DISCRETE MATHEMATICS AND NUMBER THEORY
Graphs Theory: Basic Terminology, Types of graph, paths and cycles, Euler graph and cycle, Hamiltonian graph and cycle, Shortest path algorithm (Djikstras algorithm), Graph isomorphism, Planar graph, Graph colorings and chromatic number.
Relation and Diagraphs: Product sets and partitions, Paths in relation and diagraphs, Properties of relations, Equivalence relations. Trees: Introduction, m-ary trees, Properties of trees, Spanning trees, Minimal spanning trees, Binary search trees.
Pigeonhole principle, Recurrence relation, Generating functions. Ordered relations and Structures: Partially ordered sets, Extremal elements of partially ordered sets.
Elementary divisibility properties, Division algorithm, Greatest common divisor, Least common multiplier, Euclid’s lemma.
Bezout’s lemma, Prime number, Eucledian Algorithm, Fundamental theorem of arithmetic, Congruence, Chinese remainder theorem.
- Bernard Kolmann, Robert C. Busby and Sharon Ross, Discrete Mathematical Structures, PHI Delhi, 1997.
- C.L. Liu, Elements of Discrete Mathematics, McGraw Hill, 2009.
- V. K. Balakrishnan, Introductory Discrete Mathematics, Prentice Hall, 1996.
- David M. Burton, Elementary Number Theory, McGraw Hill, 2007.
- S.K. Pundir and R.Pundir, Theory of Numbers, Pragati Prakashan, Meerut, 2012.
- Norman Biggs, Discrete Mathematics, Oxford University Press UK, 2003.
- Kenneth H. Rosen, Discrete Mathematics and Its Applications, McGraw Hill Pub. Co. Ltd., New Delhi, 2003.
- Richard Johnson Baugh, Discrete Mathematics, Pearson Education Asia, New Delhi, 2008.
- J.P. Trembly, R. Manohar, Discrete Mathematical Structures with Applications to Computer Science, McGraw Hill Pub. Co. Ltd, New Delhi, 2003.
- Ralph. P. Grimaldi, Discrete and Combinatorial Mathematics: An Applied Introduction, Pearson Education Asia, Delhi, 2002.
