Mr.
Soun Sovan, Head, Department of Mathematics, BSc
Tel: 855-12-840-581
Room: #113A, Campus 1
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Introduction
The
degrees in pure and applied mathematics equip Cambodian students with the
skills and competencies necessary to contribute to the development of Cambodia
as teachers, statisticians, scientific managers, actuaries, system analysts
and so on. After two years general education, students choose their specialisation
in third year. Students who aspire to be teachers take the pure mathematics
course, while students preparing for employment in the private sector choose
applied mathematics.
Background
Following the devastation of the education system during the years of the
Khmer Rouge regime, the degree in mathematics was originally designed to train
large numbers of secondary school teachers to meet the needs of all upper-high-schools
in Cambodia. As the Cambodian economy developed in the late nineties, RUPP
has recognised the need to prepare Cambodian students for careers in business
and industry. (Back to Top)
Admission
High School Certificate and sit the National University Entrance Examination
on Mathematics and Khmer Culture. (Back to
Top)
Assessment
Written examinations (Back to Top)
Resources
The Hun Sen library contains a large section of recently published advanced
university textbooks in mathematics in both English and French. The department
has also translated twenty important texts into Khmer, which students can
access. A small computer laboratory with appropriate mathematical software
is available. (Back to Top)
GENERAL
EDUCATION
English (see ELSU)/French
Years I-III
English streamed students are taught by the English Language Support Unit
(ELSU). French streamed students are taught by French teachers supported by
the Agencie Francophone (AUPELF). As most textbooks and research books in
Cambodia are written in English or French, foreign language acquisition is
essential for professors and students alike who want to increase their skills
and knowledge levels. (Back to Top)
Khmer
Culture and Society
Year I
Examines the meaning and value of the Khmer culture, its elements, and its
influences on other nations. Emphasis is on religion, Khmer culture in each
period, and the flow of foreign culture in it. Enhances appreciation of the
Khmer country and culture and reflects on the role of people in building their
own country. (Back to Top)
Introduction
to Logic
Year I
Students
develop their mathematical reasoning ability, in particular their ability
to read and write proofs. Topics include deductive reasoning, variables and
sets, conditional and biconditional connectives, quantifiers, proof strategies,
relations and functions, and mathematical induction. (Back
to Top)
General
Physics I & II
Year I
Students apply mechanics theories to the real world (Newton's Laws), understand
optical instruments, explain how images are produced and the function of the
human eye, examine natural electricity phenomena and calculations using Gauss
and Ampere theories, understand the use of electrical equipment in everyday
life, and learn ideas about elementary particles, atoms and radiation. (Back
to Top)
PC
Applications I & II
Year I
Students gain knowledge in MS Word and Excel Programs, practical and theoretical
knowledge in how to use and create texts, tables, pictures, WordArt, calculations,
graphics and MS Access program. (Back to
Top)
Using
Library Resources
Year I
Students learn how to use reference books, such as encyclopaedias, atlases
and dictionaries, and how to find information using technologies such as the
Internet, e-mail, CD-ROM, video and microfiche. (Back
to Top)
Introduction
to Environmental Science
Year I
Examines basic concepts in environmental science and global environmental
issues, especially problems arising in Cambodia. Introduces students to the
interdisciplinary nature of examining ecological resources and interaction
with people, environmental pollution, renewable and non-renewable energy,
and the impact of population on the environment. (Back
to Top)
BASIC
REQUIREMENTS
General Analysis I-IV
Years I & II
Students learn about the properties and topology of the set of real numbers;
numerical functions; derivative, exponential and logarithmic functions; the
Reimann integral, topologies of IRn; continuity and partial derivatives. Year
two students examine multiple integrals; surface integrals; vector analysis;
differential and partial-differential equations; numerical series; and series
of functions. (Back to Top)
General
Algebra I-IV
Year I & II
Semester I explores Sentential Logic (expression of mathematics, proposition
and prepositional functions, logical connectives, quantifiers), Sets (unions,
intersections, differences of two sets, symmetry of two sets, anti-symmetry
of two sets, families and parts of sets, cover partitions), Binary Relations
(products, equivalent relations, ordering rations, max/min, sup/inf, majorant/minorant),
and Functions and Maps (injective, surjective bijective, operation interns
and externs, natural numbers, system numberic). General Algebra II examines
the theory of sets and groups, semigroups, monoids, homomorphisms and subgroups,
cyclic and quotient groups and normality. (Back
to Top)
Analytical
Geometry
Year I
Examines the following two-dimensional geometry topics: vectors and coordinate
system, Barycenter, Cartesian Equations, parametrised equations, polar equations,
conic sections. Year two, semester one, examines three-dimensional geometry,
including vectors and coordinate system, Barycenter, lines and planes and
quadric surfaces. (Back to Top)
C
Programming Language I & II
Year II
Students gain practical ability to write C Programs. 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.
(Back to Top)
Linear
Algebra I & II
Year II
Students learn about vector spaces, algebraic operations, matrixes, determinants,
and general properties of linear equations, polynomials and Commutative Fields,
rational fractions and functions, algebraic equations, proper values and proper
vectors of endomorphism, reduction of matrixes, and symmetric bilinear and
Hermitian forms and spaces. (Back to Top)
Statistics
I & II
Year II
Examines sampling theory, estimations theory, hypotheses testing, curve fitting,
regression and correlation, and analysis of variance. Students learn to use
computer applications such as the SPSS Program. (Back
to Top)
Fundamental
Mechanics I & II
Year II
Students learn to apply mathematics skills to physics. Topics include vectors,
accelerated linear motion, projectiles, relative velocity, Newton's Laws and
connected particles, work, energy and gravity, impacts and collisions, statistics,
hydrostatics, motion in circle, differential equations, simple harmonic motion,
rigid body rotation and frameworks. (Back
to Top)
Topology
I & II
Year III
Part I analyses topological spaces, functions and homomorphism, continuity,
metric spaces, compactness and connectedness. Part II looks at linear spaces
and operators, hilbert spaces, abstract foulier series, linear functional
and operants, and dual spaces. (Back to Top)
Probability
I & II
Year III & IV
Examines random variables and probability distributions, change of variables
and convolutions. Part II examines mathematical expectations such as the functions
of random variables, variance and standard deviation, moments and Chebyshev's
Inequality. Part III deals with special probability distributions, including
Normal, Poisson, multinominal, hypergeometric, uniform, Gamma, Cauchy, Beta,
Chi-Square, bivariate and other miscellaneous distributions. (Back
to Top)
Operations
Research I & II
Year III
Students gain ability in creating mathematical models for optimisation problems.
Topics include linear programming, graphical solutions, lindo, simplex algorithms
dualism, sensitivism analysis, integer LP problems, zero-one LPs, transportation
algorithms, assignment problems, networks, PERT and CPM. (Back
to Top)
Integration
and Measure Theory I & II
Year IV
Topics include topology and metric spaces; convergence and uniform approximations;
derivatives and development on IR; Reimann integrals; curvilgne integrals
and holomorphic functions; convolution; Fourier transformation and series;
norm and Hilbert spaces; measurable and integrable functions; and products
of measure. (Back to Top)
Numerical
Analysis I & II
Year III & IV
Students learn to use numerical methods to approximate solutions of complex
analytical problems. Topics include the Taylor series, derivatives, computer
arithmetic, polynomial interpolation, spline interpolation, iteration, the
equation f(x) = 0, numerical integration, numerical differentiation, systems
of linear algebraic equations, ordinary differential equations. (Back
to Top)
PURE
MATHEMATICS
Advanced Analysis I & II
Year III
Topics include the complements of integrals, series, differential and partial-differential
equations, as well as Fourier, Z, and Laplace transformations. (Back
to Top)
Advanced
Algebra I & II
Year III
Semester I explores isomorphic groups, permutation groups, rings, ideal quotients
rings and relations in a ring, as well as some difficult theorems. In semester
II, students study unique factorisation domains, Euclidean domains, ring properties
and Euclidean rings, the highest common divisor (PGCD), roots of polynomials,
irreducible elements, ideal factorisation, and symmetric polynomials. (Back
to Top)
Complex
Analysis I & II
Year III
Introduces students to complex variables. Limits, derivatives and analytic
functions are studied. Students learn about Cauchy-Riemann equations; exponential,
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; evaluation of real integrals, conformal mapping and applied potential
theory. (Back to Top)
Calculate
Differentials I & II
Year IV
Calculate Differentials I examines Banach, Normed and Hilbert spaces, and
linear, multi-linear and differentiable mappings. Part II examines higher
order derivatives and differential equations. Topics include second order
derivatives and Shwartz theorem, Taylor's formula. (Back
to Top)
Theory
of Groups and Modules
Year IV
Abstract
Mathematics
Year IV
APPLIED
MATHEMATICS
Discrete Mathematics I & II
Year III
Students learn mathematics for advanced computer science. Topics include counting
methods and recurrence relations; graph theory; trees; network models and
Petri trees; Boolean algebra and combinatorial circuits; automata, grammars
and languages. (Back to Top)
Combinatorics
I & II
Year III
Students learn to use computers to solve mathematical problems. Topics include
an introduction to enumeration; equivalence relations, partitions, multisets;
algebraic counting techniques; graph theory; matching and optimisation; combinatorial
C designs; ordered sets; and enumeration under group action. (Back
to Top)
Engineering
Mechanics I & II
Year III
Engineering Mechanics I (Statics) prepares students for work in industry,
focuses on statical topics including forces systems, equilibrium, structures,
distributed forces, friction and virtual work. Engineering Mechanics II (Dynamics)
examines kinematics of particles, kinetics of particles, kinetics of systems
of particles, plane kinematics of rigid bodies, plane kinetics of rigid bodies,
3D dynamics of rigid bodies, and vibration and time response. (Back
to Top)
Econometrics
I & II
Year IV
Econometrics I examines the nature of regression; two variable regression
analysis; estimation; CNLRM; hypothesis testing; extensions; multiples regression
analysis; multicollinearity and micronumerosity; heteroscedasticity and autocorrelation.
Econometrics II examines dummy variables; CPM, logit, probit models; autoregressive
and distributed log models; simultaneous equation models; time series econometric
models; and forecasting with ARIMA and VAR models. (Back
to Top)
Mathematics
of Finance I & II
Year IV
Students learn about planning and actuarial preparation for banks, insurance
and investment companies. Topics include theory of interest rates; compound
interest functions; nominal rates of interest; discounted cash flow; capital
redemption policies; valuation of securities; capital gains tax; cumulative
sinking funds; yield curves immunisation; consumer credit; and stochastic
interest rate models. (Back to Top)
Mathematical
Modeling I & II
Year IV
Topics include discrete dynamical systems; discrete stochasticity; stages,
states and classes; empirical modeling; continuous models; and continuous
stochasticity. (Back to Top)
Analytical
Mechanics
Year IV
Topics are Lagrangian mechanics; calculus applications, linear oscillators,
one-dimensional systems, Hamiltonian dynamics; canonical transformations;
rotating coordinate systems; dynamics of rigid bodies; small vibrations; approximate
solutions; chaotic dynamics; and special relativity. (Back
to Top)
Mechanics
of Materials and Fluids
Year IV
THESIS
(Back
to Top)
CURRICULUM
*Explanation:
The code 3(2-1) indicates the study load and number of credits. In this example:
'3'= number of credits, '2' = number of lecture hours, and '1' = number of
tutorial or practical hours.
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YEAR ONE |
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|
Semester One |
Semester Two |
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|
General Education |
General Education |
|
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|
English/French I |
2(6-0) |
English/French II |
2(6-0) |
|
Khmer Culture and Society |
2(2-0) |
Using Library Resources |
1(1-0) |
|
Introduction to Logic |
2(2-0) |
Introduction to Environmental Science |
2(2-0) |
|
General Physics I |
3(3-1) |
General Physics II |
3(3-1) |
|
PC Applications I |
3(3-1) |
PC Applications II |
3(3-1) |
|
Basic Requirements |
|
Basic Requirements |
|
|
General Analysis I |
4(4-2) |
General Analysis II |
4(4-2) |
|
General Algebra I |
4(4-2) |
General Algebra II |
3(3-1) |
|
Analytical Geometry |
2(2-1) |
||
|
Total |
20 Credits |
Total |
20 Credits |
|
YEAR TWO |
|||
|
Semester One |
Semester Two |
||
|
General Education |
|
General Education |
|
|
English/French III |
2(6-0) |
English/French IV |
2(6-0) |
|
Basic Requirements |
|
Basic Requirements |
|
|
C Programming Language I |
2(2-1) |
C Programming Language II |
2(2-1) |
|
General Analysis III |
4(4-2) |
General Analysis IV |
4(4-2) |
|
General Algebra III |
2(2-1) |
General Algebra IV |
2(2-1) |
|
Linear Algebra I |
2(2-1) |
Linear Algebra II |
2(2-1) |
|
Statistics I |
3(3-1) |
Statistics II |
3(3-1) |
|
Fundamental Mechanics I |
3(3-1) |
Fundamental Mechanics II |
3(3-1) |
|
Total |
18 credits |
Total |
18 credits |
|
YEAR THREE – Pure Mathematics |
|||
|
Semester One |
Semester Two |
||
|
General Education |
|
General Education |
|
|
English/French V |
2(6-0) |
English/French VI |
2(6-0) |
|
Basic Requirements |
|
Basic Requirements |
|
|
Topology I |
4(4-2) |
Topology II |
4(4-2) |
|
Probability I |
3(3-1) |
Probability II |
3(3-1) |
|
Operations Research I |
2(2-1) |
Operations Research II |
2(2-1) |
|
Major Courses |
Major Courses |
|
|
|
Advanced Analysis I |
2(2-1) |
Advanced Analysis II |
2(2-1) |
|
Advanced Algebra I |
3(3-1) |
Advanced Algebra II |
3(3-1) |
|
Complex Analysis I |
2(2-1) |
Complex Analysis II |
2(2-1) |
|
Total |
18 Credits |
Total |
18 Credits |
|
YEAR THREE – Applied Mathematics |
|||
|
Semester One |
Semester Two |
||
|
General Education |
|
General Education |
|
|
English/French V |
2(6-0) |
English/French V |
2(6-0) |
|
Basic Requirements |
|
Basic Requirements |
|
|
Topology I |
3(3-1) |
Topology II |
3(3-1) |
|
Operations Research I |
3(3-1) |
Operations Research II |
3(3-1) |
|
Numerical Analysis I |
3(3-1) |
Numerical Analysis II |
3(3-1) |
|
Major Courses |
|
Major Courses |
|
|
Discrete Mathematics I |
3(3-1) |
Discrete Mathematics II |
3(3-1) |
|
Combinatorics I |
3(3-1) |
Combinatorics II |
3(3-1) |
|
Engineering Mechanics I |
3(3-1) |
Engineering Mechanics II |
3(3-1) |
|
Total |
20 Credits |
Total |
20 Credits |
|
YEAR FOUR – Pure Mathematics |
|||
|
Semester One |
Semester Two |
||
|
Basic Requirements |
|
Basic Requirements |
|
|
Statistics III |
3(3-1) |
Statistics IV |
3(3-1) |
|
Integration and Measure Theory I |
4(4-2) |
Integration and Measure Theory II |
4(4-2) |
|
Major Courses |
|
Major Courses |
|
|
Calculate Differentials I |
4(4-2) |
Calculate Differentials II |
4(4-2) |
|
Theory of Groups and Modules |
4(4-2) |
Abstract Mathematics |
4(4-2) |
|
Numerical Analysis I |
3(3-1) |
Numerical Analysis II |
3(3-1) |
|
Elective |
3(3-1) |
or Thesis |
9 Credits |
|
Total |
21 Credits |
Total |
18 Credits |
|
YEAR FOUR – Applied Mathematics |
|||
|
Semester One |
Semester Two |
||
|
Basic Requirements |
Basic Requirements |
||
|
Probability I |
3(3-1) |
Probability II |
3(3-1) |
|
Integration and Measure Theory I |
3(3-1) |
Integration and Measure Theory II |
3(3-1) |
|
Major Courses |
|
Major Courses |
|
|
Econometrics I |
3(3-1) |
Econometrics II |
3(3-1) |
|
Mathematics of Finance I |
3(3-1) |
Mathematics of Finance II |
3(3-1) |
|
Mathematical Modeling I |
3(3-1) |
Mathematical Modeling II |
3(3-1) |
|
Analytical Mechanics |
3(3-1) |
Mechanics of Materials and Fluids |
3(3-1) |
|
or Thesis |
9 credits |
||
|
Total |
18 Credits |
Total |
18 Credits |
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