on the assignments in groups, although you should hand them in individually. Do not neglect the assignments: experience shows there is a strong correlation between the work you put into them and how much you learn in the course, which will of course be reflected in your exam performance.
The assignments are normally due on Mondays and will be graded and returned to you on the Monday of the following week. Late assignments will not be accepted.

Here are some guidelines for turning in your assignments that have been suggested by one of your graders (Olivier Martin). I am posting them here and you should take them to heart!

All assignments:

1. should be presented as cleanly and clearly as possible. If your handwriting is less legible no you might want to consider typing your assignments.

2. Must be stapled individually (no paper clips, no tape, no origami, no plastic pockets, etc). Remember that there is a stapler in the 10th flor office where you hand back your assignments, should you need it.

3. Must be handed in on time. Remember that late assignments will not be accepted.

4. Should present problems in order.

5. Should clearly bear the name and McGill ID of the student at the top of the first page.

Tips for writing proofs: When writing a proof, make sure to proceed linearly. For instance, say you want to prove the identity A=Z. If you know A=B, B=C, etc, write A=B=...=Z. This makes the proof easy to read as the reader only has to check each statement independently. In highschool some of you may have acquired the bad habit of writing the same proof by starting with A=Z, which you do not know to hold a priori (this already gives a hard time to the grader, who is left to guess whether you know what you are doing or are instead assuming what you were asked to prove), then proceed to write B=Y (since A=B, Y=Z this holds if and only if A=Z holds), C=W, ... up to L=M say. But you know L=M to be true so going up the chain this means A=Z. This is logically correct but very confusing and hard to follow as the proof is essentially written upside down. I did not penalize anyone for this on the first assignment because MATH 235 is one of the first proof based courses but make sure to write proofs where, proceeding from the top to the bottom, every statement can be deduced from the previous statements. Finally, some of you seem to be fervent advocates of the LHS, RHS school of proof writing. Note that if one can proceed linearly to show LHS=A=B=...=Z=RHS one should try to avoid showing that LHS=A=...=Z=Z', RHS=A'=B'=...=Z' which implies LHS=RHS. If lenghty computations are involved and one has difficulty using the first method of proof then one is justified in using the second.

Finally, let me add a suggestions of my own:

When writing up your proof, make sure that you explain your reasoning clearly and fully, using complete sentences. Mathematical notation, although admirable in its conciseness and power in many contexts, is no substitute for clearly written prose. Remember that in an exam or assignment, a wrong answer preceded by an almost correct, cogently argued justification will earn you (a lot of) extra credit. The same answer with no explanation of what led you there will earn you no points at all: the grader, unable to read your mind, will be forced to assume the worst...

1. Assignment 1 (pdf). Due: Monday, Sept. 24.
Solutions to Assignment 1
2. Assignment 2 (pdf). Due: Wednesday, Oct. 10. Note the revised due date, taking into account the Canadian Thanksgiving.
Solutions to Assignment 2
3. Assignment 3 (pdf). Due: Monday, Oct 29
Solutions to Assignment 3
4. Assignment 4 (pdf). Due: Monday, Nov. 12
Solutions to Assignment 4
5. Assignment 5 (pdf). Due: Wednesday, Nov. 28
Solutions to Assignment 5
6. Practice Final (will not be graded) (pdf).
To be discussed in class: Wednesday, Dec. 5
Solutions to practice final.