Topic outline

• Discrete Mathematics : The journey begins here.
  

  Discrete Mathematics : The journey begins here.

  
  

  • Announcements Forum
  • Instructor's Information

    
    

    Name: Mohammad Monirul ISlam
    Designation: Senior Lecturer
    email: monirul@diu.edu.bd
    Office address: Room#316, AB-4 Building, DSC

  • Welcome to Discrete Mathematics course

    Are you wondering about what sorts of mathematics you need to learn for Computer Science? Yeah, then Discrete Mathematics is going to be an answer though this is just an introductory course. In this course, you will get an opportunity to learn about Propositional Logic, Logical Equivalence, Propositional Function, Predicates and Quantifiers, Nested Quantifiers, Rules of Inferences, Set theories, and operations, Functions, Mathematical Induction, Relations, and its properties and closures, and most essentially Graphs and Trees. These are some of the essential ingredients in the toolkit of every computer scientist.

    You are welcome to browse the page.

    Hope we will have a memorable journey together.
    

    
    

  • Course Rationale: 

    Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in all branches of computer science, such as computer algorithms, programming languages, cryptography, outomated theorem proving, and software development. It helps improving reasoning power and problem-solving skills. Therefore, it can be considered as the backbone of computer science.

  • Course Objective

    • The goal of this course is to introduce students to ideas and techniques from discrete mathematics that are widely used in science and engineering for thinking logically and mathematically and apply these techniques in solving problems. 
    • To achieve this goal, students will learn logic and proof, sets, functions, mathematical reasoning as well as key topics involving relations, graphs, and trees.
      

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  • Course Outcome(CO's)

    After completing this course satisfactorily, a student will:

     

    CO1	Be able to comprehend formal logical arguments as well as to construct logical proofs with the ability to verify them
    CO2	Demonstrate skills in expressing mathematical properties formally via the formal language of propositional logic and predicate logic
    CO3	Gain experience in using various techniques of mathematical induction to prove simple mathematical properties of a variety of discrete structures
    CO4	Be able to specify and manipulate basic mathematical objects such as sets, functions, and relations and will also be able to verify simple mathematical properties that these objects possess
    CO5	Demonstrate knowledge on some basic properties and types of graphs and trees and will also, be able to apply it to solve fundamental engineering problems

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  • Reference Textbooks File

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    Discrete Mathematics and Its Applications, K.H. Rosen
    

  • Course Outline File

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• Week 1 : (Propositional Logic)
  

  Week 1 : (Propositional Logic)

  Topics of Discussion:

  • Propositional logic.
  • Translation of natural language to symbolic form.
  • Simple and Compound proposition with propositional logic.

  Expected Learning Outcomes:

  • Understand the basics of Propositional Logic.
    
  • Abel to translate natural language into Propositional Logic
    
  • Apply different connectives to represent compound Propositions.
  • Able to construct truth table for Simple and compound propositions.

  Resources of Learning:
  

  • Lesson 1: Introducing Class-- [Discussion in order to make students familiar about the outcome of the  course and formal introduction with Students and teacher]
  • Lesson 2: Propositional Logic [PPT Lecture Slide]
• Week 2 : (Logical Equivalence)
  

  Week 2 : (Logical Equivalence)

  Topics of Discussion:

  • Basics of Logical equivalence.
  • Proof of Logical equivalence.
  • Proof propositional equivalence using truth table and series of logic.

  Expected Learning Outcomes:

  • Understand the basics of logical equivalences.
  • Proof whether two given propositions are equivalent or not
  • Apply the knowledge to prove whether to given propositions are equivalent or not by using Truth tables
  • Apply the knowledge to prove whether to given propositions are equivalent or not by developing a series of logical equivalences

  
  

  Resources of Learning:
  

  • Lesson 3: Logical Equivalences
  • Lesson 4: Practices on Logical Equivalences
• Week 3 : (Predicates and Quantifiers)
  

  Week 3 : (Predicates and Quantifiers)

  Topics of Discussion:

  • Propositional function.
  • Discussion on Universal and Existential quantifiers.
  • Conversion of natural language into propositional function and vice-versa.

  Expected Learning Outcomes:

  • Understand the basics of the propositional function
  • Understand about Universal and Existential quantifiers
  • Convert natural languages into propositional function 
  • Implement propositional functions using quantifiers

  Resources of Learning:
  

  • Lesson 5: Predicates and Quantifiers
  • Lesson 6: Practices on Predicates and Quantifiers

  
  
• Quiz
  

  Quiz
• Week 4 : (Negation and Nested Quantifiers))
  

  Week 4 : (Negation and Nested Quantifiers))

  Topics of Discussion:

  • Discuss on negation and nested quantifiers
  • Discuss on De Morgan's law on quantifiers.
  • Nested Quantifiers to represent complex mathematical functions

  Expected Learning Outcomes:

  • Understand how to negate quantifiers
  • Learn about Nested quantifiers
  • Apply De Morgan's law on quantifiers
  • Apply Nested Quantifiers to represent complex mathematical functions

  Resources of Learning:

  • Lesson 7: Negation of Quantifiers and Nested quantifiers
  • Lesson 8: Practices of Negation of Quantifiers and Nested Quantifiers
• Week 5 : (Rules of Inference)
  

  Week 5 : (Rules of Inference)

  Topics of Discussion:

  • Discuss on Argument, Premises, and validity of the argument.
  • knowledge on different rules of inferences .
  • Way of rules of inferences  to prove the validity of arguments.

  Expected Learning Outcomes:

  • Able to demonstrate knowledge on Argument, Premises and validity of the argument.
  • Able to demonstrate knowledge on different rules of inferences .
  • Able to apply rules of inferences  to prove validity of arguments.

  Resources of Learning:
  

  • Lesson 21: Rules of inference
  • Lesson 22: ------?
• Week 6 : (Set, Set Operations and Function)
  

  Week 6 : (Set, Set Operations and Function)

  Topics of Discussion:

  • Concept of Set theory.
  • Discuss different types of set operations.
  • Different kinds of set operations using Ven diagram

  Expected Learning Outcomes:

  • Understand the concepts of Sets.
  • Represent sets using set builders.
  • Understand about cardinality, power set and cartesian product of sets
  • Understand different kinds of set operations.
  • Apply different kinds of operations using Ven diagram.

  Resources of Learning:

  • Lesson 9: Sets
  • Lesson 10: Set operations
• Week 7 : (Mathematical Induction)
  

  Week 7 : (Mathematical Induction)

  Topics of Discussion:

  • Discuss the concept of mathematical induction.
  • How to derive formula from a given mathematical sequence.
  • Prove derived formula using Mathematical Induction.

  Expected Learning Outcomes:

  • Demonstrate the conception of Mathematical Induction .
  • Able to derive formula from a given mathematical sequence.
  • Able to prove derived formula using Mathematical Induction .

  Resources of Learning:
  

  • Lesson 19: Mathematical Induction
  • Lesson 20: --------?
• Week 6 : (Function)
  

  Week 6 : (Function)

  Topics of Discussion:

  • Define and concept of function.
  • Discuss different types of functions.
  • Composite functions.

  Expected Learning Outcomes:

  • Understand the concept of Functions.
  • Identify different types of Functions
  • Derive composite Functions

  Resources of Learning:

  • Lesson 11: Function
  • Lesson 12: In this lesson, a discussion on relations and its closure operations will be continued.

  
  
• Week 7 : - [Midterm Exam]
  

  Week 7 : - [Midterm Exam]

  
  
• Week 8 : (Graph)
  

  Week 8 : (Graph)

  Topics of Discussion:

  • Basic concept of Graph.
  • Converting natural phenomena into graphs.
  • Types of basic graphs.
  • Handshaking Theorem.

  Expected Learning Outcomes:

  • Able to understand the basics of Graphs.
  • Able to represent natural phenomena into graphs
  • Able to apply Handshaking Theorem
  • Able to classify Graphs
  • Able to identify Bipartite Graphs using coloring algorithm

  Resources of Learning:

  
  

  • Lesson 13: Graph URL

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  • Lesson 13: Graph terminologies URL

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  • Lesson 13: Bipartite graph URL

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• Assignment
  

  Assignment
• Week 9 : (Representing Graphs, Isomorphism and Euler circuit)
  

  Week 9 : (Representing Graphs, Isomorphism and Euler circuit)

  Topics of Discussion:

  • Graph representation in various ways.
  • Basic terminologies of the graph.
  • Discuss the way to identify a graph isomorphism or not.
  • How to find the shortest path using Dijkstra algorithm. 

  Expected Learning Outcomes:

  • Able to represent Graphs using matrix.
  • Able to determine path lengths from any given vertex to any other vertex.
  • Able to identify isomorphic graphs.
  • Able to apply Dijkstra algorithm to find shortest path.

  Resources of Learning:
• Shortest Path and Tree
  

  Shortest Path and Tree

  • Shortest path URL

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  • Tree URL

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  • Spanning Tree URL

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  • Minimum Spanning Tree URL

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• Week 10 : (Relation, it's properties and closures)
  

  Week 10 : (Relation, it's properties and closures)

  Topics of Discussion:

  • Discuss the basic properties of relation.
  • Discuss the closure of relation. 
  • Differentiate graph and tree. 
  • Concept of Minimum spanning tree. 
  • How to derive minimum spanning tree  from weighted graphs

  Expected Learning Outcomes:

  • Able to differentiate between Graphs and Trees
  • Able to demonstrate basic concepts of Tree
  • Able to apply algorithms to derive minimum spanning tree  from weighted graphs
  • Able to demonstrate knowledge about relation
  • Able to identify properties of the relation
  • Able to identify closures of relations

  Resources of Learning:
  

  • Lesson 17: Graph Representation
  • Lesson 18: ----[Relation/Euler path]

  
  
• Week 13
  

  Week 13

  
  
• Week 14:- [Final Exam]
  

  Week 14:- [Final Exam]

  
  
• Topic 18
  

  Topic 18
• Topic 19
  

  Topic 19
• Topic 20
  

  Topic 20