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1. All courses are 3
credit hours each, unless otherwise indicated.
2. Normally, a course will
not be run without a minimum enrolment of students.
A
course designed for the non-specialist. The course treats fundamental
quantitative methods and how they are used in real life. For example,
straight
line graphs and their equations are applied to predictions (regression)
and
product mix (linear programming). Basic statistical measures and
concepts and
their practical use are given broad treatment.
MTH110:
College Algebra
Literal expressions,
variables, equations, factoring, laws of exponents, straight line
graphs, quadratic equations and parabolas.
MTH111:
Trigonometry and Analytic Geometry
Circular functions,
triangle relationships, identities, inverse trig functions, vectors,
complex numbers. Cartesian coordinates, equations of functions. Prerequisite:
MTH110 or equivalent.
MTH112:
Calculus I
Functions of a single
variable. Differential calculus: limits; continuity; the derivative and
applications; extrema; Integral Calculus: the definite integral;
fundamental theorem of calculus. Prerequisite: MTH111 or
equivalent.
Further
integration: indefinite integral; techniques and applications of
integration;
sequences, series, convergence tests, power series; parametric
equations; polar
coordinates; gradients. Prerequisite:MTH112 or equivalent.
MTH120:
Introductory Statistics
Measures of central
tendency and dispersion. Distributions: binomial and normal. Raw and
standard scores. Correlation and Regression. Price indices and seasonal
adjustment. Sampling: confidence intervals and hypothesis testing. Prerequisite:
MTH110 or permission of the instructor.
Operations
with sets: Venn diagrams, fuzzy sets. Boolean algebras. Symbolic Logic:
truth
tables, conjunction and disjunction; Aristotelian and fuzzy logics.
Nature of
proof: deduction and induction; proof by mathematical induction. Prerequisite:
MTH111 or instructor’s consent.
MTH214:
Calculus of Several Variables
Partial
differentiation, Maxima and minima of functions of several variables,
the
Jacobian matrix, and integral theorems of vector calculus. Multiple
integration. Line integrals. Prerequisite: MTH113.
MTH240:
Mathematics of Finance
Applications
of Mathematics to Business and Finance: compound interest, annuities,
present
value, repayment of loans, continuous compounding and exponential
growth.
Common and Natural Logarithms and their applications. Prerequisite:
MTH113
MTH250:
History of Mathematics
Development
of mathematics, emphasizing underlying principles and motivations. Prerequisite:
MTH113.
Rigorous
treatment of calculus of single and several variables. Topics include
topology
of the real line, uniform continuity, metric spaces, Riemann integral,
implicit
function theorem, and integral theorems of vector calculus. Prerequisites:
MTH113, MTH190, MTH343.
Mathematics
related to Physics: Vector, scalars, dot and cross products, vector
projections. Vector equations of lines and planes. Line integrals and
multiple
integration. Div, grad, curl. Green’s theorem. Stokes’ theorem. Prerequisite:
MTH214
Engineering
mathematics: Laplace transforms. Fourier series. Special functions:
Bessel
functions, Gamma function. Prerequisite: MTH214
MTH320:
Intermediate Statistics
Theory
of probability distributions, including Poisson, student’s t, and
F-distributions. Multiple regression techniques. Analysis of Variance:
degrees
of freedom, interaction, post-hoc tests. Chi-square analysis. Prerequisite:
MTH220
Permutations
and combinations. Sample spaces. Probability Distributions. Random
variables.
Conditional probability: probability trees, Bayesian anaylsis. Prerequisite:
MTH220.
Multiple
regression. Autocorrelation. Homoscedasticity. Factor analysis. Cluster
analysis. Applications to the social sciences. Prerequisite:
MTH320.
MTH323:
Applied Statistics for Social Science Research
Sampling
frames, questionnaire design; simple random, systematic, stratified,
and
cluster sampling methods, comparing domain means, contingency table
analysis. Prerequisites:
MTH220, MTH320
MTH330:
Mathematical Methods in Economics and the Social Sciences
Supply
and Demand functions, marginal supply, demand and revenue. Matrix
applications:
input-output models, stochastic matrices and Markov chains. Times
series
analysis. Cobb-Douglas production functions and their partial
derivatives. Prerequisites:
MTH214, MTH220.
MTH332:
Introduction to Complex Analysis
Complex algebra, analytic
functions, Cauchy-Riemann
equations, integration in the complex plane, Cauchy integral theorem,
infinite
series. Prerequisite: MTH214 or MTH316.
MTH334:
Ordinary Differential Equations
Methods
and theory of ordinary differential equations. Boundary conditions.
Power
series solutions. This course is recommended for science/engineering
students. Prerequisites:
MTH113 and MTH212 or MTH343.
MTH335:
Differential and Difference Equations
Concepts of Differential
Equations: general and particular solutions, linear equations,
separation of variables and other methods. Partial differential
equations. Introduction to power series solutions. Prerequisites:
MTH214, MTH330.
MTH336:
Introduction to Partial Differential Equations
Boundary
value problems; transform methods; Fourier series; Bessel functions.
Applications to heat transfer and fluid dynamics. Prerequisite:
MTH334.
Graphical
and simplex methods. Sensitivity analysis from simplex matrix. Integer
programming. Introduction to Game Theory.
MTH343:
Elementary Linear Algebra
Linear
systems, matrices, vectors and vector spaces, linear transformations,
determinants, inner product spaces, basis vectors, change-of-basis
matrices,
and eigenvectors. Prerequisite: MTH112 or MTH119.
Inventory
analysis: continuous and discrete models under risk and uncertainty.
Networks:
PERT networks, GANTT charts, critical path method. Queuing theory. Prerequisites:
MTH220, MTH214.
MTH362:
Survey of Geometry
Logical
structure of Euclidean, non-Euclidean, and finite geometries. Prerequisites:
MTH112, MTH190.
Groups:
abelian groups, normal subgroups, factor groups. Rings, fields, vector
spaces,
homomorphisms and isomorphisms, matrices, field extensions, etc. Prerequisites:
MTH190, MTH343
MTH401:
Advanced Topics in Mathematics.
This
course will vary according to the areas of specialization of
instructors.
Topics may include numerical methods, combinatorics, topology, number
theory,
advanced analysis, operators in Hilbert space, advanced probability,
and
advanced statistics.
MTH497:
Seminar in Mathematics (1-3 credits)
Topics
to be chosen from the special interests of instructors or of students. Prerequisite:
permission of the instructor.
MTH498:
Senior Research Thesis (1–3 credits)
Prerequisite: permission of the Dean
of the College of Science and Technology.
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DISCLAIMER:
THE UNIVERSITY OF CAMBODIA RESERVES THE RIGHT TO MAKE CHANGES TO THESE CATALOGS AS IT SEES FIT, SO THAT WE HAVE THE NECESSARY FLEXIBILITY IN AN EVER-EVOLVING WORLD. |
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