CMPE 016 - Applied Discrete Mathematics, Fall 2006.

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News	12/14/06 The final grades have been uploaded. You can pick up your graded finals in front of CCRG (E2 315) If you have a very strong argument to change your grade, please send me email to set an appointment.

Class Description	This course provides introduction to applications of discrete mathematical systems. It requires minimal mathematical sophistication. The core topics covered in this course are: Logic: propositions, proofs using propositional equivalences. Predicates, quantifiers, sets and set operations: union, intersection, difference Functions and relations, sequences and summations. Modular arithmetic, mathematical induction. Mathematical induction, recursive definitions. Counting arguments, pigeonhole principle, permutations and combinations. Discrete probability, generalized permutations and combination Introduction to solving recurrence relations, n-ary relations. Boolean algebra. Optional topics include trees and incudction on trees, generating functions, inclusion-exclusion principle, and applications of the binomial coefficient and factorials. Examples are drawn from computer science and computer engineering. Prerequisites: Eligibility to enroll in Mathematics 19A (completion of Mathematics 2B or 3 or Mathematics Placement Exam score of 40 or higher) or completion of Mathematics 19A or 11A.

Grading	The following grading system takes into account class participation, exams, homeworks, and reqwards extra effort inside and outside the classroom: Homeworks (10%): Weekly homeworks and homework grading Up to seven Quizes (15% total): Weekly quizes lasting a short time (e.g., 3 questions, 15 min) Midterm 1 (20%) closed book Midterm 2 (25%) closed book and open book Final Exam (30%) closed book and open book Quizes are closed book, closed notes. Midterm 1 is closed book, closed notes. Midterm 2 and the final consist of a closed-book part and an open-book part. There are no curves in this class. Your effort determines your grade. The grading scale for the class will be approximately: A+ (96%-100%), A (92%-96%), A- (88%-92%), B+ (84%-88%), B (80%-84%), B- (77%-80%), C+ (74%-77%), C (70%-74%), D (60%-70%), F (below 60%). I will use my discretion to deal with borderline cases. As we discuss in class, students who demonstrate very good to excellent performance up to the second midterm can exempt the final with extra effort.

Student Responsibilities	Students enrolled in this class are agreeing to the following: Work turned in for quizes, exams, and extra-point projects must be the result of individual effort. Homeworks can be solved in teams, but each student is responsible for submitting a homework report. Attendance to my lectures is not mandatory. By popular demand, attendance to at least one of the discusion sessions is not mandatory. Each student can attend as many of these sections as she or he wants. If any work claimed by a student to be his/her own is found to be shared with other students, that will be considered a violation of academic integrity and will be handled accordingly. Students are responsible for grading fairly based on the instructions given by the TAs. Students are also responsible for checking the class web page frequently for updates, schedule changes, etc.

Academic Integrity	In this course we encourage students to get involved in discussions about the class material in- and outside class. However, all work submitted for the class is to be understood by each student. It is fine to solve homework problems as a group, provided that each group member understands the answers she/he submits. Students should be familiar with the University Academic Intergity Policies, violations of which will not be tolerated. Students who violate University standards of academic integrity are subject to disciplinary sanctions, including failure in the course accompanied by a report which will be part of the student's file, and suspension from the University. If you have questions or doubts about the UCSC Academic Integrity policies, please see the instructor or the TA.

Textbook	Our textbook is: K.H. Rosen, Discrete Mathematics and Its Applications, Sixth Edition, McGraw-Hill, 2007. ISBN-13 978-0-07-288008-3 We will follow the textbook very closely. We use the Sixth Edition, because it puts more emphasis on proofs.

Syllabus	The following list maps the topics that we will cover in class to the textbook sections and class dates. Remember this is a tentative schedule and will most likely be updated over the course of the quarter. Check this page often. Sept 22: Introduction Sept 25: Sec. 1.1 Sept 27: Sec. 1.2 Sept 29: Sec. 1.2 Oct 2: Sec. 1.2, 11.2, 11.3 Oct 4: Sec. 11.3, 11.4 Oct 6: Sec. 1.3 Oct 9: Sec. 1.4 Oct 11: Q1 40 min Oct 13: Sec. 1.5 Oct 16: Sec. 1.6, 2.1 Oct 18: Sec. 1.6 Oct 20: Sec. 1.7, 2.1, 2.2 Oct 23: Q2 15 min and then Sec. 11.1, 2.2 Oct 25: Sec. 2.3, 2.4 Oct 27: Sec. 2.3, 2.4 Oct 30: MIDTERM 1 1 hour Nov 1: Sec. 3.1, Appendix A3 Nov 3: Sec 3.4, 4.1 Nov 6: Sec. 4.1 Nov 8: Sec. 4.1 Nov 10: Holiday Nov 13: Q3 15 min and then Sec. 4.2, 4.3 Nov 15: Sec. 5.1 Nov 17: Sec. 5.2, 5.3 Nov 20: 5.4 Nov 22: Sec 6.1, 6.2 Nov 24: Holiday Nov 27: MIDTERM 2 1 hour Nov 29: Sec. 5.5, 6.2, 6.3 Dec 1: Review. Sec. 7.1, 7.2 are cancelled. Dec 7: FINAL (12:00-3:00 pm)

Lecture Notes	Sample questions for quizes You are responsible for going over all class material, even if you do not attend class (you can always ask classmates what was covered). Any notes complementing the textbook would be posted here.