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Department of Computer Science College of Engineering University of the Philippines Diliman, Quezon City


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CS 30 Discrete Mathematics for Computer Science 3 units First Semester, AY 2012-2013 Nestine Hope S. Hernandez COURSE DESCRIPTION

Mathematical logic; Methods of proof. Mathematical induction and recursion. Permutations and Combinations; Counting principles. Graphs and Trees. Applications to computer science problems. CLASS SCHEDULE (THX) Tuesdays and Thursdays, 2:30 PM -4:00 PM, CLR1 (THY) Tuesdays and Thursdays, 4:00 PM -5:30 PM, CLR1 COURSE OUTLINE 1. Mathematical Logic • Equivalence and Implication • Predicates and Quantifiers • Rules of Inference • Methods of Proof • Mathematical Induction and Recursion First Exam 2. Combinatorics and Computing • Basics of Counting – Rules of Sum and Product – Principles of Inclusion and Exclusion – Pigeonhole Principle • Permutations and Combinations – Binomial Coefficients – Generalized Permutation and Combination – Generating Permutation and Combination 1

– Stirling Numbers – Catalan Numbers – Arrangements with Forbidden Positions Second Exam 3. Graphs and Trees • Graphs – – – – – – – –

Basic Concepts in Graph Theory Representation of Graphs Graph Isomorphisms Paths, Cycles and Connectivity Eulerian and Hamiltonian Graphs Matching Theory Coloring and Planarity Applications of Graphs in Computer Science

• Trees – Introduction to Trees – Minimum Spanning Trees Third Exam

GRADING SYSTEM Requirements: Long Exams Quiz/Homework

75% 25% GENERAL AVERAGE 93 - 100 88 - below 93 85 - below 88 82 - below 85 78 - below 82 74 - below 78 70 - below 74 65 - below 70 60 - below 65 55 - below 60 below 60

FINAL GRADE 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 4.00 5.00


EXAMS. Submit bluebooks a week before the date of examination. No make-up exam will be given unless with a valid excuse. Two missed exams would have one exam be graded zero, plus he/she will be obliged to take the final exam regardless if his/her grade is above the exemption cutoff. Three missed exams would automatically incur a grade of 5.00. Complaints regarding examination results will be entertained only within a period of one week after the release of the examination papers. Use black or blue pen when taking examinations. Otherwise, no complaints regarding the examination results will be accepted. ATTENDANCE. Students who exceed the maximum allowed absences (6) are advised to drop assuming that the deadline for dropping has not yet lapsed. Otherwise, he/she will be given a grade of 5.0. FINAL EXAM. In the event that the student’s pre-final grade falls below 65%, the student will be obliged to take the final exam. The final grade would then be computed as follows: Final Grade = ( 32 * Pre-final Grade) + ( 13 * Final Exam Score) Exempted students may opt to take the final examination with the chance of either pulling their grades up or down. CHEATING. Cheating in any form will be subjected to proper disciplinary action and will merit a final grade of 5.0. DURING CLASS HOURS. No smoking. No eating. No sleeping. Turn off your cellular phones or put them in silent mode.

REFERENCES 1. Kenneth Rosen, Discrete Mathematics and Applications, Sixth Edition, 2007 2. Kenneth Rosen, Applications of Discrete Mathematics, 2007 3. T Veerarajan, Discrete mathematics with Graph Theory and Combinatorics, 2007 4. David Hunter, Essentials of Discrete Mathematics, 2009 5. Kevin Ferland, Discrete Mathematics: an introduction to proofs and combinatorics, 2009 6. Cliff Stein, Robert Drysdale and Kenneth Brogart, Discrete Mathematics for Computer Scientists, 2010 7. Susanna Epp, Discrete Mathematics with Applications, Fourth Edition, 2011 8. Gareth Janacek, Mark Lemmon Close, Mathematics for Computer Scientists, 2011 Other references on discrete mathematics.


[Hernandez 1213A] Syllabus30 a12 13