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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

Truth Tables2Handouts6-8
Laws of Logic3Handouts9-14
Application of Logic6Handouts21-27
Set Theory7Handouts28-31
Venn Diagram8Handouts32-43
Set Identities9Handouts44-50
Applications of Venn Diagram10Handouts51-58
Assignment # 1 (Lecture 1 to Lecture 8)
Types of Relations12Handouts66-75
Matrix Representation of Relations13Handouts76-81
Inverse of Relations14Handouts82-86
GDB # 1 (From Lec 9 to Lec 14)
Types of Functions16Handouts97-107
Inverse Function17Handouts108-118
Composition of Functions18Handouts119-127
Quiz # 1 (From Lec 09 to Lec 20
Recursion I21Handouts142-146
Recursion II22Handouts147-150
Mid term Examamination
Mathematical Induction23Handouts151-159
Mathematical Induction for Divisibility24Handouts160-166
Methods of Proof25Handouts167-172
Proof by Contradiction26Handouts173-179
Division Algorithm28Handouts184-187
Quiz # 3 (Lecture 19 to Lecture 26)
Tree Diagram33Handouts213-219
Inclusion-Exclusion Principle34Handouts220-224
Quiz # 4 (Lecture 27 to Lecture 34)
Laws of Probability36Handouts231-238
Conditional Probability37Handouts239-244
Random Variable38Handouts245-252
Introduction to Graphs39Handouts253-260
Paths and Circuits40Handouts261-266
GDB # 2(Lecture 39to Lecture 43)
Matrix Representation of Graphs41Handouts267-273
Isomorphism of Graphs42Handouts274-281
Planar Graphs43Handouts282-288
Spanning Trees45Handouts295-304
Final Examination
Any kind of change in the schedule during semester will be announced on VULMS
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