Discrete Mathematics

Spring, 2008

Professor: | Jessen Havill | Phone: | 587-6582 |

Office: | Olin 208 | E-mail: | havill@denison.edu |

Web site: | http://personal.denison.edu/~havill/ | Mailbox: | Olin 201 |

Office hours: | Please see the schedule outside my office. |

#### Description

A solid background in mathematics is essential for success in computer science. Studying mathematics will give you specific tools you will need to reason about the algorithms you write, as well as general problem solving and abstract thinking skills. By their very nature, computers are discrete entities; they are only capable of storing and operating upon a finite number of objects. For this reason, much of the mathematics that will be essential to your study of computer science falls under the general umbrella ofdiscrete mathematics. In this course, we will study a broad array of interrelated topics: counting, number theory and cryptography, recurrences, and probability. Tying all of these topics together is mathematical proof. As we will see, reading and writing proofs is an important skill. In addition to verifying your work (and programs), proofs serve to improve your understanding of the problem at hand, and often illuminate relationships to other, sometimes surprising, ideas.

#### Required Text

Discrete Mathematics for Computer Scienceby K. Bogart, C. Stein, and R. L. Drysdale, Key College Publishing, 2006.

#### Attendance and Other Responsibilities

In order to do well in this class, it is imperative that you take an active role in the learning process. I cannot simply transfer knowledge to you. Rather, learning must be an active process in which the instructor is but an important resource. Your attendance is expected at each class meeting. It is in your own best interest to attend class, as your grade will almost certainly suffer indirectly if you choose not to attend. In addition, I reserve the right to consider attendance in instances of borderline grade assignments. Of course, excused absences (sickness, family emergencies, varsity athletic participation) will not be held against you. Such absences should be communicated to mein advance. You are responsible for the content of reading assignments, lectures and handouts, as well as announcements and schedule changes made in class whether or not you are present. If you must miss a class, be sure to check with me or another student to get what you missed. Exams will be given in class on the day scheduled and maynotbe made up. It is very important that you keep up with the assigned reading. Read your book on a daily basis. The material in the course is, by necessity, cumulative.Be warned that if you fall behind, you will not be able to catch up easily.Be especially sure to read the material in the appropriate chapterbeforecoming to class so you will be ready to ask questions. Each section of our text is preceded by exercises that I expect you to think through and answer prior to coming to class.

#### Homework Policies

There will be a number of written and programming assignments given during the semester which will be duein classon the date specified.No late homework assignments will be accepted, unless arrangements have been made with me well in advance.Since it will most likely not be obvious how long an assignment might take, you are well advised to start early.Like other classes at Denison, it is expected that you devote at least 3 hours to these assignments for each hour of class time. Homework assignments must be presented neatly (preferably typed).

#### Academic Integrity

The students and faculty of Denison University and the Department of Mathematics and Computer Science are committed to academic integrity and will not tolerate any violation of this principle. Academic honesty, the cornerstone of teaching and learning, lays the foundation for lifelong integrity. Academic dishonesty is, in most cases, intellectual theft. It includes, but is not limited to, providing or receiving assistance in a manner not authorized by the instructor in the creation of work to be submitted for evaluation. This standard applies to all work ranging from daily homework assignments to major exams. Students must clearly cite any sources consulted - not only for quoted phrases but also for ideas and information that are not common knowledge. Neither ignorance nor carelessness is an acceptable defense in cases of plagiarism. It is the student's responsibility to follow the appropriate format for citations. As is indicated in Denison's Student Handbook, available through my.denison.edu, instructors must refer every act of academic dishonesty to the Associate Provost, and violations may result in failure in the course, suspension, or expulsion. (For further information, consult the student handbook on the web at http://www.denison.edu/student-affairs/handbook/ar03s02s01.html.) In this class, you may discuss homework problems with other students in the class, but written (and typed) workmustbe your own. In other words, you may talk about homework problems with your peers, butwhen it comes time to write your solutions, you are on your own. You may have general conversations about problem strategies, but you must leave these conversations without having written anything down. Keep in mind that it is quite easy for me to tell when two students have been working too closely. You may not get help from students outside the class. If you have questions, come see me and I will be happy to help. You are also quite welcome to send me e-mail or call if you would like to discuss an assignment.

#### WWW Resources

I will maintain a class web page containing reading assignments, homework assignments, answer keys, sample programs, and other useful resources. Refer to this page often for updated information. The class home page can be found at:http://www.denison.edu/~havill/174/

#### Grade Determination

The following relative weights will be used to determine your final grade:

Homework Assignments 30% 4 Mid Term Exams 50% Final Exam 20%

#### Topics

Here is a list of the topics that we will cover during CS 174:Any student who feels he or she may need an accommodation based on the impact of a disability should contact me privately as soon as possible to discuss his or her specific needs. I rely on the Office of Academic Support in 104 Doane to verify the need for reasonable accommodations based on documentation on file in their office.

- Counting (sets, lists, combinations, permutations)
- Cryptography and number theory (modular arithmetic, GCD, RSA)
- Writing proofs
- Induction, recursion, and recurrences
- Probability
- Matrices and Gaussian elimination

Have a great semester! If you need anything, please let me know.

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On 14 Jan 2008, 10:15.