M 401-Mathematics |
Sets and functions : |
Groups, Semigroups and monoids, Cyclic semigroups and submonoids, Subgroups
and Cosets, Congruence relations on Semigroups. Morphisms, Normal subgroups. Structure of cyclic
groups, permutation groups, dihedral groups. Elementary applications in coding theory.
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Rings and Boolean Algebra : |
Rings, Subrings, morphism of rings, ideals and quotient rings. Euclidean
domains. Integral domains and fields. Boolean Algebra - direct product, Morphisms. Boolean sub-algebra.
Boolean Rings. Applications of Boolean algebra in logic circuits and switching functions. |
Recursion and Recurrence Relation : |
Basic idea, Sequence and discrete function. Generating functions
and applications.
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Graph Thoery : |
Graphs, Digraphs, Isomorphism, Walks, Paths, Circuits, Shortest Path Problem, Dijkstra's
Algorithm, Trees, Properties of Trees, Cotrees and Fundamental Circuits, Shortest Spanning Trees -
Kruskal's Algorithm,Prims Algorithm, DFS, BFS, Cut Sets, Fundamental Cut Sets and Cut Vertices,
Planar and Dual Graphs, Metric Representation of Graphs, Networks, Flow Augmenting Path, Ford-
Fulkerson Algorithm for Maximum Flow.
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Text Books: |
1. Liu C. L., “Introduction to combinatorial mathematics”, McGraw Hill, 1968.
2 Mott J. L., Kandel A. and Baker T. P., “Discrete mathematics for Computer Scientists and
Mathematicians”, PH, 1986.
3 Rosen—Discrete Mathematics, 2/e,TMH
4 S.K. Mapa—Higher Algebra (Abstract & Modern)
5 Robert J. McElice , Robert B. Ash & Carol Ash, “Introduction to discrete
Mathematics”, Tata McGraw Hill
6 Deo N., “Graph Theory with Applications to Engineering and Computer Science”, PHI, 1980
7 Tremblay and Manohar, “Discrete mathematical structures with applications to computer
science”, McGraw Hill, 1975
8 Kolamn, Busby and Ross, “Discrete mathematical structures”, 3/ed, PHI, 1996.
9 Fraleigh J. B., “A first course in abstract algebra Narosa”, 1990
10 Smullyan R. M., “First Order Logic Springer Verlag”, 1968
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Reference: |
1.Lipschutz—2000 Solved Problems in Discrete Mathematics, TMH
2.Balakrishnan—Graph Theory (Schaum),MH
3.Hararay—Graph Theory
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