Applied Mathematics

Core Courses: |
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ICBI 101 |
Biology |
4 (4-0-8) |

Prerequisites: - Chemistry of life; structure and function of macromolecules; cell structure and function; metabolism; genetics; microbial forms and functions; plant forms and functions; animal forms and functions; Biotechnology. |
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ICBI 102 |
Integrated Laboratory in Biological Sciences I |
2 (0-4-2) |

Prerequisites: - Cell structure and function, tissue, cell division, ecology, movement of molecules, respiration, and photosynthesis. |
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ICCH 210 |
General Chemistry I |
4 (4-0-8) |

Prerequisites: - Comprehensive general concepts and principles of chemistry; atomic structure; chemical bonding; stoichiometry; gases, solids, liquids and solutions; chemical thermodynamics and kinetics. Syllabus |
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ICCH 224 |
Integrated Laboratory Techniques in Chemistry I |
2 (0-4-2) |

Prerequisites: ICCH 210 General Chemistry I Laboratory practicals for general chemistry: measurements; stoichiochemistry; solids, liquids and solutions; gases; thermochemistry; equilibrium; acids and bases; electrochemistry; kinetics. |
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ICMA 106 |
Calculus I |
4 (4-0-8) |

Prerequisites: Placement test or ICNS 100 Intensive Mathematics A brief review of trigonometry; limits and continuity; differentiation and its techniques; derivatives of algebraic and trigonometric functions; graph sketching; applications of the derivatives; antiderivative and integration; area under a curve and between two curves. |
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ICMA 213 |
Calculus II |
4 (4-0-8) |

Prerequisites: ICMA 106 Calculus I Derivatives of logarithmic and exponential functions; techniques of integration; improper integrals and indeterminate forms; applications of the derivative and integration; infinite series; functions of several variables; limits and continuity; partial derivatives. |
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ICPY 132 |
Principles of Physics |
4 (4-0-8) |

Prerequisites: - Measurement, units and dimensions; vectors; description of motion; Newton’s Laws of Motion; work kinetic energy, potential energy, conservation of energy; linear momentum and it’s Law of the Conservation; equilibrium and elasticity; periodic motion; one dimensional wave motion; sound and hearing; hydrostatics; heat and thermal properties of mater; electricity and magnetism; geometrical optics; nuclear physics. |
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ICPY 341 |
Integrated Laboratory in Physics I |
2 (0-4-2) |

Prerequisites: - Laboratory practice on mechanics, heat, optic and electricity. |
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ICSC 302 |
Scientific Research and Presentation |
4 (4-0-8) |

Prerequisites: – Scientific method of discovery; developing a hypothesis and testing, interpretation of the results; proper format for presenting papers in public and in a scientific forum; practical sessions and participation in scientific seminars included. Syllabus |
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ICSC 303 |
Statistics |
4 (4-0-8) |

Prerequisites: ICMA 106 Calculus I Statistical ideas and concepts, probability and conditional probability, distribution functions, expected value, estimators, good estimators and hypothesis testing. |
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Required Courses |
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ICCS 100 |
Computer Fundamentals and Concepts |
4 (4-0-8) |

Prerequisites: - Broad overview of the following topics: computers and their operations; algorithms and problem solving; computer arithmetic and number systems; computer hardware and software components. |
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ICCS 101 |
Introduction to Computer Programming |
4 (3-2-7) |

Prerequisites: ICCS 100 Computer Fundamentals and Concepts Fundamental principles of computer programs; basic three programming constructs, namely sequence, conditions, and iterations; logic of programs in the problem solving process; object-oriented programming fundamentals. |
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ICMA 214 |
Ordinary Differential Equations |
4 (4-0-8) |

Prerequisites: ICMA 106 Calculus I Introduction to ordinary differential equations, linear first order equations, nonlinear first order equations, applications of first order equations, second order linear equations, applications of second order linear equation, higher order linear equations. |
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ICMA 219 |
Calculus of Several Variables |
4 (4-0-8) |

Prerequisites: - Vectors, three-dimensional space, cylindrical and spherical coordinates, functions of several variables, partial derivatives, calculus of vector-valued functions, multiple integrals, line and surface integrals of vector-valued functions, Green’s theorem, the divergence theorem, and Stokes’ theorem. Syllabus |
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ICMA 200 |
Principles and Mathematical Concepts |
4 (4-0-8) |

Prerequisites: - Symbolic logic, proof techniques, sets, relations, functions, the real numbers, introduction to number theory. |
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ICMA 321 |
Linear Algebra |
4 (4-0-8) |

Prerequisites: - Matrices, determinant, linear equations, system of linear equations, vector spaces, linear transformations, eigenvalues and eigenvectors, inner product spaces.Syllabus |
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ICMA 322 |
Advanced Calculus |
4 (4-0-8) |

Prerequisites: - Real and complex number systems; functions; continuity; convergence; differentiation; integration. |
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ICMA 335 |
Complex Variables |
4 (4-0-8) |

Prerequisites: - Complex numbers, analytic functions; Cauchy-Riemann equations; conformality; Cauchy’s Theorems, maximum modulus principle, Liouville’s Theorem, Residue Theorem and evaluation of real integrals, principle of arguments, Rouche’s Throrem. . Syllabus |
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ICMA 337 |
Numerical Methods |
4 (4-0-8) |

Prerequisites: ICCS 100 Computer Fundamentals and Concepts, and ICCS 101 Introduction to Computer Programming Introduction to the use of computers to solve scientific problems, numerical solution of nonlinear equations, linear algebra systems, the interpolation and approximation of functions, differentiation and integration, and differential equations. |
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ICMA 424 |
Abstract Algebra |
4 (4-0-8) |

Prerequisites: - Partitions and equivalence relations, binary operations, groups, subgroups, permutations, cyclic groups, isomorphism, direct products, cosets, normal subgroups, factor groups, homomorphism, rings, fields, integral domains. |
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ICMA 444 |
Research Project in Applied Mathematics |
6 (6-0-12) |

Prerequisites: - Small research project in Mathematics or related fields under the supervision of an advisor. |
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ICMA 445 |
Seminar in Applied Mathematics |
2 (2-0-4) |

Prerequisites: - วิชาบังคับก่อน: – Student presentations and discussions of research; review of topics. |
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Elective Courses |
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ICSC 301 |
Data Collection and Laboratory Methods |
4 (3-2-7) |

Prerequisites: - Data collection and testing of scientific hypotheses; a survey of techniques used to quantify information, including methods of measuring and sampling, and potential errors in data collection; laboratory techniques include planning and conducting experiments in the laboratory, developing skills in the laboratory, and controlling experimental, environmental variables. |
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ICCH 333 |
Physical Chemistry I |
4 (4-0-8) |

Prerequisites: ICCH 210 General Chemistry I Concepts of classical physical chemistry; behaviour of gases; First Law of thermodynamics, Second and Third Laws of thermodynamics; chemical equilibrium; phases and solutions; phase equilibria. |
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ICCH 334 |
Physical Chemistry II |
4 (4-0-8) |

Prerequisites: ICCH 333 Physical Chemistry I Concepts of classical and non-classical physical chemistry; electrochemical cells; kinetics; composite reaction mechanisms; quantum mechanics; atom structure and chemical bond. Syllabus |
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ICCS 200 |
Data Structures and Algorithms |
4 (4-0-8) |

Prerequisites: ICCS 101 Introduction to Computer Programming Basic data structures including linear data structures, trees, and graphs; storage allocation, design and evaluation of algorithms for manipulating data structures, data structure in programming languages, criteria for selecting data structures to fit their applications. |
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ICCS 202 |
Intermediate Computer Programming |
4 (3-2-7) |

Prerequisites: ICCS 101 Introduction to Computer Programming Solid basis on object-oriented program design; development of comprehensive text-based applications, GUI-based applications, multi-tasking applications, and network applications. |
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ICMA 222 |
Introduction to Mathematical Software |
4 (3-2-7) |

Prerequisites: - Introduction to the use of several software packages which are useful to Mathematics students. Software for symbolic computing, software for numerical computing, and software for mathematical documents, introduction to spreadsheets. |
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ICMA 231 |
Theory of Interest |
4 (4-0-8) |

Prerequisites: - Simple interest; compound interest; effective rate of interest; effective rate of discount; annuities; amortization schedule and sinking found; yield rates; bonds and other securities; installment loans. |
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ICMA 242 |
Discrete Mathematics |
4 (4-0-8) |

Prerequisites: - Basic logic, set theory, relations, functions, integers, counting technique, algorithms, method of proof, Boolean algebra, topics from graph theory, tree, modeling computation. |
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ICMA 313 |
Number Theory |
4 (4-0-8) |

Prerequisites: - Divisibility, primes and their distribution, congruence, Fermat’s theorem, Euler’s generalization of Fermat’s theorem, primitive roots and indices, quadratic reciprocity, quadratic congruence, perfect numbers. |
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ICMA 316 |
Introduction to Graph Theory |
4 (4-0-8) |

Prerequisites: - Graphs and subgraphs, isomorphic graphs, graph and matrices, connectivity, Eulerian and Hamiltonian circuits, planarity, Euler’s Formula, digraphs, graph colorings problems and chromatic polynomial, trees, shortest path minimal spanning tree, Ramsey number. |
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ICMA 319 |
Introduction to Combinatorial Mathematics |
4 (4-0-8) |

Prerequisites: – Counting principles, inclusion-exclusion principle, recurrence relations, partitions and generating functions, Stirling’s approximation, permutations and groups, graphs, counting patterns, Polya’s Theorem. |
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ICMA 323 |
Partial Differential Equations |
4 (4-0-8) |

Prerequisites: - Heat equation, method of separation of variables, Fourier series, wave equation, Laplace’s equation. |
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ICMA 324 |
Real Analysis |
4 (4-0-8) |

Prerequisites: ICMA 322 Advanced Calculus Infinite series, sequence and series of functions, power series, fourier series. Syllabus |
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ICMA 331 |
Special Functions |
4 (4-0-8) |

Prerequisites: ICMA 214 Ordinary Differential Equations Orthogonal polynomials, gamma functions, beta functions, hypergeometric functions, Legendre functions, spherical harmonics in p dimensions, Bessel functions. |
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ICMA 333 |
Boundary Value Problems |
4 (4-0-8) |

Prerequisites: ICMA 323 Partial Differential Equations Sturm-Liouville eigenvalue problems, nonhomogeneous problems, Green’s function and generalized Green’s function. |
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ICMA 341 |
Fluid Dynamics พลศาสตร์ของไหล |
4 (4-0-8)๔ (๔-๐-๘) |

Prerequisites: ICMA 214 Ordinary Differential Equations Review of fluid mechanics, including one dimensional flow, two dimensional motion, Eulerian methods and momentum, the pressure equation, general equations of motions, irrotational motion, viscous fluid, stream functions, complex potential, method of images, and basic singularities. |
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ICMA 344 |
Time Series Analysis |
4 (4-0-8) |

Prerequisites: ICSC 303 Statistics Basic principles of representing time series in both the time and frequency domains; Box and Jenkins technique of fitting data to autoregressive moving average models in the time domain; model construction; evaluation and forecasting; analysis of time domain and digital filtering; methods of estimating and interpreting the spectrum. |
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ICMA 346 |
Optimization |
4 (4-0-8) |

Prerequisites: ICMA 337 Numerical Methods Introduction to the theory and algorithms of linear and nonlinear programming, linear programming, simplex method, duality theory and sensitivity analysis, large-scale linear programming, unconstrained nonlinear optimization, constrained optimization problems. |
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ICMA 348 |
Numerical Methods for Partial Differential Equations |
4 (4-0-8) |

Prerequisites: ICMA 323 Partial Differential Equations and ICMA 337 Numerical Methods Forming and solving elliptic difference equations, relaxation, conjugate gradient and multigrid solution algorithms, discrete maximum principles and error estimates, explicit and implicit difference schemes for parabolic equations and systems, stability of difference schemes, parabolic free boundary problems, Stefan problems, Stochastic algorithms, first-order hyperbolic equations and systems in one space variable. |
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ICMA 350 |
Probability |
4 (4-0-8) |

Prerequisites: ICMA 219 Calculus of Several Variables Sample spaces; basic axioms of probability; conditional probability and independence. Random variables, expectation and moment-generating functions. Discrete and continuous distributions. Multidimensional distributions and transformations. Central limit theorem. Sampling distribution theory. |
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ICMA 352 |
Experimental Design |
4 (4-0-8) |

Prerequisites: ICSC 303 Statistics Basic principles of experimental design; completely randomized design; randomized block design; Latin square design; factorial experiments; confounding; split-plot experiment. |
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ICMA 353 |
Actuarial Mathematics I |
4 (4-0-8) |

Prerequisites: - Stochastic approach to life insurance models using the life table and mathematics of finance; calculation of net premiums and reserves for life insurance; types of annuity products. |
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ICMA 354 |
Actuarial Mathematics II |
4 (4-0-8) |

Prerequisites: ICMA 353 Actuarial Mathematics I Survival probability; joint life probabilities; last survivor and compound status functions; premiums; life insurance for other status; annuities; annuities paid after death. Syllabuss |
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ICMA 355 |
Introduction to Operation Research |
4 (4-0-8) |

Prerequisites: - Introduction to quantitative analysis, formulation of linear optimization, algebraic and geometric models, simplex method, sensitivity testing, duality, optimization in network, network algorithm. |
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ICMA 356 |
Decision Analysis |
4 (4-0-8) |

Prerequisites: ICSC 303 Statistics Decision models; expected monetary values; decision flow diagrams; probability assessment; optimization techniques; perfect information; opportunity losses; uncertain payoffs; biased measurements; utility theory; judgmental probability; normal form of analysis; economics of sampling; risk sharing. |
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ICMA 360 |
Sampling Techniques |
4 (4-0-8) |

Prerequisites: ICSC 303 Statistics Survey methods and planning a survey; elements of random sampling; choices of sampling units; estimation of sample size; techniques of sampling such as simple random, unequal probability, stratified, systematic, cluster, two-stage sampling and miscellaneous survey techniques. Errors and non-response. |
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ICMA 393 |
Special Topics in Applied Mathematics I |
4 (4-0-8) |

Prerequisites: - Topics of current interest. |
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ICMA 395 |
Special Topics in Applied Mathematics II |
4 (4-0-8) |

Prerequisites: - Topics of current interest. Syllabuss |
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ICMA 423 |
Set Theory |
4 (4-0-8) |

Prerequisites: - Historical introduction, classes and sets, functions, relations, partially orders classes, axiom of choice and related principle, natural numbers, finite and infinite sets, arithmetic of cardinal numbers, arithmetic of ordinal numbers. |
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ICMA 425 |
Introduction to Topology |
4 (4-0-8) |

Prerequisites: - Topological spaces, closed sets, open sets, homeomorphisms, continuous functions, metric topology, connected spaces, compact spaces, countability axioms, separation axioms, normal spaces, Urysohn lemma, Urysohn metrization theorem. |
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ICMA 432 |
Multivariate Analysis |
4 (4-0-8) |

Prerequisites: ICSC 303 Statistics Multivariate normal distribution; multiple and partial correlation; Wishart distribution; Hotelling’s T distribution; multivariate analysis of variance; discriminant analysis; factor analysis. Syllabus |
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ICMA 434 |
Introduction to Fourier Analysis |
4 (4-0-8) |

Prerequisites: ICMA 322 Advanced Calculus and ICMA 335 Complex Variables Fourier coefficients and Fourier series, L2 spaces, convolution and the delta function, Fourier transforms. |
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ICMA 435 |
Regression Analysis |
4 (4-0-8) |

Prerequisites: ICSC 303 Statistics Simple and multiple regression, diagnostics, model selection, models with categorical variables. |
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ICMA 441 |
Viscous Fluid |
4 (4-0-8) |

Prerequisites: ICMA 214 Ordinary Differential Equations Couette and Poiseuille Flow, Navier-Stokes Equation, Small Reynolds number flows, Flow in Convergent and Divergent Chanels, Boundary Layer Analysis, Flow Along a Fat Plate; Displacement Thickness; Curves Walls and Separation; Instability of Vortex Motion. |
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ICMA 450 |
Introduction to Mathematical Modeling |
4 (4-0-8) |

Prerequisites: ICMA 214 Ordinary Differential Equations, ICMA 321 Linear Algebra and ICMA 337 Numerical Methods Concepts of mathematical modeling. modeling methods, understand the problem, choosing variables, making assumptions, solving the equations, interpreting the solution and validating the model. improving the Model. Classic models such as Predator-prey Interaction, numerical methods for Mathematical Models. |
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ICMA 484 |
Special Topics in Applied Mathematics III |
4 (4-0-8) |

Prerequisites: - Topics of current interest. |
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ICMA 485 |
Special Topics in Applied Mathematics IV |
4 (4-0-8) |

Prerequisites: - Topics of current interest. |
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ICMB 203 |
Microeconomics |
4 (4-0-8) |

Prerequisites: - Introduction to microeconomics principles, pricing theory, economic scarcity, consumer behavior, production costs, market structure, utility analysis, and distribution of income. |
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ICMB 204 |
Macroeconomics |
4 (4-0-8) |

Prerequisites: - Introduction to macroeconomics principle, theories of output, consumption, inflation, unemployment, fiscal and monetary policy, international monetary system. |
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ICMB 211 |
Fundamental Financial Accounting |
4 (4-0-8) |

Prerequisites: - Business transactions and financial statements. evolution of accounting, recording and classifying financial transactions, the preparation of financial statements, characteristics of various types of accounts, the accounting principles, and the usefulness and limitations of accounting information. Syllabus |
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ICMB 362 |
Quantitative Methods for Business |
4 (4-0-8) |

Prerequisites: - Management decision processes, utilizing statistical methods, the use and application of probability concepts, statistical estimation and regression in the analysis and solution of business problems regarding income and cost estimation, sales forecasting, performance evaluation. |
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ICMB 371 |
Business Finance |
4 (4-0-8) |

Prerequisites: ICMB 211 Fundamental Financial Accounting An introduction to the principles of financial management, the role of finance within the firm, the firm and its objectives, time value of money, valuation of financial assets, capital budgeting techniques, risk and return, costs of capital, estimation and forecasting of cash flows, project evaluation, and other financial management tools. Syllabus |
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ICMF 372 |
Financial Management |
4 (4-0-8) |

Prerequisites: ICMB 371 Business Finance Financial policies affecting decision making in financial management, the differences in the need for finance in terms of the operational characteristics of particular industries, long-term financial planning, net working capital management, asset pricing theory, efficient market hypothesis, capital structure, and dividend policy. |
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ICMF 379 |
Investment Analysis and Portfolio Management |
4 (4-0-8) |

Prerequisites: ICMF 372 Financial Management Introduction of developments in investment theory, valuation principles and practices, stock, bond and derivatives analysis, specification and evaluation of asset management, quantitative and qualitative aspects of risk and return associated with investment decisions, and fundamental, technical, and random-walk approaches to valuation. |
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ICBE 342 |
Intermediate Microeconomics |
4 (4-0-8) |

Prerequisites: ICMB 203 Microeconomics Consumer theory, theory of production and cost, market structure, price determination in factor market, general equilibrium analysis, introduction to welfare economics theory. Syllabus |
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ICBE 343 |
Intermediate Macroeconomics |
4 (4-0-8) |

Prerequisites: ICMB 204 Macroeconomics Relationship between product, money, security, labour markets and foreign economy, classical theory, Keynesian theory, analysis of macroeconomic problem and policy. Syllabus |
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ICBE 448 |
Econometrics |
4 (4-0-8) |

Prerequisites: ICMB 203 Microeconomics and ICMB 204 Macroeconomics Statistical and economic theory for analyzing economic data, simple regression analysis, multiple regression analysis and limitations. |