ENG101-ENG410 English Language III – VI

English Language Support Unit

Years II & III, Semesters I & II

As most textbooks and research books in Cambodia are written in English or French, foreign language acquisition is essential for professors and students alike. The development of students’ knowledge base and research skills across all disciplines at the Royal University of Phnom Penh is an outstanding goal of this foreign language program.

BASIC REQUIREMENTS

SMA201 C Programming Language I

SMA206 C Programming Language II

Department of Computer Science

Year II, Semesters I & II

In this course, students gain a practical ability to write programs in C Programming Language. Topics covered include data types, operators, control flow, functions and recursion, pointers, arrays, strings, structures, unions, pre-processors, file I/O and the standard C Library. At the end of the module, students implement their own application in C Language.

SMA202 General Analysis II

SMA207 General Analysis III

Mr. Suon Sovann, Mr. Chea Sophal, Mr. Ngov Simrong

Year II, Semesters I & II

In this year-long course, students learn about the derivative, the derivative of inverse functions, exponential and logarithmic functions, inverse trigonometric functions, the hyperbolic and hyperbolic inverse functions, integrals, Reimann integrals, the improper integral, multi-variable functions, continuity and partial derivatives, gradients, sequences, infinite series, convergences and divergences of series, the comparison test, the Cauchy test, the D’Alembert ratio test, alternative series, the Leibniz test, absolute and conditional convergence, vector analysis, vector valued functions, multiple integrals and surface integrals.

SMA203 General Algebra II

SMA208 General Algebra III

Mr. Chhim Meng, Mr. Lav Chhiv Eav

Year II, Semesters I & II

This course continues from the Foundation Year course Algebra I. Students learn about binary operations, internal and external operations, groups, semigroups, monoids, subgroups, Lagrange’s theory, normal subgroups, the quotient and cyclic groups, homomorphism, isomorphism of groups, important isomorphism theorems, rings, fields, subrings, subfields, ideals, quotient rings, integral domains, the homomorphism and isomorphism of rings, numeric systems, and fields of complex numbers.

SMA204 General Mechanics I

SMA209 General Mechanics II

Mr. Ly Srouch, Mr. Asley Evann

Year II, Semesters I & II

In this course, students learn to apply mathematical skills to physics. Topics covered include vectors, accelerated linear motion, projectiles, relative velocity, Newton’s Law and connected particles, work, energy and gravity, impacts and collisions, statics, hydrostatics, motion in circles, differential equations, simple harmonic motion, rigid body rotation and associated frameworks.

SMA205 Analytical Geometry

Mr. Ly Srouch, Mr. Seam Ngonn

Year II, Semester I

Students examine two-dimensional and three-dimensional geometry. Topics include vectors and coordinate systems, the centriod (barycenter), Cartesian, parameterized and polar equations, conic sections, lines and planes, tangent lines, tangent
planes, translations, rotations, homotheties, quadric surfaces, level curves and level surfaces.

SMA210 Differential Geometry

Mr. Ly Srouch, Mr. Seam Ngonn

Year II, Semester II

Students learn about the differential geometry of lines, curves and surfaces. Topics covered include line elements, curves, arc lengths, curvature, torsion, analysis-tangent vectors, tangent spaces, normal vectors and surface integrals.

SMA301 Topology I

SMA306 Topology II

Mr. Kao Muysan

Year III, Semesters I & II

This year-long course introduces students to the fundamentals of topology. In Semester I, students analyse the topology of lines and planes, topological spaces, bases and subbases, continuity in topological spaces, metric spaces, and normed spaces. In Semester II, students learn about countability, separation axioms, compactness, product spaces, connectedness and functional spaces.

SMA302 Advanced Analysis

Mr. Suon Sovann

Year III, Semester I

In this course, students conduct an in-depth study of improper integrals, the complements of integrals, numerical series, the series of functions, differential and partial-differential equations, as well as Fourier, Z, and Laplace transformations.

SMA303 Linear Algebra I

SMA308 Linear Algebra II

Mr. Mauk Pheakdei

Year III, Semesters I & II

In this course, students learn about vector spaces; subspaces; linear combinations and systems of linear equations; linear dependence and linear independence; bases and dimensions; linear transformations; null spaces and ranges; matrix representations of a linear transformation; invertibility and isomorphisms; elementary matrix operations; rank of a matrix and matrix inverses; theoretical and computational aspects of systems of linear equations; determinants; eigen values; eigen vectors; diagonalizations; invariant subspaces and the Cayley-Hamiltom theorem; the Gram-Schmidt process; linear operators; Bilinear and quadric forms; and canonical forms.

SMA304 Probability I

SMA309 Probability II

Mr. Hun Touch, Mr. Uy Chanravuth

Year III, Semesters I & II

The course Probability I and II examines counting principles, permutations, combinations, random experiments, sample points, sample space, events, the algebra of events, probability definitions and axioms, theories of probability, conditional probability, independent events, and Bayes’ theorem and its applications. Students also learn about random variables, distribution functions, concepts of mathematical expectation (variance), standard deviations, conditional expectations, generating functions, two dimensional random variables, joint, marginal and conditional distribution, discrete distribution including Binomials, Poisson, Geometric and Negative Binomials, and continuous distributions including uniform, exponential, Gamma, Beta and Normal distributions.

SMA305 Operations Research I

SMA310 Operations Research II

Mr. Lim Sokly, Mr. Yim Akyuvathnak Vichea

Year III, Semesters I & II

Students learn to formulate mathematical models to optimize problem solving. Topic include linear programming, the graphic method, simplex algorithms, solutions by Lindo and interpretations, duality, sensitive analysis, integer linear programming, problem-solutions by brand and bind, solutions by 0-1 programming, transportation algorithms, stepping stones and UV methods for optimal solutions, assignment problems, networks like minimal spanning tree, shortest path problem, PERT and CPM.

SMA307 Complex Variables

Mr. Suon Sovann

Year III, Semester II

This course introduces students to complex variables, limits, derivatives and analytic functions. Students learn about Cauchy-Riemann equations, exponentials, trigonometric and hyperbolic functions, logarithms, general power and mapping, line integrals in the complex plane, Cauchy’s integral theorem, indefinite integrals and Cauchy’s integral formula, derivatives of analytic functions, and the residue integration method. They also study Power, Taylor, and Laurent series and the evaluation of real integrals.

SMA401 Mathematical Statistics I

SMA406 Mathematical Statistics II

Mr. Lim Sokly, Mr. Sao Sovanna

Year IV, Semesters I & II

This course deals with moment generating functions, characteristic functions, other miscellaneous distributions like Binomial, Hypergeometric, Multi-normal, Cauchy, Laplace, Chebyshev’s and Kolomogorov inequalities, the weak law of large numbers, the central limit theorem, correlation, regression analysis, concepts of sampling, sampling distribution and tests of significance. Students also learn about sampling bias, the theory of point estimation, consistency, efficiency and sufficiency, maximum likelihood estimates and their properties, confident intervals, testing of hypotheses, and variable analysis. As part of this course, students learn to use statistical computer applications such as SPSS.

SMA402 Measure Theory I

SMA407 Measure Theory II

Mr. Suon Sovann

Year IV, Semesters I & II

In this course, students consolidate their knowledge of topology and also learn about matrix spaces, convergence and uniform approximation, derivatives and development on R, Riemann integrals, curvature integrals, holomorphic functions, convolution, Fourier transformation and series, norms and Hilbert spaces, measurable and integratable functions, products of measure, Lebesgue measure and the Lebesgue integral.

SMA403 Differentials in Banach Space I

SMA408 Differentials in Banach Space II

Mr. Ly Srouch

Year IV, Semesters I & II

The first part of this course examines Banach, Normed and Hilbert space. Students learn linear, multi-linear and differential mapping, as well as the Mean Value Theorem, local inverse series, and implicit functions. The second part examines higher order derivatives and differential equations. Topics covered include second order derivatives, the Shwartz theorem, Taylor’s formula and optimizations in Banach Space.

SMA404 Group Theory

Mr. Hak Sokheng, Mr. Lav Chhiv Eav

Year IV, Semester I

This course is an in-depth exploration of theorems concerning homomorphism, the isomorphism of groups, permutation groups, subgroups, normal subgroups, quotient groups, direct products of groups, fundamental theorems of finite abelian groups and group actions on sets, as well as Sylow Theorems and their applications.

SMA405 Numerical Analysis I

SMA410 Numerical Analysis II

Mr. Seam Ngon, Mr. Asley Evann, Mr. Kao Muysan

Year IV, Semesters I & II

In this course, students learn to use numerical methods to approximate solutions to complicated analytical problems. Topics include the Taylor series, derivatives, computer arithmetic, polynomial interpolation, spline interpolation, iteration, solutions of equations by numerical methods, numerical differentiation, numerical integration, systems of linear equations and solving ordinary differential equations by numerical methods.

SMA409 Module Theory

Mr. Hak Sokheng, Mr. Lav Chhiv Eav

Year IV, Semester II

Module theory examines modules, submodules, modules generated by subsets, the sum of submodule families, homomorphism and isomorphism of modules, quotient modules, important isomorphic theorems, A-module, Hom (M-N) and Foncteur Hom, exact sequences, direct sums of A-module, direct products and internal direct sums of submodules.