DESCRIPTION OF COURSES

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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