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

COURSE NO. COURSE TITLE COURSE CREDIT SEMESTER INSTRUCTOR EMAIL ADDRESS

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CS 30 Discrete Mathematics for Computer Science 3 units First Semester, AY 2012-2013 Nestine Hope S. Hernandez nshernandez@dcs.upd.edu.ph 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

CLASS POLICIES 2