No need to extend, expect both in 4 hours.
You may need to work on your real name for question 9

Math 106 – Section 08 – Final Exam
Due Friday 12/11 by 11:30pm the latest in Canvas
Emailed Copies Will NOT be accepted
It’s finally here! Our last assignment. Collaborations are welcome but everyone needs to make
sure your write-ups are completely original. Please make sure to read the directions to each
problem CAREFULLY.
Best of luck!
-Prof Matt
Part 1: Questions about the course. (10 pts each)
Your response to problems 1-3 should be at least four sentences long.
1. Do you have the same opinion about Mathematics as a subject now as you did prior to
taking Math 106? Why?
2. No, it seemed quite tough when I started. Now I understand many concepts.
2. Out of all the topics in the class, which did you enjoy the most. Why? Which did you enjoy the
least. Why?
The one I enjoyed the most is on vertices because the concept was new and understanding it was
quite easy. The one I enjoyed the least was on numbers, because I tended to disregard most of
the concepts assuming to be knowledgeable.
3. What do you think will be the biggest contribution of math to our society over the next 10
years?
Math is very practical. We all apply it unconsciously every day. With widespread knowledge of
math knowledge, our society will improve in terms of math-based analysis, quantitative analysis,
and statistics, which implies that doing things will with precision will improve.
Part 2: Math Problems
4. (10 pts) Come up with your own example (this means your answer should not look like any of
your classmates’ answers) of a voting scenario with 3 or more candidates (Name them whoever
you’d like) where someone wins using the plurality method but there is NO winner using the
majority method.
Also, YOU MUST INCLUDE, the calculation of the majority value using the formula n/2 + 1 if the
total number of votes is even or (n+1)/2 if the total number of votes is odd to verify your answer.
Answer
The candidates are James, Jane, June.
The preference table is:
1
1
3
3
3
1st choice (James)
James
James
Jane
June
2nd choice (Jane)
James
Jane
Jane
June

3rd choice (June)
James
June
Jane
June
With plurality method will consider the first choice for James. Which come to 1+3 = 4 votes.
Jane and June get 3 votes each, from first choice.
With Majority method, the winner has to have more than half the total votes calculated as n/2
+ 1. The total is 10. To win, one should get 10/2 +1 = 6. James gets 4 in first choice, Jane gets 4
in second choice, and June also gets 4 in third choice. Thus no one wins.

5. (10 pts) Come up with your own example...