To introduce students to the theory of functions of a complex variable and to explore techniques for integration in the complex plane.
Functions of a complex variable, geometry, conformal mappings; Cauchy Riemann equations, analytic functions, harmonic conjugate; Line integrals, complex integration; Cauchy’s Integral Theorem, Cauchy’s Integral Formula, applications; Taylor and Laurent expansion; Theory of residues, applications, evaluation of real integrals.
PALIOURAS, J.D., Complex Variables for Scientists and Engineers, (Macmillan), 1975.
GROSSMAN, S.I., Multivariable Calculus, Linear Algebra and Differential Equations, (Harcourt, Brace, Jovanovich), 1986.
KREYSZIG, E., Advanced Engineering Mathematics, (Wiley), 1988.
LEVINSON, N., REDHEFFER, R., Complex Variables, (Holden Day), 1970.
MARSDEN, J.E., Basic Complex Analysis, (Freeman), 1973.
To explore the capabilities of computers in mathematical problem solving and to enable students to develop expertise in such applications.
Computer logic; computer arithmetic, logic elements. Boolean algebra; application to switching circuits.
Number representation; number bases, machine representable numbers, floating point arithmetic, error analysis.
Combinatorics, graph theory, applications.
Non-linear algebraic equations; iteration, Newton Raphson method, secant method. Numerical integration.
Polynomial interpolation; Lagrange interpolation, errors in interpolation, numerical differentiation, spline functions.
Systems of linear equations; Gaussian elimination, band systems.
Ordinary differential equations; Taylor series and Runge-Kutta methods, stability. Mathematical software, use of packages.
CHENEY, W., KINCAID, D., Numerical Mathematics and Computing, (Brooks Cole), 1980.
GARNIER, R., TAYLOR, J., Discrete Mathematics for New Technology, (Adam Hilger), 1992.
MORRIS, J.L., Computational Methods in Elementary Numerical Methods, (Wiley), 1983.
QUINNEY, D., An Introduction to the Numerical Solution of Differential Equations, (Wiley), 1987.
WAIT, R., Numerical Solution of Algebraic Equations, (Wiley), 1979.
To provide an introduction to the theory of probability and to statistical techniques in a manner which will foster understanding of concepts and development of expertise in their applications.
Description of sample data; graphical representation, measures of location and dispersion, mean and standard deviation. Probability theory; applications.
Random variables; discrete and continuous, expectation and variance. Probability distributions; binomial, poisson and normal distributions. Sampling theory; random sampling, sampling distributions.
Estimation; point and interval estimates, Student's t distribution. Hypothesis testing; error types.
Correlation and regression; least squares, errors. Testing methods; chi square test, F test, non parametric tests.
HOEL, P., Elementary Statistics, (Wiley), 1976.
FRANK, H., Introduction to Probability and Statistics, (Wiley), 1974.
HOGG, R., CRAIG, A., Introduction to Mathematical Statistics, (Collier Macmillan), 1978.
MENDENHALL, SCHEAFFER, WACKERLY, Mathematical Statistics with Applications, (Duxbury), 1986.
To present the algebraic structures of groups, rings and fields in order to foster an understanding of their central importance in modern mathematics and of their relevance to engineering and science.
Groups; axioms and examples, subgroups, mappings and symmetries, applications of symmetry groups.
Subgroups; cosets, Lagrange's theorem. Groups of small order; isomorphism. Binary codes; application of group codes, error correction.
Conjugacy; normal subgroups, factor groups, homomorphism, isomorphism. Permutation groups; Cayley's theorem.
Rings; axioms and examples, polynomial rings. Subrings; ideals, quotient rings, ring homomorphisms, isomorphisms.
Integral domains; integers. Congruences; Fermat's theorem, Euler's theorem, application of Euler's theorem to public key codes.
Fields; axioms and examples, polynomials over a field.
DURBIN, J.R., Modern Algebra, (Wiley), 1979.
FRALEIGH, J.B., A First Course in Abstract Algebra, (Addison Wesley), 1976.
KIM, K.H., ROUSH, F.W., Applied Abstract Algebra, (Ellis Horwood), 1983.
LEDERMANN, W., Introduction to Group Theory, (Oliver and Boyd), 1973.
WHITELAW, T.A., Introduction to Abstract Algebra, (Blackie), 1988.