Most recent message posted: 05/11/2011
| Instructor | Teaching Assistant | Teaching Assistant | |
| Name | David Kempe | Mahyar Salek | Bei (Penny) Pan |
| Office | SAL 232 | SAL 227 | PHE 328 |
| Office Hours | Wednesday, 10:30-12:00 Tuesday/Thursday, 12:20-1:00or by appointment |
Monday, 3:00-5:00 | Friday, 1:30-3:30 |
| Phone | (213)-740-6438 | e-mail is better | e-mail is better |
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The grading scale is given here. These are not curves or class percentages, but your percentages. For instance, if the weighted average percentage of your grades is 55%, then you get at least a B. Since I have not taught this class before, if I find that the exams were a bit too demanding, the grading scale may become a little nicer. It will not become tougher.
| p | Grade |
| 80% | A+ |
| 72% | A |
| 66% | A- |
| 60% | B+ |
| 54% | B |
| 49% | B- |
| 44% | C+ |
| 39% | C |
| 34% | C- |
| 29% | D |
Homework will be assigned roughly once per week, and graded. Of all assignments, the worst one will be dropped in calculating your grades. Homeworks are due in class on the date specified. Each student can submit up to 3 homeworks up to one day late. Late submissions should be made to a TA or instructor in office hours, no later than office hours on the day after the due date. Submissions more than one day late will not be accepted. Once 3 homeworks have been submitted late, subsequent late submissions will not be accepted.
Homeworks will from time to time contain "chocolate problems". Chocolate problems do not affect your grade in the course. They are intended to be significantly more challenging, for students looking for a challenge. Chocolate problems will be marked with a number of chocolate bars. Solutions that are (mostly) correct will lead to the solvers getting that number of chocolate bars. Contrary to regular homework problems, chocolate problems can be solved in groups of up to 3 students (who will then share the chocolate). Chocolate problem submissions should be on separate sheets of paper, as they will be graded by the instructor, not the TAs/grader. Feel free to mark your preferred type of chocolate with your submission.
The course covers the fundmantals of discrete mathematics as they relate to computer science. Many of the problems computer scientists are most frequently called upon to solve involve discrete structures such as trees, graphs, and - even more fundamentally - natural numbers. Furthermore, since execution of programs necessarily proceeds in discrete time steps, to truly understand what it means for a computer program to solve a problem correctly and efficiently, it is necessary to have a solid understanding of the tools used in program analysis. The topics that will be covered in depth in this class are:
While each of these topics is important in its own right, the main goal of the class is to familiarize students with a mathematical mindset in thinking about problems, and the precision and clarity of thinking promoted by proving mathematical statements.
The textbook is
The (rough) syllabus for the course is as follows. Topics may be added or removed depending on available time:
All students are expected to maintain the utmost level of academic integrity. Any attempts to cheat will lead to appropriate sanctions. Please consult the USC Student Conduct Code (general overview) for details on what is and is not appropriate, and for the possible consequences of infractions.
Homeworks should be solved mostly individually. Asking classmates for small hints is ok. For bigger hints, ask the TA or instructor. Substantial collaboration, in particular in writing up solutions or during (rare) programming assignment, is not appropriate. Nor is of course copying classmates' solutions. It is also never appropriate to search for solutions online and try to pass them off as your own work.
05/11/2011: The percentages posted on Blackboard are now final. I also posted the resulting grades. If the given grade differs significantly from what you thought you would get, please let me know ASAP. (Don't bother to ask me to "round up" your grade, though.)
The final grade distribution was: 3 A+, 5 A, 6 A-, 5 B+, 5 B, 9 B-, 6 C+, 3 C, 3 C-, 4 D, 1 F.
05/11/2011: The final exam grades are now posted on the Blackboard Site. The minimum score (out of 46 possible) was 7.5, while the maximum was 44 and the average about 25.5. In recognition of a difficult semester with two challenging exams, the entire grading scale has been slid down one percentage point.
05/01/2011: Office hours for the time until the final exam are
as follows:
Monday (05/02): 2:00-4:00 (David)
Tuesday (05/03): 11:00-1:00 (Mahyar)
Wednesday (05/04): 10:30-12:00 (David), 2:00-3:00 (Mahyar)
Thursday (05/05): 11:00-1:00 (Penny)
Friday (05/06): 11:00-12:00 (Penny), 2:00-4:00 (David)
Monday (05/09): 2:00-4:00 (David)
As usual, these are drop-in: just show up. After the final exam, you can view your exam in David's office on Wednesday, 05/10, from 10:30-12:00 or from 2:00-4:00. That is the time frame during which you can ask for regrades. After that, the grading on your exam will be considered final, and grades will be submitted by 5:00pm on Wednesday. If you cannot make it at those times, you can designate (by e-mail to David) another student to view your exam for you.
04/26/2011: There will be one more review session each on Friday, 04/29, and on Monday, 05/02. Monday will repeat the material from Friday (as usual), so feel free to come to Friday's instead if it fits your schedule.
04/22/2011: There is a small mistake in our sample solution to problem 9.2(54) from Homework 9. The correct answer is 8, not 7, because we gave a wrong formula for the number of node pairs.
04/19/2011: The final exam will be on Tuesday, May 10, from 11:00-1:00, in room SLH 102 (not our classroom).
04/19/2011: The fifth quiz will be in class on Thursday, 04/28.
04/18/2011: The eleventh homework assignment consists of the
following problems:
Section 9.5: (16), (28), (34).
Section 9.6: (18), (26), (30).
Section 9.7: (12), (24), (32).
Section 9.8: (18), (20), (36).
Section 10.1: (10), (46).
Section 10.2: (36).
Section 10.3: (10).
Section 10.4: (24), (30).
The chocolate problem (worth up to 3 chocolate bars, depending on the quality of your reuslts) is the following: Find a (reasonably large, i.e., at least 25-node) graph that you are interested in. This could be all your Facebook friends and their friendships, or a road system in the US, something from biology, computer networks, or whatever else excites you. Apply concepts from this class to this graph to determine some meaningful quantities (such as degrees, short paths, tour lengths, chromatic number, planarity, ...) and report on your findings in suitable forms (diagrams, tables, ...) You might want to code up some of the algorithms discussed here. In addition to raw data, provide some interpretation of your findings in terms of what it means for the particular domain your graph is drawn from.
Homework 11 is due in class on Thursday, 04/28, though the chocolate problem can be submitted until Tuesday, 05/03, in David's office.
04/16/2011: For a very nice illustration of some of the recent graph-theoretic concepts we have discussed, check out this cartoon.
While we're on cartoons, this one captures quite aptly how to approach math (and connects with some conversations in class).
04/12/2011: The fourth quiz will be in class on Tuesday, 04/19.
04/12/2011: The tenth homework assignemnt is posted as a PDF. It is due on Tuesday, 04/19/2011.
04/07/2011: The chocolate problem on HW 9 has been changed.
04/04/2011: The ninth homework assignment consists of the following problems: Section 6.4: (6), (10), (32), (36); Section 9.1: (24), (28); Section 9.2: (16), (22), (46), (54); Section 9.3: (6), (28), (32), (40).
The chocolate problem (worth one chocolate bar) is posted as a PDF. (Note that this is different from the originally posted chocolate problem (which was too easy and boring).)
Homework 9 is due in class on Tuesday, 04/12.
03/23/2011: The third quiz will be at the beginning of class on Tuesday, 03/29/2011.
03/23/2011: For those of you who bought the international edition of the textbook: it seems to be missing the entire Chapter 6 on discrete probability (and shift the numbers of all subsequent chapters). Make sure you get the correct Chapter 6 to review the material and solve the homework.
03/22/2011: The eighth homework assignment consists of the following problems (no chocolate problem this time): Section 6.1: (14), (16), (26); Section 6.2: (8), (14), (16), (18), (34), (36); Section 6.3: (6), (10), (12), (18);
It is due in class on Tuesday, 03/29.
03/21/2011: The midterm grades are now posted on the Blackboard Site. The minimum score (out of 35 possible) was 5, while the maximum was 35 and the average about 17.6.
03/03/2011: The midterm on March 10 will be held in room MHP 101.
03/03/2011: The seventh homework assignment consists of the following problems: Section 5.2: (6), (10), (18), (24), (36), (40); Section 5.3: (12), (24), (28); Section 5.4: (10), (22), (24).
It is due in class on Thursday, 03/10.
The chocolate problem (worth two chocolate bars) is the following: Penny and Mahyar recently received some chocolate as presents. Penny got several bars of dark chocolate, while Mahyar got several bars of milk chocolate. Penny's bars have sizes p1, p2, p3, ..., while Mahyar's have sizes m1, m2, m3, ... Each of the sizes is measured in pieces of chocolate, so each is an integer, between 1 and n. Of course, some of the bars may have the same sizes.
Mahyar also likes dark chocolate, while Penny also likes milk chocolate. So they would like to trade some (or all) of their chocolate. But both are also very eager to be fair, so they only want to trade if each gets exactly the same total number of pieces of chocolate from the other. And of course, they can only trade entire bars, not break them apart. Prove that if each of them has at least n bars of chocolate (the same n that formed an upper bound on the sizes of the bars), then they always have non-empty sets that they can trade with each other.
To gain some feel for the problem, you may want to prove first that if one of them - say, Penny - only has n-1 bars, then even if the other one has a really large number of bars, they may not be able to find any trade.
02/25/2011: For some nice applications of the pigeonhole principle, see this cartoon.
02/23/2011: The sixth homework assignment consists of the following problems: Section 4.5: (4),(8),(12) End of Chapter 4: (12), (36) Section 5.1: (16), (24), (38), (44), (50), (60).
It is due in class on Thursday, 03/03.
The chocolate problem (worth one chocolate bar) is the following: Suppose that we have n people with some friendships between them. Let's say that everyone has an odd number of friends. (This will be important only for tie-breaking.) Every person uses either an Android or an iPhone, with some given initial assignment. Now, the n people go in round-robin fashion. When it is person i's turn, he looks at all his friends, and gets the same kind of phone that the majority of his friends use. (He may later change his mind to the other one again, of course.) Prove that after a finite number of steps, no more changes will occur, i.e., everyone sticks with the phone they have at that point.
02/16/2011: The second quiz will be at the beginning of class on Tuesday, 02/22/2011.
02/15/2011: Due to Presidents Day, there will be no review session on Monday, 02/21. The material will be covered Friday, 02/18; though if everyone shows up then, the room may be very crowded.
02/14/2011: The fifth homework assignment consists of the following problems, all from the textbook: Section 4.1: (68), (70). Section 4.2: (4), (12), (30) Section 4.4: (10), (22), (38), (40) It is due in class on Tuesday, 02/22.
The chocolate problem (worth two chocolate bars) is the following: Suppose that we have n students and n different chocolate bars. Each student gets to list all the chocolate bars he/she would like. (Some students might not like particular types of chocolate.) In the end, we want to give exactly one chocolate bar to each student. Sometimes, this is not possible; for instance, if all students are only interested in chocolate bar 1, then only one student can get the bar. More generally, if there is a set S of students such that all of them are only interested in chocolate bars in T, and T is smaller than S, then it is obviously impossible to satisfy all students simultaneously. Prove that the converse is also true: If for every set of students S, the set of bars that they are jointly interested in (meaning, the set of bars such that at least one student in S is interested in it) contains at least as many bars as S contains students, then there is a way of giving every student a chocolate bar he/she likes.
02/07/2011: The fourth homework assignment consists of the following problems, all from the textbook: Section 1.7: (10), (20), (24), (36), (42). (It may help to read Section 1.7); Section 4.1: (4), (6), (20), (26), (38), (64). It is due in class on Tuesday, 02/15.
The chocolate problem (worth one chocolate bar) is the following: Is it possible to take the digits 0,1,2,3,4,5,6,7,8,9 (once each) and combine them into numbers whose sum is 100? Either give a solution, or prove that no solution exists.
02/06/2011: Those of you remembering our first lecture may relate to this cartoon.
02/03/2011: The first quiz will be at the beginning of class on Thursday, 02/10/2011.
01/31/2011: The third homework assignment consists of the following problems, all from the textbook: Section 1.3: (10),(24),(32),(62); Section 1.4: (24),(32),(52); Section 1.5: (16),(24),(28); Section 1.6: (22),(34). It is due in class on Tuesday, 02/08.
The chocolate problem (worth two chocolate bars, though not poisoned ones) is the following: Suppose that you have two chocolate bars, the first one having n pieces and the second one m pieces. On each bar, one piece is poisoned and green (i.e., recognizable as such). Whoever eats a poisoned piece loses. Two players take turns eating one or more piece of chocolate each. The rules are as follows: the current player must always eat pieces from the (currently) larger chocolate bar, and the number of pieces he eats must be a positive integer multiple of the number of pieces in the smaller bar. (For example, if one bar has 3 pieces, and the other 10, then the player could eat either 3, 6, or 9 pieces from the bar with 10 pieces.) Give a complete characterization of the values of m and n for which the first player is guaranteed to win (and prove it).
01/22/2011: The second homework assignment has been posted. It is due on 02/01/2011.
01/17/2011: The first homework assignment consists of the following problems, all from the textbook: 2.1(6), 2.1(22), 2.2(2), 2.2(26), 2.2(48),2.3(6),2.3(12),2.3(16),2.3(30),2.4(14),2.4(20). It is due in class on Tuesday, 01/25.
The chocolate problem (worth one chocolate bar) is the following: Suppose that you hike up to Mt. Wilson one day, starting at 8:00am, and reaching the top at 6:00pm. The next day, you take a different trail down, starting at 8:00am, and reaching the bottom (your starting point the previous day) at 6:00pm. The trails you take may go up and down multiple times. Prove that there is some time of day when you were at exactly the same height on both days.
