Course Description :
Introduction to discrete
mathematical structures; Formal logic and predicate calculus; Sets, relations
and functions; Proof techniques; Graphs and trees; Primes, factorization,
greatest common divisor, residues and application to cryptology; Boolean
algebra; Permutations, combinations and partitions; Recurrence relations and
generating functions; Introduction to error-correcting codes; Formal languages
and grammars, finite state machines.
Textbook :
T1.
Kolman,
Busby, Ross and Rehman, Discrete Mathematical Structures for Computer Science,
Pearson Education, 5th Edition, 2003.
Topics :
Week No.
|
Topics
|
Reference to
Text Book
|
1
|
Sets,
Operations on sets, Sequences, Matrices
|
T1-Ch.1
|
2
|
Propositions,
Conditional statements, Induction
|
T1-Ch.2
|
3
|
Pigeonhole
Principle, Recurrence Relations
|
T1-Ch. 3.3,
3.5
|
4
|
Relations
and Digraphs, Paths in Relations, Equivalence Relations
|
T1-Ch. 4.2
- 4.5
|
5
|
Operations
on Relations, Transitive closure
|
T1-Ch. 4.7
– 4.8
|
6
|
Functions,
Function for Computer Science Permutation functions
|
T1-Ch.
5.1,5.2,5.4
|
7
|
Partially
ordered sets, Lattices, Boolean Algebras
|
T1-Ch.6.1,
6.3, 6.4
|
8
|
Review and
Problem Solving
|
|
Syllabus
for Mid-Semester Test: Topics covered in the first eight weeks
|
||
9
|
Graphs,
Euler Paths,
|
T1-Ch 8.1 –
8.3
|
10
|
Trees,
Labeled Trees
|
T1-Ch.7.1,
7.2
|
11
|
Tree
Searching, Undirected Trees
|
T1-Ch. 7.3,
7.4
|
12 – 13
|
Minimal
Spanning Trees
|
T1-Ch. 7.5
|
14
|
Semi
groups, Products and Quotients of Semi groups
|
T1-Ch.9.1,
9.2
|
15
|
Groups,
Products and Quotients of Groups
|
T1-Ch.9.3,
9.4
|
16
|
Review and
Problem Solving
|
|
Syllabus
for Comprehensive Exam (Open Book) All topics given in Plan
|
||
Reference
Books :
R1.
D.S.
Malik and M.K. Sen, Discrete Mathematical Structures: Theory and Applications,
Thomson, 2004.
R2.
Goodaire
& Parmenter : Discrete Mathematics & Graph Theory, Pearson Education,
2000.
R3.
Kenneth
H. Rosen, Discrete Mathematics and its Applications, Tata McGraw Hill, 5th
Ed., 2004.
R4.
C.L.
Liu, Elements of Discrete Mathematics, 2nd Edition, McGraw Hill,
1986.
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