# Virtual University of Pakistan

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## MTH202 : Discrete Mathematics

### Course Overview

#### Course Synopsis

The course uses the patterns found in Sets, Relations and Functions. Mathematical ideas and concepts relevant to Logic, Combinatorics and Probability will be studied in this course. Matrices will be used to solve problems. The course also include: Mathematical Induction, Algorithm and Graph theory.

#### Course Learning Outcomes

At the end of the course, you should be able to:

• Express statements with the precision of formal logic
• Analyze arguments to test their validity
• Apply the basic properties and operations related to sets
• Apply to sets the basic properties and operations related to relations and functions
• Define terms recursively
• To prove a given statement using mathematical induction
• To prove statements using direct and indirect methods
• To compute probability of simple and conditional events
• Identify and use formulae of Combinatorics in different problems
• Illustrate the basic definitions of graph theory and properties of graphs

#### Course Calendar

 Topic Lecture Resource Page Logic 1 Handouts 1-5 Truth Tables 2 Handouts 6-8 Laws of Logic 3 Handouts 9-14 Bi-Conditional 4 Handouts 15-18 Argument 5 Handouts 19-20 Application of Logic 6 Handouts 21-27 Set Theory 7 Handouts 28-31 Venn Diagram 8 Handouts 32-43 Set Identities 9 Handouts 44-50 Applications of Venn Diagram 10 Handouts 51-58 Relations 11 Handouts 59-65 Types of Relations 12 Handouts 66-75 ASSIGNMENT # 1 Matrix Representation of Relations 13 Handouts 76-81 Inverse of Relations 14 Handouts 82-86 Functions 15 Handouts 87-96 Types of Functions 16 Handouts 97-107 Inverse Function 17 Handouts 108-118 Composition of Functions 18 Handouts 119-127 Quiz # 1 Sequence 19 Handouts 128-133 Series 20 Handouts 134-141 Recursion I 21 Handouts 142-146 Recursion II 22 Handouts 147-150 Mid term Examamination Mathematical Induction 23 Handouts 151-159 Mathematical Induction for Divisibility 24 Handouts 160-166 Methods of Proof 25 Handouts 167-172 Proof by Contradiction 26 Handouts 173-179 Algorithm 27 Handouts 180-183 Division Algorithm 28 Handouts 184-187 Combinatorics 29 Handouts 188-194 Permutations 30 Handouts 195-201 Combinations 31 Handouts 202-206 K-Combinations 32 Handouts 207-212 Tree Diagram 33 Handouts 213-219 Inclusion-Exclusion Principle 34 Handouts 220-224 Probability 35 Handouts 225-231 ASSIGNMENT # 2 Laws of Probability 36 Handouts 231-238 Conditional Probability 37 Handouts 239-244 Random Variable 38 Handouts 245-252 Introduction to Graphs 39 Handouts 253-260 Paths and Circuits 40 Handouts 261-266 Quiz # 2 Matrix Representation of Graphs 41 Handouts 267-273 Isomorphism of Graphs 42 Handouts 274-281 Planar Graphs 43 Handouts 282-288 Trees 44 Handouts 289-294 Spanning Trees 45 Handouts 295-304 Final Examination Any kind of change in the schedule during semester will be announced on VULMS