Mathematics Programme – Courses at a Glance MTH101: Discrete Mathematics MTH101 Discrete Mathematics is part of a foundation suite of level 1 courses designed to provide students with a broad foundational set of mathematical skills and techniques. The course will prepare students for both higher level mathematical studies as well as the study of other and related subjects that contains mathematical content. The course uses Mathcad.
MTH102: Transformation and Matrices MTH102 Transformations and Matrices is part of a foundation suite of level 1 courses designed to provide students with a broad foundational set of mathematical skills and techniques. The course will prepare students for both higher level mathematical studies as well as the study of other and related subjects that contains mathematical content. The course uses Mathcad.
MTH103: Calculus and Statistics MTH103 Calculus and Statistics is part of a foundation suite of level 1 courses designed to provide students with a broad foundational set of mathematical skills and techniques. The course will prepare students for both higher level mathematical studies as well as the study of other and related subjects that contains mathematical content. The course uses Mathcad.
MTH104: Calculus and Algebra MTH104 Calculus and Algebra extends the calculus introduced in MTH103, and introduces a number of abstract algebraic structures. Complex numbers, congruences and some basic group theory are introduced. Various methods of proof, such as mathematical induction, are discussed. The aim is to prepare students for higher level mathematics. The course uses Mathcad.
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MTH205: Analysis I: Limits, Sequences and Series MTH205 Analysis I: Limits, Sequences and Series introduce essential and basic analysis to understand the foundations of the theory of calculus. Important formal topics include Numbers, Sequences, Series and Continuity, all of which establish a firm starting point for understanding the theory of calculus and its applications.
MTH206: Analysis II: Power Series and Calculus MTH206 Analysis II: Power Series and Calculus develops the ideas introduced in MTH205 to formally analyze the theory of differentiation, integration and power series representation of functions. MTH207: Linear Algebra MTH207 Linear Algebra introduces essentials of linear algebra and shows the relationships between matrices, determinants, vector spaces, eigenvalues, eigenvectors and linear transformations.
MTH209: Introduction to Group Theory MTH209 Introduction to Group Theory introduces the fundamentals of group theory. Group theory is a tool for working with patterns, such as counting the ways a symmetric object can be colored etc.
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MTH211: Fundamentals of Mathematical Methods and Mechanics MTH211 Fundamentals of Mathematical Methods and Mechanics is about the use of mathematics to solve real-world problems. Part of it deals with the representation of relevant aspects of the real world in the form of mathematical models; another part is concerned with the mathematical methods that are useful in working with these models. The material of the course is organized in a way that reflects these broad divisions. By far the most important element of the models part of the course is the study of Newtonian mechanics. Newtonian mechanics is the basic source of models of the motion of objects of ordinary size moving with ordinary speeds (or not moving at all), and it underpins much of physical science and mechanical engineering. The methods part of the course also tends to concentrate on one subject, though perhaps not so closely as the models part; the subject in question is differential equations. This is because the study of motion or of change in general, almost necessarily lead to differential equations. In addition, however, the course covers aspects of the theory of vectors, ordinary calculus and basic numerical analysis. The course uses Mathcad. MTH213: Fundamentals of Mathematical Modeling Fundamentals of Mathematical Modeling introduces mathematical modelling techniques associated with a variety of standard model scenerios and applies such models to real life applications that are generally useful in many areas of applied mathematics. The course uses Mathcad.
MTH215e: Further Mathematical Methods and Mechanics MTH215e Further Mathematical Methods and Mechanics exploits manly matrix related techniques to solve applied mathematics problems related to coupled systems and extended objects. The course uses Mathcad, and this is a blended ecourse.
MTH217: Numerical Methods and Advanced Calculus MTH217 Numerical Methods and Advanced Calculus considers more advanced mathematical techniques to solve various problems in applied mathematics and prepares students for higher level 3 studies in applied mathematics. The course uses Mathcad. Copyright © 2012 SIM University
MTH219: Fundamentals of Statistics and Probability MTH219 Fundamentals of Statistics and Probability aims to provide students the essential and important concepts of Statistics and Probability for data analysis. Illustrative examples in various disciplines will be discussed. Emphasis will be on understanding data variability and uncertainty; cultivating statistical thinking and applying statistical techniques to solve real-life practical problems. Descriptive statistics and useful probability models will be introduced. The Course uses SPSS. MTH220: Statistical Methods and Inference MTH220 Statistical Methods and Inference is a natural continuation of MTH219 and it aims to equip students with more in-depth statistical knowledge and skills to solve real-world problems and to make intelligent decisions. Students will be able to apply a wide range of concepts and statistical methods for analysing data, carrying out hypothesis testing, estimation and drawing inferences. Correlation analysis, regression methods, nonparametric techniques and inferential statistics will be introduced. The course uses SPSS.
ICT271: Introductory Programming Techniques in C++ ICT271 Introductory Programming Techniques in C++ introduces the design and development of computer programs to solve problems. Topics include the fundamental programming constructs as well as using the taught software development procedure to implement applications using C++ language.
ICT272 Object Oriented Programming in C++ ICT272 Object Oriented Programming in C++ introduces the fundamental objectoriented concepts. Topics include object-oriented features including Class, Objects, Encapsulation, Inheritance and Polymorphism, and implementing applications using C++ language.
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MTH221e: Principles of Financial Mathematics MTH221e Principles of Financial Mathematics is the application of mathematics to finance. What is finance? Generally, it concerns the study of how one allocates resources over time. Activities of allocating resources are usually called investments. In plain words, an investment is the current commitment of dollars for a period of time to derive future payments that will compensate the investors for the time the funds are committed, the expected rate of inflation, and the uncertainty of future payments. MTH221 aims to provide an introduction to the fundamentals of financial mathematics such as the theory of interest, utility theory, risk aversion and singleperiod portfolio optimization.
MTH222: Foundations of Asset Pricing MTH222 Foundations of Asset pricing mainly studies investments which comprise a single period: money is invested at the initial time, and payoff is attained at the end of the period. Examples are investments in zero-coupon bonds that will be held to maturity, investments in a physical project that will not provide payment until it is completed, etc. Obviously, many common investments such as publicly traded stocks are not of such type, since they can be liquidated at will and may return dividends periodically. Why then do we need to study single-period investments? Because it is sometimes a good approximation, and usually makes our analysis on such a singleperiod investment much more simplified without losing much generality.
MTH223: Introduction to Mathematics in Computing MTH223 Introduction to Mathematics in Computing introduces certain mathematics relevant to computing and shows how this mathematics is useful in computing. In particular, it will make you familiar with the mathematics necessary for a formal approach to the production of software. It is an introductory course at the formal or theoretical end of the range of computing courses and is primarily designed for students who intend to specialize in computer science. It includes no practical computing.
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MTH224: Further Mathematics in Computing MTH224 Further Mathematics in Computing further expands mathematics relevant to computing and shows how this mathematics is useful in computing. In particular, it will make you familiar with the mathematics necessary for a formal approach to the production of software. It is an continuation course of MTH223 at the formal or theoretical end of the range of computing courses and is primarily designed for students who intend to specialize in computer science. It includes no practical computing MTH301: Fundamentals of Complex Analysis MTH301 Fundamentals of Complex Analysis introduces complex numbers, complex functions and the analysis of functions of one complex varaible.
MTH302: Applied Complex Analysis MTH302 Applied Complex Analysis develops some deep theorems of complex analysis and applies them to areas such as fluid mechanics and complex sets.
MTH303e: Principles of Graph Theory MTH303e Principles of Graph Theory has been designed to emphasize the close tie between the theoretical and algorithmic aspects of graph theory. It covers the following topics: different types of graphs or digraphs, trees, connectivity and network flow, matching, planar graphs, vertex and edge coloring of graphs, as well as basic data structure and complexity analysis for basic algorithms.
MTH304: Applications of Graph Theory MTH304 Applications of Graph Theory discusses some traditional applications of graph theory. It includes the following topics: scheduling, circuit analysis, geometric design, kinematic design, coding theory and block design.
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MTH305: Principles of Applied Probability MTH305 Principles of Applied Probability discusses chance, plays an important part in all aspect of life. We take chances everyday: whether we catch the bus or just miss it; whether or not we are caught in a sudden shower. Chance or random variations is also an essential features of almost all working systems: scientist taking measurements in a laboratory; an economist studying price fluctuations; a surgeon studying heartbeat patterns on a electrocardiogram. In all these processes, some elements of chance or randomness are present.
MTH306: Further Applied Probability MTH306 Further Applied Probability is further applied probability on modeling and problem-solving. A practical situation is described and then a probability model is developed to describe the main features. Usually the model is of a simplified version of the actual process. The model is then analyzed mathematically in order to discover the possible ways in which the situation might develop, and the probabilities associated with them.
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MTH307: Principles of Regression Analysis MTH307 Principles of Regression Analysis is the first of two sequential courses on applied regression analysis. It aims to lay the theoretical foundation essential to regression analysis. Topics include review on probability & statistics review, an overview on regression analysis, simple linear regression, and multiple linear regression. The second of the two sequential courses, Applications of Regression Analysis, will focus on the treatment of practical and application issues pertinent to regression analysis. Topics include model building & variable screening, deviation from standard assumptions, residual analysis, and selected advanced techniques. Linear regression models are widely used today in science and technology, engineering, business administration, economics, and the social, health and biological sciences. Successful applications of these models require a sound understanding of both the underlying theory and the practical problems that are encountered in using the models in real-life situations. Linear regression, as a subject of applied statistics, offers a superb opportunity for students to learn the process of mathematical modelling: understanding the working principles pertinent to the a problem and making appropriate assumptions to obtain an initial model, using sample data to estimate the values of the parameters in the model, evaluating the adequacy of the model, refining the model, and applying the model in evaluation and predication, etc. The primary objectives of this course are for students: (1) to develop a sound understanding of the statistical concepts in regression analysis; (2) to develop the ability to apply these concepts correctly; (3) to develop the ability to interpret the results of a regression analysis properly; and (4) to develop the ability to communicate effectively, in writing, the results and proper interpretation of a statistical analysis.
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MTH308: Applications of Regression Analysis MTH308 Applications of Regression Analysis is the second of two sequential courses on applied regression analysis. It will focus on the treatment of practical and application issues pertinent to regression analysis. Topics include model building & variable screening, deviation from standard assumptions, residual analysis, and selected advanced techniques. Linear regression models are widely used today in science and technology, engineering, business administration, economics, and the social, health and biological sciences. Successful applications of these models require a sound understanding of both the underlying theory and the practical problems that are encountered in using the models in real-life situations. Linear regression, as a subject of applied statistics, offers a superb opportunity for students to learn the process of mathematical modelling: understanding the working principles pertinent to the a problem and making appropriate assumptions to obtain an initial model, using sample data to estimate the values of the parameters in the model, evaluating the adequacy of the model, refining the model, and applying the model in evaluation and predication, etc. The primary objectives of this course are for students: (1) to develop a sound understanding of the statistical concepts in regression analysis; (2) to develop the ability to apply these concepts correctly; (3) to develop the ability to interpret the results of a regression analysis properly; and (4) to develop the ability to communicate effectively, in writing, the results and proper interpretation of a statistical analysis. MTH309: Nonlinear Optimization Methods and Applications MTH309 Nonlinear Optimization Methods and Applications objective is the optimization and selection of the best possible decision for a given set of circumstances without having to enumerate all of the possibilities. From experience, designers learn to recognize good proportions and critical restrictions so their preliminary work will not require significant modification and improvement. The subject which formulates and explains this talent is a branch of applied mathematics known as optimization theory, a science that studies the best .In recent years the subject of optimization has matured and is widely used in numerous applications, e.g., petroleum refining operations, routes for commercial aircraft, livestock feed blending and missile trajectories.
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MTH310: Linear Optimization Methods and Applications MTH310 Linear Optimization Methods and Application develops and applies linear optimization techniques and linear programming models where all the objective functions and constraints are linear.
MTH311: Number Theory MTH311 Number Theory extends the number theory introduced in Unit 4 of MTH104. The aim of the course is to prepare students for courses in advanced number theory.
MTH313: Mathematical Logic MTH313 Mathematical Logic is a demanding third level course on mathematical logic. Although there is no prerequisite, a higher level of thinking is needed. The aim of the course is to prepare students for courses in advanced mathematical logic.
MTH315: Advanced Mathematical Methods MTH315 Advanced Mathematical Methods is on boundary value problems of partial differential equation (PDE), with support from vector differential and integral calculus and special types of ordinary differential equations (ODE) e.g. those of Legendre, Bessel and Hermite’s. As an introduction to boundary problems we look at special as well as general types of ODEs, and this lead us into eigenvalue problems and also some numerical methods for solutions. In PDE we study their types and their methods of solution based on characteristic curves and variable separable, subject to different boundary conditions in different curvilinear coordinate systems. Here vector calculus is an indispensable tool, frequently employed in these areas. Two major PDEs are the heat equation and the wave equation which have manifestations in Laplace equation, and their solution can depend on ODEs, Fourier series and eigenvalues and Eigen functions. For this reason we also include the study of Sturm-Liouville eigenvalue problems in differential equations, from a linear operator approach, emphasizing on their properties and characteristics.
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MTH317: Mathematics of Fluids MTH317 Mathematics of Fluids involves mainly the applications of vector field calculus, ordinary (ODE) and partial (PDE) differential equations in curvilinear coordinates, aided by physical laws, to the study of fluid behaviour. The emphasis is on the mechanics of flow, i.e. on the kinematic and dynamic aspects of fluids. This principally concerns momentum transport, over energy transport or mass transport, and manifests itself in pathlines, streamlines and stream functions and in Euler’s and Bernoulli’s momentum equations. For supporting materials that will be needed throughout, boundary value problems and vector calculus are revisited at the start of the course and emphasis is also stressed on dimensional analysis of physical variables, because this forms an integral and indispensable part of fluids. The static properties of fluids is studied in terms of pressure exerted on an immerse body, and atmospheric models for pressure or temperature variation with height are also investigated in the process. Vorticity and circulation, e.g. streaming and swirling flow across a cylindrical surface, are studied in terms of Stokes’ and Kelvin’s theorem for inviscid fluids. Viscosity of Newtonian fluids is studied with respect to the Navier Stokes equation, and this covers laminar flows, Reynolds number, Hagen-Poiseuille pipe flow and boundary layers. The closing unit looks at gravity water waves, represented by a harmonic wave function, propagating in infinite and finite depths.
MTH401: Topology of Euclidean Spaces MTH401 Topology of Euclidean Spaces is an introduction to analysis in a slightly more abstract setting than encountered in the 1-variable analysis course. Fundamental concepts from the 1-variable case are abstracted and generalized. Basic topological properties of Euclidean spaces are introduced. These provide the framework for tackling difficult problems in advanced analysis. The aims of this course include enabling the students to develop further their ability to think in a critical manner; formulate and develop mathematical arguments in a logical manner; improve their skills in acquiring new understanding and expertise; and acquire an understanding of topological concepts in advanced analysis.
MTH402: Analysis in Euclidean and Metric Spaces MTH402 Analysis in Euclidean and Metric Spaces aims to develop further students ability to think in a critical manner; formulate and develop mathematical arguments in a logical manner; improve their skills in acquiring new understanding and expertise; acquire an understanding of concepts of advanced mathematical analysis; and acquire an ability to apply results from advanced analysis.
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MTH401: Topology of Euclidean Spaces MTH401 Topology of Euclidean Spaces is an introduction to analysis in a slightly more abstract setting than encountered in the 1-variable analysis course. Fundamental concepts from the 1-variable case are abstracted and generalized. Basic topological properties of Euclidean spaces are introduced. These provide the framework for tackling difficult problems in advanced analysis. The aims of this course include enabling the students to develop further their ability to think in a critical manner; formulate and develop mathematical arguments in a logical manner; improve their skills in acquiring new understanding and expertise; and acquire an understanding of topological concepts in advanced analysis.
MTH402: Analysis in Euclidean and Metric Spaces MTH402 Analysis in Euclidean and Metric Spaces aims to develop further students ability to think in a critical manner; formulate and develop mathematical arguments in a logical manner; improve their skills in acquiring new understanding and expertise; acquire an understanding of concepts of advanced mathematical analysis; and acquire an ability to apply results from advanced analysis.
MTH499: Mathematics Capstone Project MTH499 Mathematics Capstone Project is a stand-alone project developed by students under supervision of a Associate Tutor on an agreed topic. The project requires the analysis and synthesis of problems in mathematics and application of the various principles learnt to solve practical problems in an academic manner under the supervision of a project tutor. The project may take any one or a combination of the following forms: feasibility study, computer modeling and analysis, design and construction, testing and experimental investigation. The project thesis is submitted individually and runs over two semesters. MTH499 can only be taken by UniSIM invited honours students from January 2011 (beginning honours year in 2011).
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