MATHEMATICS FOR COMPUTER SCIENCE ---- SEM I

Mathematics for Computer Science

UNIT I

Mathematical Logic: Statement Calculus – Connectives – normal forms – Predicate Calculus – Theory of inference for statement Calculus – Predicate Calculus including theory of inference.

UNIT II

Set Theory: Basic concepts of set theory – relations and ordering – functions –recursion.

UNIT III

Algebraic Structures: Semigroups – monoids- grammars and languages – groups and subgroups – Polish experiments and their compilation.

UNIT IV

Roots of Equations: Graphical Method – Bisection Method – False- Position Method – Fixed-Point Iteration – Newton-Raphson Method – Secant Method – Roots of Polynomials: Conventional Methods – Muller’s Method – Bairstow’s Method. Algebraic Equations: Gauss Elimination –Gauss-Jordan – LU Decomposition – Matrix Inverse –Gauss-Seidel.

UNIT V

Numerical Differentiation - Integration: Trapezoidal Rule – Simpson’s Rule – Romberg Integration – Differential equations: Taylor’s method – Euler’s method –Runge-Kutta 2nd and 4th order methods – Predictor – corrector methods.

Text Books

(i) J.P. Tremblay and R. Manohar, 1975, Discrete Mathematical Structures with Applications to Computer Science, Tata McGraw-Hill, New Delhi (ii) S.S. Sastri, 1977, Introductory Methods of Numerical Analysis, Prentice Hall India, New Delhi

Reference Books

(i) J. Truss, 1999, Discrete Mathematics for Computer Scientists, 2nd Edn., Addison Wesley, Boston. (ii) S. C. Chapra and R. P.Canale, 2002, Numerical Methods for Engineers, Fourth Edition, McGraw Hill International Edition. (iii) Kolman, Busby and Ross, 2005, Discrete mathematical structures, 5th edition, PHI, New Delhi. (iv) P.Niyogi, 2003, Numerical Analysis and Algorithms, Tata McGraw Hill, New Delhi.