course CPCS-222 (Data Structure)

Course File - Course Specifications

Faculty of Computing and Information Technology

Spring 2020

Department of Computer Science

Printed as of: Sunday March 29 20201

The objective of this course is to study the logical and algebraic relationships between discrete objects. This course cultivates clear thinking and creative problem solving by developing students’ mathematical maturity in several core areas: logic and proofs, sets, functions, relations, and counting techniques.

Introduction The Foundations: Logic & Proofs Basic Structures: Sets, Functions, Sequences, and Sums Relations Counting Mathematical Induction, Strong Induction, and Well- Ordering

1 5 3

2 2 2

Catalog Description

Meet 50 minutes 3 times/week or 80 minutes 2 times/week

Lab/Tutorial 90 minutes 1 times/week

Class Schedule

9780073383095

Textbook

0073383090

Kenneth Rosen, , "Discrete Mathematics and Its Applications", McGraw-Hill Education; 7 edition (2011-06-14)

ISBN-13 ISBN-10

Discrete Structures (I)CPCS-222

College Required Prerequisite: None

4 5 7 8 9 11 11 12 14 15 15 16

Homework Assignments 1 Quiz 1 Homework Assignments 2 Exam 1 Homework Assignments 3 Homework Assignments 4 Quiz 2 Exam 2 Homework Assignments 5 Graded Lab Work Quiz 3 Comprehensive Final Exam

Assessment 3 3 3 20 3 3 3 20 3 5 4 30

Week Grade %

Grade Distribution

Relationship to Student Outcomes

x

Find the truth value of propositions and compound propositions using truth tables. (a) Prove Propositional Equivalences. (a) Identify the truth value of quantifiers. (a) Negate quantified expressions, nested or otherwise. (a) Identify the validity of arguments in Propositional logic and use Rules of Inference to build arguments. (a) Use direct proof, proof by contraposition, proof by contradiction, exhaustive proof and proof by cases to prove the validity of theorems. (a) Use set notation to express sets and represent sets graphically using Venn diagrams. (a) Calculate the union, intersection, complement, cardinality, power set, and Cartisian product of sets. (a) Determine the equality of sets using membership tables and Set Identities. (a) Determine the domain, co-domain, range, type, inverse, and composition of functions. (a) List and produce the terms of a sequence and find its formulae. (a) Express the sum of a sequence and compute its value. (a) Represent a relation using digraphs and matrices. (a) Analyze the properties and combinations of relations. (a) Find the inverse, complement, composition, and closure of a relation. (a) Apply the basic counting principles, the pigeonhole principle, permutations and combinations to solve counting problems. (a) Use mathematical induction, strong induction, and the well-ordering property to prove the validity of statements. (a)

Course Learning Outcomes (CLO) By completion of the course the students should be able to

a b c d e f g h i j k l m n

3 ( Theory: 3, Lab: 0, Practical: 1)

Last Articulated October 23, 2017

Dr. Vijey Thayananthan, Associate Professor

Dr. Amal Almansour, Assistant Professor

Coordinator(s)

1.

2. 3. 4. 5.

6.

7.

8.

9.

10.

11.

12. 13. 14. 15.

16.

17.

CPCS-222 Syllabus

Classification:

Credit:

Topics Coverage Durations WeeksTopics