**DESCRIPTION OF COURSES**

**BI 503/ CA 551 MATHEMATICAL FOUNDATIONS IN COMPUTER APPLICATION (4L+0P) I**

**Objective**

This course is designed to give basic foundations in mathematics that are needed to complement and improve the understanding of courses based on algorithm and problem solving.

**Theory**

UNIT I

Matrix algebra: Basic operations on matrices, Rank and inverse of matrices.

UNIT II

System of linear equations, Characteristic roots and equations, Eigen values and eigen vectors; Basic Differentiation, Integration and Differential Equations; Vector algebra: Double and Triple Product of vectors.

UNIT III

Coordinate geometry: circles and conic sections; Three dimensional geometry: point, straight line, plane and sphere.

UNIT IV

Sets: Set theory, subsets, operations on sets, set cardinality and counting; Functions: Bijective functions, pigeon-hole principle, Boolean functions, permutation functions, Boolean algebra, recursion relations.

UNIT V

Theory: Binary arithmetic, exponentiation, induction, sequences, Fibonacci sequence, big-oh notation, GCD, Euclidean algorithm, partially ordered sets, congruence and equivalence relation, encryption scheme, linear homogenous recurrence relations with constant coefficients.

UNIT VI

Graph Theory: Graphs, trees, LAN, Eulerian cycles, Hamiltonian cycles, graph coloring, graph algorithms; Mathematical Logic: Propositional calculus, proposition, logic connectives and compound statements, conjunction, disjunction, truth tables, duality, tautologies and fallacies; Turing Machine: DFA, NFA.

**Suggested Readings**

- Abertson, M.O. and Hutchinson, J.P. 1988.
*Discrete Mathematics with Algorithms.*John Wiley. - Deo, N. 1984.
*Graph Theory with Application to Engineering and Computer Science.*Prentice Hall of India, New Delhi. - Knuth, D.E. 1968.
*Art of Computer Programming, Vol. I. Fundamental Algorithms.*Addison Wesley. Tremblay, J.P. and Manohar, R.P. 1975.*Discrete Mathematical Structures with Applications to Computer Science.*McGraw Hill.