Cluster University Generic Elective-Prof Sem 2 Mathematics in Computing(GE) Syllabus
 

Cluster University Generic Elective-Prof Sem 2 Mathematics in Computing(GE) Syllabus

Course Code (BCA-CR2103) Semester-II
Course Title: Mathematics in Computing
Total Credits: 06
Maximum Marks: 90
External (Theory): 60
Internal Assessment:30

Unit-I
Sets & Relations: Sets, representation of sets, types of sets, subset, power set, number of
subsets of a finite set, universal set, operation on sets, union, intersection, difference,
complement of a set, algebra of sets, De Morgan's law.
Cartesian product of sets, relation, types of relations, domain and range of a relation,
Equivalence relation, partial ordering relation.

Unit-II
Function: Definition and types of function, injective, surjective and bijective functions.
Algebraic systems: Binary operations, groups & Semi groups, Abelian groups, examples,
(Z,+),(Q, +),(Q*,x),(R, +), (R*,x), set of cube roots of unity/ 4 fourth roots of unity/ n nth
roots of unity form groups under multiplication, Group of integers modulo n, general
properties of groups.

Unit-III
Mathematical logic: Statement, conjunction, disjunction, negation, Conditional and Biconditional
statements, Tautology, Contradiction, Validity of argument, Logical equivalence
(truth tables) and principle of duality, Boolean Algebra, Basic theorems, applications of
Boolean algebra to switching circuits.

Unit-VI
Graph Theory: Basic definitions (Graph, types, vertex, edge, incidence, degree). Walks, paths
and circuits. Connected graphs, disconnected graphs & components, A simple graph with n
vertices and k components cannot have more than (n-k)(n-k+1) edges.

Regular graph, Complete graph, Isomorphism, Konigsberg bride problem, Eular graph, A
connected graph is Eularian if and only if its all vertices are of even degree, traveling-salesman
problem, Hamiltonian paths & circuits. Graph colouring, five colour theorem.

Text Books Recommended
(1) Discrete Mathematics and its applications by Kenneth H. Rosen, Mcgraw Hill Education.
(2) Introductory discrete mathematics by V. Balakrishnan, Dover Books on Computer
Science.