Diana Chisholm's Section of MATH 135 (Section 009)

Class

Contact Info

• Email: dkchisho AT uwaterloo DOT ca
• Phone: (519) 888-4567 x33418
• Office: DC 2136
• Office Hours: Tuesdays 12 - 2 pm

Exam time office hours (all in DC 2136)

• 12 - 2 on Tuesday Dec 4
• 12 - 2 on Thursday Dec 6
• 10 - 4 on Friday Dec 7
• 10 - 2 on Wednesday Dec 12

Grades now available online

If you go into Angel, there is now a link to view all your grades in the course so far in the "Assignments, Exams, Outlines, and Solutions" section. Click on the link (it's only visible to Section 009 students) and select "Grades" at the top. Then scroll all the way down to see your grades. Alternatively, you can select "Gradebook Grades" at the side and you'll see a graph with your marks as well as the class average (of our section only) for each component.

If you notice any discrepencies, please let me know and bring me the assignment and I'll change it on the web.

Maple on Assignment 8

Notes on Assignment 7

• Remember to reduce your congruences to the lowest non-negative representative from that congruence class
• For 3b), while x=2^(p-2) is correct for the inverse of 2 (mod p), we were looking for a simpler solution making use of the fact that p is an odd prime. x=(p+1)/2 is guaranteed to be an integer since p is odd. Then for 3c), there are three solutions: 0, (p+1)/2, and (p-1)/2.

Typo in Assignment 6

The final exam for MATH 135 will be on Thursday, December 13 from 9:00 - 11:30 am in the PAC (main gym)

Notes on Assignment 4

• When you're asked to find the solutions, be sure to explicitly list the x and y value(s).
• In question 5, don't forget the n=0 case
• In question 6, the remainder could be a degree 0 polynomial (a constant) or the zero polynomial (if g(x) is a factor of f(x))

Notes on Assignment 3

• Remember, the remainder has to be greater than or equal to 0, even if the divisor or quotient are negative.
• That's pretty much it, this assignment was very well done!

Notes on Assignment 2

• Hardly anyone forgot to staple this time, I was impressed!
• Unfortunately, one assignment was late so got 0. Try to get it in before 8:25 at the latest
• In question 5, make sure to state the contrapositive correctly (see the solutions)
• In question 6, many people did not state the converse before trying to disprove it
• In question 7a)ii, (the square root of x)^3 is x^(3/2), but 3/2 is not an integer, so it's not a polynomial. Polynomials have to have integer powers of x.
• Also, in 7a)iii, a constant *is* a polynomial. Its degree is 0, not undefined - the only polynomial with undefined degree is the zero polynomial, 0.

Notes on Assignment 1

• DON'T FORGET TO STAPLE THEM! :)
• Please write your ID#
• Please try to submit to the right box for the right section (slot 7 is for last name A-L, slot 8 is for last name M-Z)
• Thank you for listing your acknowledgements, keep it up!

• don't forget to state the induction hypothesis: assume formula holds for n=k, k a positive integer
• for induction conclusion, consider n = k + 1
• prove that LS and RS are equal (start with what you're given, not with the formula for k+1)
• say when you're using the induction hypothesis
• at the end: therefore, by POMI (principle of mathematical induction), the result is true for all positive integers n

• justify your steps (i.e. using product rule)

• you need to use the fact that n is positive (otherwise the inequality would switch from >= to <=)
• also, be careful not to do it backwards - you can't start by assuming the result is true

• in a, draw a diagram
• in b, when you prove the formula using induction, you have to explain why drawing the (k+1)st line adds k+1 regions, not just assume it

Class notes

• Proofs Part 3 (Induction examples)
• Proofs Part 4 (Other techniques of proof)

Assignment Tips

• You don't have to print out the assignment template and fill it in, it was just a formatting guide
• If the questions are really long, you don't need to write out the whole thing, just the statement of what the problem is asking for (e.g. on Assignment 1, for 7 you could write "a) How many line segments are there in total?", "b) Determine the total number of "red ends" among all the line segments", etc))
• Remember to submit your assignment to the right box! Diana Chisholm, section 009 (slots 7 and 8)
• Don't leave submitting to the last minute, there are tons of people crowding around! They're due at 8:20, so you shouldn't have to be late for class :)