DISCRETE MATHEMATICS
Paper Code:
MAT101
Credits:
3
Contact Hours:
45.00
Max. Marks:
100.00
Unit I:
I
9.00
Counting and Recursion: Permutations and Combinations, Principle of Inclusion & Exclusion, Pigeonhole Principle, Mathematical induction, Recurrence relation, Generating Functions.
Unit II:
II
9.00
Relation & Diagraphs : Product sets & Partitions, Relations & diagraphs, paths in relation & diagraphs, properties of relations, Equivalence relations, computer representation of relations & diagraphs, manipulation of relations.
Unit III:
III
9.00
Ordered Relations & Structures: Partially ordered sets, extermal elements of partially ordered sets, Bounding Elements, Well Ordered Set, Lattices, Principle of Duality, Bounded, Distributed, and Complemented Lattices, Finite Boolean algebra, functions on Boolean algebra.
Unit IV:
IV
9.00
Trees: Introduction, labeled trees, m-ary trees, undirected trees, properties of tree, Spanning tree, Minimal spanning tree, Binary search trees.
Unit V:
V
9.00
Graphs Theory: Basic Terminology, types of graph, paths & cycles, Euler graph & cycles, Hamiltonian graph & cycles, shortest path algorithm ( Djikstras algorithm), Graph Isomorphism, Planar Graph, Graph colorings and chromatic number.
Essential Readings:
- Bernard Kolmann, Robert C. Busby and Sharon Ross, ”Discrete Mathematical Structures”, Third edition, PHI, 1997.
- C.L. Liu, “Elements of Discrete Mathematics”, McGraw Hill,2009
- V. K. Balakrishnan, Introductory discrete mathematics, Prentice Hall, 1996.
- Richard Johnsonbaugh, Discrete Mathematics, 7th Edition, Pearson Education, 2008.
References:
- Theory and problems of Advanced Cal. - Schaum’s outline series New York, 2011.
- H.S.Dhami,Differential Calculus,New Age Int. Ltd.,New Delhi, 2012.
- Akhtar&Ahsan, A text Book of Differential Calculus ,PHI Ltd.New Delhi, 2002.
- G.N.Berman, A Problem book in Mathematical Analysis, Mir Publishers, Moscow, 2004.
Academic Year:
