Bidang Matematik

Real numbers: absolute values and inequalities. Complex numbers: operations on complex numbers, equalities of complex numbers, Argand diagrams and polar form. Relations and functions: domains and ranges. 1-1 functions, onto functions, composite functions, inverse functions, polynomials, rational fu…

Matrix Algebra: addition and scalar multiplication, matrix multiplication. Elementary row operation, reduced row-echelon form, singular matrix, inverse of a matrix. Systems of linear equations: solving by matrix method, homogeneous and nonhomogeneous systems. Differentiation: definition of derivativ…

Organization and description of data: pie chart, bar chart, frequency distribution, cumulative frequency distribution, histogram, frequency polygon and ogive. Measures of central tendency and measures of variation: mean, median, mode, mean deviation, variance and standard deviation. Probability: ran…

Definition of matrices: addition and scalar multiplication, matrix multiplication, transpose of matrix, symmetric matrix, skewed symmetric matrix, diagonal matrix and identity matrix. Elementary row operation, reduced row-echelon form, singular matrix and nonsingular matrix, inverse of a matrix. Sys…

Limits, continuity and differentiability. Definition and proofs of important theorems via the application of ed concept. Power series: radius of convergence, interval of convergence, differentiation and integration of power series. Taylor series: expansion of basic functions (e.g., sin x, cos x, log…

Correlation and regression: simple linear regression, confidence intervals, hypothesis testing, analysis of variance in regression, correlation computation, interpretation, confidence intervals, hypothesis testing and application. Multiple linear regression, coefficient estimation and inference, mod…

Definitions and terminology of differential equations. Methods of solution for first order differential equations: separable, exact, homogeneous, linear and nonlinear Bernoulli equations. Some basic mathematical models. Second order linear differential equations: homogeneous equations with constant …

Introduction to numerical algorithms, error, polynomial interpolation, numerical differentiation and numerical integration, solution of systems of linear equations and solution of systems of nonlinear equations.Eigenvalues and eigenvectors. Power method, shifting power method and inverse power metho…

Axioms of probability. Probability law. Marginal and conditional probabilities. Random variables and distributions. Expectation, moment generating functions. Central limit theorem. Markov and Chebyshev inequalities. Law of large numbers. Discrete and continuous distributions. Distribution of joint …

Real number: infimum and supremum, completeness principle, rational number system. Archimedes principle, extended real number system (introduction only), Schwartz and Minkowski inequalities (in Rn). Set and functions (review), countability. Sequences and subsequences: Cauchy sequence, complete metri…

Scientific methods and operations research. Examples of application of operations research dan modelling in problem-solving and in decisin analysis. Linear programming. Problem formulation and solution. Graphical solution of two-variable linear programming and simplex method. Sensitivity anlysis. Pr…

Review of power series and analytic functions. Power series solutions about regular and singular points (Frobenius method). Special functions: Gamma, Bessel, Legendre and Hermite functions. Boundary value problems for linear second order equations. Regular and singular Sturm-Liouville eigenvalue pro…

Revision on probability theory, order statistics, limiting distribution and stochastic convergence. Point estimation: estimation using maximum likelihood method, method of moments and minimum chi-square method. Properties of estimators: consistency, unbiasedness, efficiency and sufficiency. Complete…

Introduction to partial differential equations, its degree and order. Classification of partial differential equations to canonical form, parabolic, hyperbolic and elliptic, heat equation, wave equation and Laplaces equation. Separation of variables, Legendre and Bessel equations. Homogeneous and no…

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Introduction to complex numbers. Algebraic properties, conjugate, absolute value, geometric representation. Powers and roots. Functions of complex variables. Introduction to limit, continuity and derivatives. Analytic function, the Cauchy-Riemann equation, Rational functions, polar form and zeros. B…

Revision on factorial experiments. Balanced (including balanced incomplete block) and unbalanced design. Nested design. Split-plot design. 2k and 3k designs. 2m 3n design. Confounding. Factorial fractional design. Orthogonal array. Analysis of covariance. Regression approach to analysis of variance.…

Equivalence relations and functions, binary operations, groups and simple properties of groups, symmetric groups, subgroups, order of an element of a group, cyclic subgroups, Lagranges theorem and its applications, quotient groups, homomorphisms of rings and fields.References:1. Durbin, J.R. (2004).…

Project titles will be chosen by students/lecturers and supervised by lecturers. Students are required to carry out the project and write a report in the form of a dissertation.