Math 315 Applied Combinatorics
Department of Mathematics
Combinatorics can be described as the art of counting. Polya once said that "an idea which can be used only once is a trick. If one can use it more than once it becomes a method." Our course will discuss several powerful combinatorics methods and their applications. We will emphasize important interplay between ("discrete") finite objects and the ideas of ("continuous") analysis.
The course is designed to develop advanced problem-solving skills, as well as the skills needed to effectively communicate the solutions of problems. Most mathematicians use aesthetics to guide their work; we will attempt to convey the sense of what is beautiful (and, occasionally, what is not) in mathematics.
|TEXT||Concrete Mathematics, by Graham, Knuth, and Patashnik, 2nd edition.|
|CALCULATOR||Will not be needed.|
|GRADING|| There will be written homework, mini-homework, two mid-term tests,
and a comprehensive final examination. The two mid-semester test scores will contribute 20% each toward the final grade.
Written homework will count 30% and the final 30%. Mini-homework will count as a letter-grade adjustment at the end of the course.
This course will use a different correspondence between the numeric grades and the letter grades than the more usual 90-80-70 scheme. The percentage score 80% is the dividing line between A and A-; 72% and above is a B; and 60% is (barely) a C. For written homeworks, this means that the score of 20 of 25 is an A; 18 of 25 is a B; and please try not to get below 15 too often. On the exams, this means that you can skip a problem and still get an A, if all the other problems are solved correctly.
This grading scheme takes into account the level of difficulty of the assignments and the exams as well as the rigorous grading style of your instructor.
Test 1: Wednesday, October 3
Test 2: Wednesday, November 7
Final: Monday, December 17, 8:00am
Written homework will be assigned bi-weekly. It is a very important part of the class. You are encouraged to
work in teams, but the solutions should be written up individually. I will have high expectations for the
clarity of solutions; and it is a good idea to show me drafts of your solutions for feedback.
Your written homework score (the one that's worth 30% of your final grade) is the average of the grades you get for each problem when you submit the work for the first time. In addition, you will lose up to 10 points on both mid-term exams, as well as on the final, unless you revise (i.e., solve correctly by the revision cut-off date) each of the homework problems that received a bad score. The revisions have to be done individually; each revision should be a self-contained solution of the problem.
The grading scheme for homework problems is explained in the Homework Guide. To get the full 10 points on the exam, you need to have a grade 4 or higher for each of the homework problems. To get 5 points, you need to have a grade of 3 or higher for each of the problems. If there is a problem with the grade 2 or lower, the homework component grade will be 0.
Revisions can be submitted any time, in person or electronically, before the start of the corresponding exam. There is one restriction (meant to discourage procrastination): you can submit only three revised solutions in any 24 hour period.
This homework will be assigned after every class and will be due the next class period.
Typically, it will consist of a reading assignment and some of the routine exercises.
You will not need to hand in anything, instead, two to four students will be volunteered
to present the solutions at the board, while the rest of the class will be expected
to discuss the reading assignment with me or will complete a short quiz.
If your presentations and participation/quizzes are consistently good (feel free to ask me for feedback if you are not sure), I will add a third of a letter grade to your final grade. At worst (if you are not ready or miss the class half the time), I will subtract one full letter grade from your final grade.
Class attendance is expected. If you miss a class, it is your responsibility
to get the material and the homework assignment from your fellow students.
You should expect to spend a considerable amount of time working on this course outside of class. According to the US Department of Education definition, a credit hour is ''an amount of work that reasonably approximates not less than one hour of classroom ... instruction and a minimum of two hours of out of class student work each week for approximately fifteen weeks''. This is a 4-credit hour course, so you need to budget 8 hours per week for independent work on this course. At the same time, try to be efficient. If you are spending a lot of time on homework without making much progress, talk to me. You are welcome and encouraged to ask me for help with course material during the office hours or by making an appointment.
The use of external to the course sources of solutions to homework problems is allowed, provided the source is fully cited and the material is critically evaluated. If you do not cite a source for the information, or copy a solution without a credible attempt to understand it, then you are violating the University's Academic Integrity Policy.
Tests and quizzes are to be written strictly individually. University's Academic Integrity Policy will be enforced; everyone caught cheating on any assignment will face a range of penalties, up to a failing grade in the course.
Normally, no make-up tests will be given; if for some reason you are not able to take a test, please, let me know as soon as possible.
If you have questions or concerns about the course, be sure to discuss them with me during my office hours or by appointment.
Everyone participating in this course is expected to be respectful of each other without regard to race, class, linguistic background, religion, political beliefs, sex, gender identity or expression, sexual orientation, ethnicity, age, veteran's status, or physical ability. If you feel these expectations have not been met, please feel free to discuss it with me or with the designated diversity liaison Dr. Elizabeth Goode.
|OTHER IMPORTANT DATES||
Drop without W deadline: Wednesday, September 5
Withdrawal deadline with W: November 5
Thanksgiving break: November 21 - 25
Last class: Monday, December 10.