- 12/18: I will be out of town until 12/25. If you have any questions about your grade, then please wait until after Christmas to contact me. Even though campus is closed between Christmas and New Year, I will be responding to email at that time.
- 12/18: Your score on the final, as well as your grade for the course have been posted on WebCT.
- 12/18: The two lowest homework scores have been dropped and the highest counted double, as announced.
- 12/14: Your final grade will be posted on WebCT as soon as it becomes available. So there is no need to give me preadressed postcards or to send me emails about this. I plan to have the grade available by Sunday night at the latest.
- 12/8: Homework can be picked up at this office hour or will be returned at the final. I can also put it in an envelope at my office door, but if you want me to do so, then you have to indicate so on your homework assignment (or in an email to me before Monday.)
- 12/8: There will be an office hour on Tuesday 12/13, 1:15-2:15PM.
- 12/8: You must bring a student ID to the final!
- 12/8: The final exam is on Thursday 12/15. Please refer to the course information sheet for the exact time.
- 12/4: In HW11#6 there needs to be an additional hypothesis of "n at least 3" (this has now been included in the pdf file.) Observe that the graph is not necessarily connected.
- 12/4: In HW11#10 you may assume that in order to model (NOT x) you may only use L, x, and parenthesis (but not T or F) in your expression.
- 12/2: Study guide for Final Exam.
- 12/2: Practice Final Exam. This was last semesters final exam -- we didn't do groups this semester, so I would not ask a question like #6.
- 11/30, HW 10#14d): Use part a)-c) to first answer the following question:
If you have x recursive trees on n vertices, and y recursive trees on n+1 vertices, then how are x and y related? This will be the key ingredient in finding the answer in closed form and then proving it by induction.
- 11/19: Homework 10 has been posted.
- 11/19: Lecture 21 has been posted already, and lecture 19 has been updated a little bit.
- 11/16: There will be 11 assignments altogether. The lowest 2 will be dropped, and to make up for the assignment next week your best score is counted twice.
- 11/16: Assignment 10 will be assigned this weekend and be due 12/1. It will be a longer assignment since it will cover 3 lectures.
- 11/16: There will be no homework due next week, and the next assignment is due the week after that. The schedule has been update to reflect that.
- 11/16: Somebody left a black jacket at the exam. Please pick it up from me after class.
- 11/14: I have decided that if your final is better than your lowest exam score, then that exam score will be replaced by the final. So if you did uncharacteristically poorly on one of these exams, then here is your chance to make up for it. Take this as motivation to keep working hard for the next month.
- 11/14: The exam scores have now been posted. 4 points have been added to each exam.
- 11/11: The solutions to Exam 2 have been posted, but I have not finished grading it.
- 11/8, HW9#1a: Actually much more is true: whenever you take ANY eleven integers (not necessarily powers of the same integer n), then there will be two of them whose difference is divisible by 10.
- 11/5, HW9#2: The midpoint of two points in the plane is the point that is exactly halfway between them.
- 11/4: Study guide for Exam 2.
- 11/2: Practice Exam 2.
- 10/31, HW8: For any question in which you do some counting you don't need to "prove" your counting, just give a good explanation of why the way you count is correct.
- 10/31, HW8#9a): There are several possible choices for the range, please use B. Explain why this choice is appropriate.
- 10/31, HW8#4: Look at Pascals triangle.
- 10/31, HW8#3: Induction should work.
- 10/31, HW8#2: Think about the x and y coordinates of the 4 corners of the recatngle.
- 10/31, HW8#1: The divisor of 1000!+n depends on n.
- 10/27: The notes for Lecture 16 have been somewhat changed to reflect the content of the lecture I gave more accurately.
- 10/25, HW7#3b: The substitution x2=z is useful here.
- 10/25, HW7#9-10: If you have a hard time getting a handle on these I suggest picking concrete examples for A,B,C and computing both sides to see if/why they are equal.
- 10/25, HW7#10a-c: You want to show that two sets are equal.
- 10/25, HW7#4-8: No "proof" needed, but just writing 3 x 24 = 72, for example, isn't enough. Explain what the terms 3 and 24 mean and why the answer can be obtained by just multiplying them.
- 10/25, HW7#10d: try to prove this using 10a-c.
- 10/22, HW7#3b: the an-4 should be a bn-4 and this has been fixed in the pdf file.
- 10/21, HW7#4-8: For each of these counting questions the answer should be an actual number, that is it needs to be fully multiplied out.
- 10/16: As soon as I receive assignment 5 from the grader, I will make midterm grades for all students based on the first 5 assignments and, most significantly, exam 1.
The letter grade will be assigned according to the grading scheme announced on the syllabus (without +/-). For some students I am obliged to report these grades (to enhance their advising), but I will post midterm grades for all students on WebCT.
- 10/15, HW6#9: The right-hand-side should be fnfn+1 (this mistake has been fixed in the pdf file assignment 6).
- 10/14, HW6#8,9: fn refers to the Fibonacci numbers from lecture.
- 10/12: 6pts have been added to your exam 1 score.
- 10/9, HW5#2b: Don't use induction straightout, but deal with top and bottom separately.
- 10/9, HW5#10: strong induction is probably the best way to go here..
- 10/9, HW5#4b: The sum on the left has 2n terms, so for example for n=2 the left side is 1+1/2+1/3+1/4.
- 10/9: The exam is not yet fully graded, but it will be graded by tomorrow night. Grades will be posted and the exam will be returned by Tuesday morning.
- 10/6: A black knit jacket was left behind from the 10AM section today.
It is now in the math department office.
- 9/30: Assignment 5 will be posted today, but will only be due in 2 weekis.
- 9/29: I have an off-campus appointment today, so I need to leave right
from my office hours, and I won't be back until after the homework is due.
- 9/26: Practice Exam 1.
- 9/26: Study guide for Exam 1.
- Hints on Assignment 4:
- 9/27, for #5: follow the proof that root 2 is irrational, except that the contradiction will arise here from the fact that both the numerator and denominator are divisible by p.
- 9/27, for #6: there is a typo since after 42 should be a - and not a +. The signs alternate, as is indicated by (-1)n.
- 9/26, for #8: if the previous hint doesn't help, then the best way of proceeding is evaluating the first few terms, factoring them, and looking for a pattern (observe that this grows "like n3"). If the previous hint is applied correctly it definitely leads to a simpler approach.
- 9/25, for #1: Divide x by 4.
- 9/25, for #3: (c) is easy if an appropriate condition is chosen in (b).
- 9/25: do #7 before #6, since #7 is easier.
- 9/25, for #8: k(k+1)=k2+k.
- 9/22: Remember that you can't just copy somebody elses solution and pass it off as your own. That constitutes plagiarism and will be reported to the Dean of Students office. Specifically, if you find a solution to a problem someplace (like a webpage, book, or notes from a previous class), then you MUST state your source, then rewrite the solution so that the write-up is in your own words.
- 9/16: The new assignment and practice solutions are now posted.
- 9/16: The scores for assignment 1 are now in the WebCT grade book. Please check the grade book every now and then to ensure that your scores are recorded correctly.
- 9/10: Solutions to practice assignment 2 are now posted.
- 9/10: I will not post here anymore when a specific file has been put on WebCT, so please make sure to check every now and then if you expect something to be there. If I am more than half a day overdue, then feel free to email me.
- 9/9: Assignment 2 and the solutions to assignment 1 are now posted.
- 9/6: Develop a strategy for learning all definitions before too many of them pile up.
- 9/6: The solutions to practice assignment 1 have been on WebCT since the weekend.
- 9/2 (just after midnight): Assignment 1 has now been posted.
- 9/1: Some students had problems with accessing the lecture notes
last class. The mac browser SAFARI worked on all the machines I tried.
If you still have problems, let me know.
- 8/30: An old copy of Epp's book is on 2 hour reserve in the library.
- 8/30: Office hour from 1:00-2:00 on 9/1.
- 8/30: The first homework will be assigned on Thursday and be due
next week.
- 8/30: You will also be able to check your grades on WebCT.
- 8/30: All solutions to exams and homework problems will be posted
at the WebCT link above. Login and password are the same as for your
student account.
- 8/30: In the past students found the following webpage useful:
www.mathworld.com.
- 8/30: Some books for supplementary reading:
- If you are mostly interested in more examples with worked
out solutions, then you can consider the Discrete Math books
in the "Schaum's outline" series.
- A book with very detailed explanations is
"Epp: Discrete Mathematics with Applications". A copy of this book
is on 2 hour reserve
- There are many other good books in the library ...
- 8/30: Funny proof techniques on the web:
Basic,
hazardous, and then
some (in the middle).
- 8/30: To get a good idea of what to expect in this course, I strongly
suggest you should read pages xxiii,xxiv and section 1.1.
- 8/30: Welcome to Math 370.
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