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Syllabus BCA-SEM-II-CC-111

Mathematical Foundation of Computer Science

Gujarat University FY BCA Sem - II New Syllabus (Revised) Effective from June, 2011

Course Introduction:
This course introduces students to become reasonably good at problem solving and algorithm development. Students also enhance their ability to think logically and mathematically.

Objectives:
The objective of this course is to present the foundations of many basic computer related concepts and provide a coherent development to the students for the courses like Fundamentals of Computer Organization, RDBMS, Data Structures, Analysis of Algorithms, Artificial Intelligence, Computer Graphics and others.

No. of Credits: 3
Theory Sessions per week:4
Teaching Hours: 40 hours


UNIT
TOPICS / SUBTOPICS
 TEACHING HOURS
 
 
1. Group Theory
10 Hours
  • Binary Operations
  • Algebraic Structure
  • Group
  • Order of a Group
  • Abelian Group
  • Cyclic Group
  • Order of an element
  • Sub-group
  • Lagrange’s Theorem (with out proof)
  • Permutation group
  • ( Zn, + n ) & ( Zp, *p)
10 Hours
2. Relation and Ordering
10 Hours
  • Introduction to relations
  • Binary relation on a set
  • Total no. of distinct Relation from a set A to B
  • Graph of relations and relation matrix
2 Hours
  • Property of relations
  • Equivalence relations
  • Equivalence classes (sets)
  • Partition of a set
  • Partial ordering and partial ordered set
4 Hours
  • Comparable elements
  • Chain
  • Cover of an element
  • Hasse diagram
  • Least, Greatest, Maximal, Minimal elements
  • Upper and lower bounds of Posets
4 Hours
3. Lattice and Boolean algebra
10 Hours
  • Introduction to lattice
  • Definition of lattice as a Posets
  • Properties of lattice
  • Sub-lattice
2 Hours
  • Complete lattice
  • Bounded lattice
  • Distributive lattice
  • Complemented lattice
2 Hours
  • Definition and important properties of a Boolean algebra
  • Sub-Boolean algebra
2 Hours
  • Isomorphic Boolean algebras (graphically)
  • Atoms and anti-atoms
  • Boolean expressions and their equivalence
  • Min terms and max terms
  • Canonical forms
4 Hours
4. Graph theory
10 Hours
  • Introduction
  • Abstract definition of Graph and Basic Terminology
1 Hours
  • Simple Graph, Multi Graph
  • Degree of a Vertex
  • Types of Graphs
  • Sub-graph and Isomorphic Graphs
2 Hours
  • Path and Reachability
2 Hours
  • Node Base
  • Matrix Representation of Graphs
2 Hours
  • Tree and Basic Terminology
  • Binary and Complete Binary Tree
  • m-ary Tree, Different representations of Tree
3 Hours

Textbook:  
   
Discrete Mathematics  
Publisher: Oxford University Press  
By Swapankumar Chakaborty, Bikas Kanti Sarkar  

Reference Books:
 
Discrete Mathematics
Publisher: Cengage Learning
By D.S. Malik, M.K.Sen

Reference Books:
 
Discrete Mathematics & its Application
Publisher: Tata McGraw Hill
By Kenneth H. Rosen,

Reference Books:
 
Discrete Mathematics
Publisher: Tata McGraw Hill
By J.P. Trembaly, R. Manohar

Reference Books:
 
A Text book of the Discrete Mathematics
Publisher: S. Chand Publication
By Swapan Kumar, Sarkar

Reference Books:
 
Discrete Mathematical Structure (Latest Edition)
Publisher: Prentice Hall of India Pvt. Ltd
By Bernard Kolman, Robert C Busby, Sharon Roass

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