Download M.Sc.Mathematics and Statitics

Master of Science (Mathematics and Statitics)
Degree Designation
Curriculum
M.Sc. (Mathematics and Statitics)
Plan A2
Structure
Required Courses
8
Elective Courses
12
not less than
Thesis
18
Total
38
Courses Description
Plan A2
Required Courses
8 Credits
322Linear Algebra and Applications
3(3-0-6)
501
Finite-dimensional vector spaces; linear
transformations; determinants; inner product
spaces;
eigenvalues and eigenvectors;
Jordan canonical forms; applications
346501
Probability Theory
3(3-0-6)
Axiomatic treatment of probability;
random
variables
and
distributions;
expectation; joint distribution; distributions of
functions of random variables; convergence
of random variables; central limit theorem;
markov chain
322691
Seminar I
Individual
study
in
Mathematics
or
1(0-2-1)
Statistics to get the skills and experiences
with a presentation on the topic for discussion
322692
Seminar II
1(0-2-1)
Individual study in Mathematics or
Statistics to get the skills and experiences
with a presentation on the topic for
discussion, more advanced than 322-691
Elective Courses
12Credits
322Mathematical and Statistical Modelling
3(3-0-6)
502
General background in mathematics and
statistics to construct models for problems
arising from physical sciences, life sciences
and
economics;
meaning,
importance,
connection and difference of mathematical
and statistical modelling; modelling based on
differential
equations;
normal
regression,
Poisson regression and binomial regression;
model analysis; model checking; computer
software applications
322511
Abstract Algebra I
3(3-0-6)
Groups; group actions; Sylow theorems;
rings; ideals; integral
domains; principal ideal domains; unique
factorization domains; polynomial rings; fields
322512
Abstract Algebra II
Extension fields; Galois theory
3(3-0-6)
522513
Analytic Number Theory
Arithmetic
functions;
3(3-0-6)
elementary
theorems on the distributions of
primes;
Dirichlet series and the Euler products
522514
3(3-0-6)
Algebraic Semigroup Theory
Semigroups;
subemigroups;
ideals;
homomorphisms; transformation semigroups;
simple semigroups; 0-simple semigroups;
regular
semigroups;
inverse
semigroups;
congruences; quotient semigroups; Green’s
relations; generalizations of semigroups
322515
Algebraic Number Theory
Number
fields;
quadratic
cyclotomic
fields;
Dedekind
3(3-0-6)
fields;
domains;
factoring of prime ideals in extensions; ideal
class group; unit group; factoring of prime
ideals in Galois extensions
322521
Functional Analysis
3(3-0-6)
Metric spaces; normed spaces; inner
product spaces; fundamental theorems on
normed spaces
322522
Real Analysis
3(3-0-6)
Lebesgue measure; Lebesgue integral;
differentiation and integration
322523
Complex Analysis
3(3-0-6)
Analytic
functions;
integration;
sequences and series; residue and poles;
normal families
322524
General Topology
3(3-0-6)
Set theory and logic; topological spaces
and continuous functions; connectedness and
compactness; countability and separation
axioms
322533
Wavelet Theory (Prerequisite 322-501 or by 3(3-0-6)
the Program Committee approval)
Continuous wavelet transform; discrete
wavelet transform; multiresolution analysis
322541
Differential Equations
3(3-0-6)
Differential Equations and solutions;
modelling via differential equations; analytic
method; numerical method; phase plane and
qualitative solutions; linear and nonlinear
systems; Laplace transformation
322542
Partial Differential Equations (Prerequisite 3(3-0-6)
322-541 or by the Program Committee
approval)
Partial differential equations; parabolictype problem; hyperbolic-type problems;
elliptic-type
problem;
numerical
and
approximate methods
322543
Introduction to Optimization Theory
3(3-0-6)
Basic linear algebra; multivariable
calculus; one-dimensional search methods;
gradient
methods;
Newton’s
method;
conjugate direction methods; quasi-Newton
methods; convex optimization
322544
Numerical Analysis and Applications
3(3-0-6)
Linear equation systems; approximation
of eigenvalues and eigenvectors; numerical methods for ordina
322545
Numerical Linear Algebra
3(3-0-6)
Review of matrix theory and linear
systems; direct methods for linear systems;
linear
least
methods
for
square
solving
problems;
iterative
linear
systems;
eigenvalue problems
322-
Advanced Differential Equations (Prerequisite 3(3-0-6)
546
322-541 or by the Program Committee
approval)
Existence and uniqueness of solutions;
linear systems; boundary value problems;
stability;
perturbation
of
linear
system;
periodic solutions of system
322547
Inverse Problems (Prerequisite 322-521 and 3(3-0-6)
322-544 or by the Program Committee
approval)
Linear operator equation; regularization
operators; continuous regularized methods;
Tikhonov
regularization;
iterative
regularization methods
322548
Linear Programming
3(3-0-6)
The history of linear programming and
its
applications;
two-dimensional
linear
programming; convex polyhedra; standard
form; basic solutions and their properties;
geometric
view
of
linear
programming;
simplex mothod; duality; sensitivity analysis;
nonsimplex method.
322551
Graph Theory
3(3-0-6)
Graphs; digraphs; trees; networks;
connectivity and matching; planar graphs;
colouring and covering; graph labeling and
graph decompositions
322552
Combinatorial Designs
3(3-0-6)
Selected topics from design theory; latin
squares; finite geometries; finite fields; error
correcting codes; other related topics
322571
Communications
in
Mathematics
and 1(0-2-1)
Statistics
Techniques of written and oral
communications emphasizing on writing up
and presenting a dissertation in mathematics
and statistics
322581
Special Topics in Mathematics
3(3-0-6)
Special interesting topics in Mathematics
or applied Mathematics
346502
Mathematical Statistics (Prerequisite 346- 3(3-0-6)
501)
Basic concept of mathematical statistics
and inference; random samples and sampling
distributions; properties of point estimators;
methods of finding point estimators; minimum
variance and unbiased estimators; minimum
variance bound and unbiased estimators;
interval estimation; hypothesis testing and
methods of finding test statistics; basic
concept of linear models and generalized
linear models
346521
Analysis of Advanced Statistical Models 3(3-0-6)
(Prerequisite 346-502)
Definition of a statistical model;
generalized linear models; likelihood function
and parameter estimation; models for
continuous data; model for binomial data;
model for Poisson data; models for negative
binomial data; models for zero-inflated
Poisson data; computer software applications
346522
Sampling Techniques (Prerequisite 346-501) 3(3-0-6)
Simple random sampling; systematic
sampling; stratified sampling; single stage
cluster
sampling;
multi-stage
cluster
sampling; other sampling and estimation
methods; computer software applications
346531
Applied Multivariate Analysis (Prerequisite 3(3-0-6)
346-502)
Aspects of multivariate analysis; the
multivariate normal distribution; comparisons
of several multivariate means; multivariate
regression; discrimination and classification;
path analysis; cluster analysis; principal
component
analysis;
factor
analysis;
canonical correlation analysis; computer
software applications
346532
Experimental Designs (Prerequisite 346-502) 3(3-0-6)
Introduction; design and analysis of
single-factor
experiments;
single-factor
experiments having repeated measures on
the same elements; design and analysis of
factorial experiments; factorial experiments in
which some of the interactions are
confounded; Latin Squares and related
designs; analysis of covariance; repeated
measurement;
computer
software
applications
346533
Forecasting Techniques (Prerequisite 346- 3(3-0-6)
501)
Introduction to forecasting; time series;
smoothing techniques; regression analysis;
adaptive filtering; Box-Jenkins method; case
study; computer software applications
346534
Statistical Decision Theory (Prerequisite 346- 3(3-0-6)
501)
Review of probability; basic concepts of
decision
problems;
analysis;
elementary
continuous-variable
decision
decision
problems; sufficient statistics and conjugate
distributions; multivariate normal process;
sequential decision problems
346535
Research Methodology (Prerequisite 346- 3(3-0-6)
522)
Meaning and type of research; research
methodology; problem identification; literature
review; research designs; data collection;
data management and data processing; data
analysis and interpretation; report writing;
proposal writing; ethic of researchers;
computer software applications
346536
Survival Analysis (Prerequisite 346-501)
3(3-0-6)
Functions of survival time; nonparametric methods of estimating; survival
functions;
non-parametric
methods
for
comparing survival distributions; some wellknown
survival
applications;
comparing
distributions
parametric
two
and
methods
survival
their
for
distributions;
identification of prognostic factors related to
survival time
346541
Operations Research (Prerequisite 346-501) 3(3-0-6)
Operations research and its applications;
linear
dynamic
programming;
programming;
network
inventory
analysis;
control;
queuing theory; Markovian decision process;
computer software applications
346-
Simulation Techniques (Prerequisite 346-541) 3(3-0-6)
542
Principle and concept of simulation;
concepts in discrete-event; random number
generator; random events; monte-carlo
simulation; simulation examples; verification
and validation of simulation; output analysis;
comparison and evaluation of alternative
system; computer software applications
346581
Special Topics in Statistics
Special interesting topics in Statistics
Thesis
3(3-0-6)
18
Credits
Thesis
Independent research work leading to
a thesis on a topic or topics in Mathematics or
Statistics approved by the thesis committee