COURSE SYNOPSES KOS 1110 Computers in Science This course focuses on the uses of symbolic computation language to calculate, visualise, analyse and simulate scientific information. The students will also be introduced to the uses of web pages to present and communicate scientific data, building and visualising bio-molecules with property tags, molecular structure storage formats, databases and retrieving structures from the internet. KOS 1000 Islam and Science The course deals with basic issues of science, which will lead to true understanding of sciences for both Islamic and western perspectives. The main objective of the course is to eliminate the classical divergence between religious truth and scientific fact as reflected by western literature, then to discover the indispensable unity between the two. MGT 2010 Principles and Practice of Management This course is offered by the Kulliyyah of Economics and Management Sciences, IIUM. The objectives of this course are to provide the awareness on the main principles in the current world management practices, to introduce the functions of management planning, organisation, communication and control, and to relate them with the administration principles and Islamic principles and practices. Plane curves and parametric equations. Polar coordinates. Conic sections. Arc length and surface area. Vector and geometry of space. Lines and planes in space. Surfaces in space. Vector-valued function. Curvature. SMS 1292 Developing and Protecting Mathematical Ideas Collecting and interpreting data. Setting up mathematical models. Developing mathematical models. Checking mathematical models. Discrete models. Continuous models. Periodic models. Modeling rates of change. Modeling with differential equations. Modeling with integration. Modeling with random numbers. Intellectual Property. How to protect your rights? Syndicate activity. (Pre-requisite: SMS 1278) SMS 1246 Introduction to Statistics After a brief introduction to the concepts of descriptive statistics, the emphasis is on probability theory and its applications. Topics covered include Discrete and Continuous Probability Spaces, Statistical Independence, Distributions, Discrete and Continuous Random Variables, Expectations, Moment Generating Functions, and Chebyshev's Inequality and Convergence in Probability. SMS 1277 Linear Algebra Systems of linear equations. Matrices and linear equations. Solutions of linear equations. Determinants. Vector spaces. Rank and dimension. Linear transformations. Orthogonality. Eigenvalues. Diagonalisation of real symmetric matrices. Applications. SMS 1278 Calculus Mathematical induction. Elementary set theory. Relations and functions. Recursive definitions. Limits: rate of change and limits, finding limits. One-sided limits, limits involving infinity. Continuity, tangent lines. Differentiation, mean value theorem. Integration. Transcendental functions and differential equations. Logarithms, exponential function, derivative of inverse trigonometric function. First order separable differential equations, linear first order differential equation. Integration techniques. SMS 1279 Advanced Calculus Infinite series. Limit of sequences of numbers. Subsequence, bounded sequence, and Picard`s method. Series of nonnegative terms and conditional convergence. Power series. Taylor and Maclaurin series. Fourier series. Vectors in the plane and polar functions. Dot products. Vector-valued functions. Vectors and motion in space. Lines and planes in space. Multivariable functions and their derivatives. Directional derivatives, gradient vectors and tangent planes. Linearization and differentials. Multiple integrals. Areas, moments and centres of mass. (Pre-requisite: SMS 1278) SMS 2201 Computational Mathematics Solution of equations in one variable. Interpolation and polynomial approximation. Numerical differentiation and integration. Initial-value problems for ordinary differential equations. Direct methods for solving linear systems. (Pre-requisites: SMS 1279, SMS 2281) SMS 2202 Scientific Computing The course emphasises on the C++ programming structures and using it to solve some mathematical equations related to physical problems. Topics covered include Control Structures, Repetition Structures, User-Defined Functions, Data Structures and Objects, Arrays and Strings, Pointers and References, Numerical Integration, Systems of Differential Equations and Techniques in Matrix Algebra. (Pre-requisite: SMS 2201) SMS 2216 Vector Analysis Definition of vectors and discussion of algebraic operations on vectors leads to concept of tensor and algebraic operations on tensors. Also, systematic study of the differential and integral calculus of vector and tensor functions of space and time. (Pre-requisites: SMS 2282, SMS 2284) SMS 2231 Operational Research Operations research is a mathematical discipline that aims at providing qualitative and quantitative techniques to help managers make good decisions. The present course will focus mainly on the quantitative techniques that primarily use mathematical models. (Pre-requisites: SMS 1279, SMS 2281) SMS 2247 Probability and Data Analysis Introduction and data collection. Presenting data in tables and chart. Numerical descriptive measures. Descriptive measures from a population. Basic probability. Discrete probability distributions. Continuous probability distributions. Sampling distributions. Confidence interval estimation. Fundamentals of hypothesis testing: one-sample tests. Two-sample tests with numerical data. Analysis of Variance. Tests for two or more samples with categorical data. Simple linear regression. (Pre-requisite: SMS 1246) SMS 2261 Introduction to Financial Mathematics Interest rates affect everyone. Understanding how to use these rates in a range of financial calculations is a required skill for everyone. The course is to provide students with an understanding of how interest rates are used in respect of a wide range of financial transactions including annuities, housing and personal loans, bonds and the assessment of future investment projects. It also covers Islamic views on trade and commercial activity and the moral justification for rewards under the Shariah law and explains the rationale for the prohibition of riba and its consequences for finance in Muslim countries. (Pre-requisite: SMS 1278) SMS 2281 Mathematical Methods First order ordinary differential equations. Second order ordinary differential equations. Special functions. Series solutions of differential equations. (Pre-requisite: SMS 1279) SMS 2282 Advanced Mathematical Methods Laplace transforms and applications. Matrix methods for linear systems. Partial differential equations and applications. (Pre-requisite: SMS 2281) SMS 2283 Algebra and Number Theory The integers. Primes and greatest common divisors. Congruences. Fermat's little theorem. Multiplicative functions. Primitive roots. Quadratic residues. Complex numbers. Groups. Subgroups. Cyclic groups. Permutation. Rings and fields-examples and basic concepts. (Pre-requisites: SMS 1277, SMS 1279) SMS 2284 Analysis Function of two or more variables. Partial derivatives. Limits and continuity. Differentiability. Directional derivatives and gradients. The chain rule. Tangent plane. Maxima and minima. Lagrange's method. Double integrals. Iterated integrals. Applications of double integrals. Vector fields. Line integrals. Greens theorem in the plane. Surface integrals. Stokes's theorem. (Pre-requisite: SMS 1279) SMS 2285 Advanced Analysis The real and complex number systems. Basic topology. Metric spaces. Compact sets. Abstract integration. L P - spaces. Elementary Hilbert space theory. Orthonormal sets. Trigonometric series. Examples of Banach space techniques. (Pre-requisite: SMS 2284)) SMS 2291 History of Mathematics This course discusses the historical development of mathematics from early civilizations to the twentieth century. Beginning with ancient Egypt and Babylonia to ancient Greece ; from Islamic civilization through Western Europe and then the entire world. This course includes the following topics: Early number systems and symbols. Arithmetic and geometry in early civilizations. The history of p . Euclid geometry. Algebra. The advent of Muslim Mathematics. The renaissance of mathematics. Calculus developments. Probability theory. Number theory. Non-Euclidean geometry. Twentieth-century developments. (Pre-requisite: SMS 1279)

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