15-344/The Final Exam

Our final exam took place on Thursday December 17 from 2PM until 5PM, in two separate locations: at BR 200 if your last name begins with A through Ri, and at EM 119 if it begins with Ro through Z. No material other than stationary will be allowed; in particular, calculators are forbidden.

• BR 200 is Room 200, Brennan Hall, St. Michael's College, 81 St. Mary Street.
• EM 119 is Room 119, Emmanuel College, 75 Queen's Park.

The material for the term test is everything done in class or in tutorials, with a division of about one third for graph theory and two thirds for enumeration. There will be no sample exam. Most likely there will be some choice: "choose 6 out of 7", or "10 out of 12 smaller questions", or something similar. The questions will come from four sources: class material (usually, "repeat something done in class"), questions discussed at the tutorials, questions assigned as homework (for submission or not), and questions from the book that were not assigned or discussed but are similar to questions assigned or discussed.

How to prepare? We each have our own ways. My own (and it worked quite well) was concentrate on totally knowing all the material, and not so much on doing exercises. So before an exam I'd make a list of "class material divided into (say) 100 points", and then I'd go over that list again and again crossing out those points which I was confident I fully understood, until there was nothing left. Yet given my declared intent that some term test questions will coming directly from the homework assignments, you'd probably be wise to go over these too.

Pre-exam time table. Please note that the information below is subject to last minute changes. If you are unsure, it is always better to chack the website once again.

• Tuesday December 8, 10:30-11:30: Dror's office hours, Bahen 6178.
• Tuesday December 8, 3-5: Last class for the semester, MP 202.
• Thursday December 10, 3:30-5:30: TA office hours, 215 Huron room 1012. (HW10 can be submitted, HW 1-9 available for pick up).
• Thursday December 10 at 5PM through Friday December 11 at 5PM: HW10 can be submitted to a drop box near Dror's office, Bahen 6178.
• Friday December 11, 4-5: TA office hours, 215 Huron room 1012. (HW10 due, HW 1-9 available for pick up).
• Monday December 14, 1-5: TA office hours, 215 Huron room 1012. (HW 1-10 available for pick up).
• Tuesday December 15, 2-5: Dror's office hours, Bahen 6178.
• Wednesday December 16, 2-5: Dror's office hours, Bahen 6178.
• Thursday December 17, 2-5: The exam itself, in two separate locations: at BR 200 for last names A through Ri, and at EM 119 for Ro through Z.

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, "$x\in V$", does it mean "choose $x\in V$", or "we've just proven that $x\in V$", or "assume by contradiction that $x\in V$", or "for every $x\in V$" or "there exists $x\in V$"? 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!

The Results. 161 students took the test, and the results were as follows (median 49):

100 100 100 100 100 100 100 100 100 100 99 99 99 99 99 99 99 96 95 95 92 88 88 87 87 87 87 87 86 82 82 82 81 81 81 79 79 77 77 76 75 75 75 74 74 73 73 73 72 68 68 65 65 64 62 62 60 60 60 59 59 59 58 58 58 58 57 57 56 56 56 55 54 54 53 51 50 50 49 49 49 48 48 48 47 46 45 44 43 43 43 43 42 42 42 42 42 41 41 41 39 37 37 37 37 37 36 36 36 36 36 34 34 34 34 33 33 32 32 32 32 31 30 30 30 30 29 29 28 28 28 27 27 26 25 23 21 21 21 20 20 19 18 18 16 16 16 16 16 15 14 14 13 13 13 13 10 9 6 6 1

Seeing that these are low, I've applied the formula $m\to 100(m/100)^{0.72}$ to the marks, before using them to compute the course mark. This done, and after averaging with the HW marks, the TT marks, and after taking account of the good deed points (when relevant), the overall course marks were as follows (median 70):

100 100 100 99 99 99 99 99 99 98 98 97 97 97 97 96 96 95 95 95 94 93 93 93 93 92 91 91 90 90 89 89 89 88 88 88 87 87 86 85 85 85 85 84 84 84 83 83 82 82 81 81 80 79 79 79 78 78 78 78 77 77 77 77 76 75 75 74 74 74 73 73 73 72 72 72 71 71 70 70 70 70 70 70 69 69 69 69 68 68 68 68 66 66 66 66 66 66 66 66 65 65 65 65 64 64 64 64 61 61 60 60 60 60 60 60 59 59 59 59 59 59 59 58 58 58 58 57 57 57 57 56 56 55 55 54 53 53 52 51 51 50 50 50 47 47 46 45 45 39 39 39 37 36 35 35 34 34 33 33 33 31 24 19

(By university rules, "Exam No Shows" count as 0 even if there is a valid reason. Hence there are 164 marks here, and some stand to rise if makeups are given).

The exam itself is at Final-15-344.pdf.