Department of Mathematical Sciences
The Department of Mathematical Sciences offers the degrees of Bachelor of Science (B.Sc.) in Pure Mathematics,
Industrial Mathematics, and Statistics. At the graduate level, it offers the
Master of Science (M.Sc.) and Ph.D. in Pure and Applied Mathematics and Pure
and Applied Statistics.
Research Activities
The
Department of Mathematical Sciences of Isfahan University of Technology (IUT),
founded in 1976, originally as a part of the Basic Science Department, started
its activities by offering general mathematical courses for engineering
students of the University. Due to rapid growth and effective attempts of the
faculty members, it turned to an independent department with specialists in Mathematics and Statistics.
The main research areas of the department are:
Algebra, Algebraic Geometry, Dynamical
Systems, Partial and Ordinary Differential Equations, Probability Theory, Stochastic
Processes, Numerical Analysis, Coding Theory, Optimal Control, Statistical Inference, Experimental Design,
Harmonic Analysis, Logic, Fuzzy Set Theory, Time Series Analysis, Linear
Models, Topology, Functional Analysis, Sampling Theory, Computational Geometry.
Algebra
The
main research topics of interest of faculty members of this group include: The
Theory of Rings, Homological Algebra, and Hopf Algebra. The studies of
categorical and homological aspects of non-commutative rings form the basis of
the ongoing research on the subject. In particular, Morita Theory provides a
basic tool in reflecting information between context equivalent rings. These
may be homological, ring theoretical or categorical in nature. Some related
properties such as localization in non-commutative settings; Hopficity and
dimension theories are also being investigated.
Finite
groups acting on rings by automorphisms, Lie algebras acting on algebras by
derivations, and group graded rings make Hopf Algebra H, acting on H-module
algebra. Involutions, centralizers, derivations, rings of quotients, and weakly
primitive rings are also areas of ring theory that some faculty members are
interested in.
Analysis
The
main research areas in this group are: Operator Theory, Schwartz Distribution
Theory in Functional Analysis and Measure Theory. Of particular interest is the
study of minimal prime ideals in normed rings, the structure of primary closed
ideals at infinity in Banach algebras, as well as the generalized Fourier
Transforms with applications in automatic continuity.
Numerical
Analysis
Numerical solution of models arising
from various natural phenomena has important role in physics and engineering.
The main research topic of interest to this group of faculty is numerical
solution of partial differential equations.
Some famous mesh dependent families of methods
for solving partial differential equations numerically are finite difference
methods, finite element methods, boundary element methods, finite volume methods,
etc. As another class of methods, meshless methods have been considered in
recent years.
Algebraic Geometry
Algebraic
geometry is studied in different aspects such as classical, modern and
arithmetical. The problem of resolution of singularities has been involved with
all of these branches of algebraic geometry.
The
existence of a regular model for arithmetic surfaces is known. Some people have
tried to find a desingularization for arithmetical three folds in some special
cases. The main interest of the group is to resolve the singularities of those
arithmetical three-folds which are a fiber product of two arithmetic surfaces.
The group is embarking on research to find a desingularization for arithmetical
three-folds.
Dynamical Systems and Differential
Equations
The
main research topics of interest to this group are the different aspects of
qualitative behavior in the system of nonlinear differential and difference
equations, specially local and global bifurcation of higher codimension and its
application to problems in engineering, biology and economics. Role of symmetry
in bifurcation, analysis of different routes to chaos via bifurcation theory,
bifurcation in large systems, partial differential equations and evolution
equations using center manifold theory are among other interests of the group.
Fuzzy Set Theory
The
main research topics in this field are: Arithmetic of Fuzzy Numbers, Fuzzy
Statistics and Fuzzy Probability (specially, testing fuzzy hypothesis and fuzzy
confidence intervals), Regression Analysis in Fuzzy Environment, and
Applications of Fuzzy Systems in Medical Sciences, Agriculture, and Textile
Engineering.
Mathematics Education
These
studies started with in-service
training programs for high
school teachers. Some research work has been carried out into lack of interest
among students in studying mathematics, mathematics competitions, curriculum
development, and methods of popularizing mathematics in society. The activities
carried out within mathematics education are World Mathematics in the year
2000, and participating in the establishment of research centers and societies
for teachers of mathematics in different provinces.
Probability Theory
Probabilistic Number Theory, Stochastic Processes,
and Random Number Generators, 
- Stable Processes and Probabilistic Geometry form the main research topics in this area. The study of
asymptotic local and cumulative distribution of additive and multiplicative
arithmetic functions with applications in computer sciences, study of Zeta
distribution with applications in number theory and the study of the rare
events are the main interests for faculty members of this group. Some are also interested in research on
stable processes and Gaussian processes.
Statistical Inference
Research
in this area mainly concerns statistical inference with emphasis on Bayesian
and non-Bayesian approaches to statistical inference, statistical inference in
non-precise (fuzzy) environments, and inference in linear models.
Generalized Linear Mixed Models (GLMM)
GLMM
unifies estimation and inference approaches for both continuous and discrete
response data. The themes of interest in the research activities are as
follows: estimation of variance components in regression models with
restriction on the random components for continuous response data; estimation
and inference of variance components, parameters of regression models for
different types of discrete response data (ordinal, nominal, etc.) and survival
times; and power and dropout rates studies as well as their extension to
multivariate response data for the above models.
Coding Theory
Efficient
transmission of data through a noisy channel is addressed in the theory of
Error Correcting Codes. A data sequence of length k is extended to a length
n>k sequence. There is an extra cost for the transmission of n-k added bits.
Therefore, given n and k, a key problem is the construction of code C of length
n and dimension k with the largest minimum distance d. The construction of both
hard-decision and soft-decision decoding algorithms is the other main problem
in the theory of Error Correcting Codes.
UNDERGRADUATE
PROGRAM
Undergraduate
students must take 20 credits in general courses, 61, 61 and 30 credits in
basic courses, 36, 39 and 76 credits in core courses and 15, 15 and 6 credits
in elective courses (total 132, 135, 132 credits) to obtain B.Sc. in Pure
Mathematics, Industrial Mathematics and
Statistics, respectively.
UNDERGRADUATE COURSES
Curriculum for the
Degree of Bachelor of Science in Mathematics: Pure Mathematics
Semester I (Fall)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Calculus I |
4 |
|
|
General Physics I |
3 |
|
|
General Physics Lab I |
1 |
|
|
English I For Science |
3 |
|
|
General Courses |
4 |
Semester
II (Spring)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Calculus II |
4 |
|
|
Foundation of Mathematics |
4 |
|
|
Fundamentals of Computer Programming |
4 |
|
|
General Physics II |
3 |
|
|
General Physics Lab II |
1 |
|
|
General Courses |
2 |
Semester III (Fall)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Elementary Differential Equation |
3 |
|
|
Probability I |
3 |
|
|
Linear Algebra |
4 |
|
|
Mathematical Analysis I |
4 |
|
|
General Physics (Waves) |
3 |
|
|
General Courses |
2 |
Semester IV (Spring)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Algebra I |
4 |
|
|
Mathematical Analysis II |
4 |
|
|
Probability II |
3 |
|
|
Elementary Partial Differential Equation |
2 |
|
|
General Courses |
3 |
Semester V (Fall)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Discrete Mathematics |
4 |
|
|
Mathematical Analysis III |
4 |
|
|
Numerical Analysis I |
4 |
|
|
Algebra II |
4 |
|
|
General Courses |
2 |
Semester VI (Spring)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Algebra III |
4 |
|
|
Mathematics Software |
2 |
|
|
Number Theory |
4 |
|
|
Introduction to Ordinary Differential Equations |
4 |
|
|
General Courses |
|
Semester VII (Fall)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Complex Variable |
4 |
|
|
Topology |
4 |
|
|
Differential Geometry |
4 |
|
|
Elective |
4 |
|
|
General Courses |
2 |
Semester VIII (Spring)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Introductory Algebraic Geometry |
4 |
|
|
Elective |
7 |
Curriculum for the Degree of Bachelor of
Science in Mathematics: Industrial Mathematics
Semester I (Fall)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Calculus I |
4 |
|
|
General Physics I |
3 |
|
|
General Physics Lab I |
1 |
|
|
English I for Science |
3 |
|
|
General Courses |
4 |
|
|
Calculus Lab I |
1 |
Semester
II (Spring)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Calculus II |
4 |
|
|
Calculus Lab II |
1 |
|
|
Differential Equations |
3 |
|
|
General Physics II |
2 |
|
|
General Physics Lab II |
1 |
|
|
Probability
I |
3 |
|
|
General Courses |
2 |
Semester III (Fall)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Fundamentals of Computer Programming |
3 |
|
|
Probability II |
3 |
|
|
Statistical Methods |
3 |
|
|
Mathematical Analysis I |
4 |
|
|
General Courses |
3 |
Semester IV (Spring)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Applied Algebra |
3 |
|
|
Applied Linear Algebra |
3 |
|
|
Discrete Mathematics |
3 |
|
|
Elementary Partial Differential Equation |
3 |
|
|
Stochastic Processes |
3 |
|
|
General Courses |
2 |
Semester V (Fall)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Introduction to Ordinary Differential Equations |
3 |
|
|
Statistical Quality Control |
3 |
|
|
Numerical Analysis I |
4 |
|
|
Advanced Computer Programming |
3 |
|
|
Elective |
3 |
|
|
General Courses |
2 |
Semester VI (Spring)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Mathematical Modeling |
3 |
|
|
Numerical Linear Algebra |
3 |
|
|
Statistical Simulation |
3 |
|
|
Engineering Economy |
3 |
|
|
Operational Research I |
3 |
|
|
Project |
3 |
Semester VII (Fall)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Industrial Projects Control |
3 |
|
|
Elementary Econometrics |
3 |
|
|
Operation Research II |
3 |
|
|
Elective |
6 |
|
|
General Courses |
2 |
Semester VIII (Spring)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Elective |
17 |
Curriculum for the Degree of Bachelor of Science in Statistics
Semester I (Fall)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Elementary Probability and Statistics |
3 |
|
|
Calculus I |
4 |
|
|
English I For Science |
3 |
|
|
General Courses |
6 |
Semester
II (Spring)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Probability I |
3 |
|
|
Calculus II |
4 |
|
|
Fundamentals of Computer Programming |
4 |
|
|
Foundation of Economics |
4 |
|
|
General Courses |
2 |
Semester III (Fall)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Statistical Methods |
3 |
|
|
Probability II |
3 |
|
|
Foundation of Mathematics |
4 |
|
|
Elementary Differential Equations |
3 |
|
|
General Courses |
2 |
Semester IV (Spring)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Mathematical Statistics I |
3 |
|
|
Sampling Methods I |
3 |
|
|
Applied Linear Algebra |
3 |
|
|
Numerical Methods |
2 |
|
|
Mathematical Analysis I |
4 |
|
|
General Courses |
2 |
Semester V (Fall)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Mathematical Statistics II |
3 |
|
|
Sampling Methods II |
3 |
|
|
Stochastic Processes |
3 |
|
|
Regression |
3 |
|
|
Foundation of Demography |
3 |
|
|
General Courses |
|
Semester VI (Spring)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Design and Analysis of Experiments I |
3 |
|
|
Multivariate Statistical Methods I |
3 |
|
|
Nonparametric Methods |
3 |
|
|
Time Series |
3 |
|
|
Foundation of Sociology |
3 |
Semester VII (Fall)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Design and Analysis of Experiments II |
3 |
|
|
Computational Statistics |
3 |
|
|
Multivariate Statistical Methods II |
3 |
|
|
Statistical Quality Control |
3 |
|
|
General Courses |
2 |
Semester VIII (Spring)
|
COURSE CODE |
COURSE TITLE |
CREDITS |
|
|
Training |
2 |
|
|
Elective |
7 |
|
|
General Courses |
2 |
UNDERGRADUATE COURSE DESCRIPTIONS
19101 Calculus I 4 Cr.
Study of single variable calculus, numerical sequences, limits, continuity
differentiation, extreme function values, the definite integrals, applications
of the definite integrals, Inverse functions, logarithmic and exponential
functions, inverse trigonometric and hyperbolic functions, techniques of
integration, indeterminate forms, improper integrals,
Prerequisite: Precalculus
19102 Calculus II
4 Cr. Study of several variable calculus: Euclidean
geometry matrices, linear transformation, elementary topology of 
, limits, derivative as linear operator, directional and
partial derivatives, extreme function values, Lagrange multiplier,
multivariable and iterated integrals, change of variable theorem, parametric
curves and surfaces, line integral, surface integral, vector analysis, green
stokes and divergence theorem.
Prerequisite: Calculus I 19101
19104
Foundation of Mathematics 4
Cr. Introduction to logic, concept
of sets, relations, functions, Cartesian products, countable sets, cardinal
number, Schrowder-Bernstein cantor's theorems. axiom of choice, Zorn's lemma,
construction of numbers: natural numbers, integers, rational and real numbers
by set theory approach.
Prerequisite: Calculus I 19101
19114
Algebra I 4 Cr. Groups and elementary properties,
homomorphisms rings, fields, integral do-mains and their elementary properties
P.I. and V.F. domains, finite fields.
Prerequisite: Linear Algebra 19117
19115
Mathematical Analysis I 4 Cr. The real and complex number systems, basic
topology, numerical sequences and series, continuity, differentiation.
Prerequisite: Calculus II 19102; Foundation of Mathematics 19104
19116
Mathematical Analysis II 4 Cr. The Riemann-Stieltjes integral, sequences
and series of functions, some special-functions.
Prerequisite: Mathematical Analysis I 19115
19117
Linear Algebra I 4 Cr. Vector spaces. Basis, dimensions. Gram-Schmidt
process, projections, linear transformations, isomorphism, change of basis.
Eigen values and Eigen vectors, Diagonalizations, Jordon canonical forms, Hermition
matrices, exponential of a matrix.
Prerequisite: Calculus II 19102
19201 Elementary Differential Equations 3 Cr.
Methods of solving especial classes of
ordinary differential equation including linear, Bernoulli, separable and exact
first order equation, reduction of order, variation of parameter, undetermined
coefficients, power series methods, and
Prerequisite: Calculus I 19101; Calculus II 19102
19204 Elementary Partial Differential Equations 2 Cr. Fourier series, Fourier transformation and
it's applications, introduction and classification of P.D.E. of types
hyperbolic, parabolic and elliptic, separation of variables and Fourier
transform method for solving homogeneous and nonhomogeneous heat conduction
& vibrating string and Dirichlet problems, Sturm Lioville theorems and
eigenvalue problems, canonical forms and D'Alembert's solution of wave
equations.
Prerequisite: Elementary Differential Equation 19201
19301
Numerical Methods 2 Cr. Error analysis, solving nonlinear equations,
solving systems of linear and nonlinear equations, interpolation, numerical
differentiation and integrations, solving ordinary differential equations.
Prerequisite: Calculus II 19102; Elementary Differential Equation 19201
19321
Complex Variables 4 Cr. Complex numbers and their geometrical
representation, functions, mappings, limits, derivative, Cauchy-Riemann
conditions, elementary functions and their mapping, integration, Cauchy's
theorem, indefinite integrals, Cauchy's integral formula, Morera's and Liouville
theorem, power series, Laurant series, residues theorem, evaluation of certain
types of real integrals, conformal mapping. Prerequisite: Mathematical Analysis I 19115
19333
Numerical Analysis I 4 Cr. Error in arithmetic operations & computational
methods, solution of nonlinear equations, interpolation, approximation theory,
numerical differentiation, numerical integration, solution of ordinary
differential equations.
Prerequisite: Elementary Differential Equation 19201;
18101
19334
Numerical Analysis II 4 Cr. Solution of linear simultaneous
equations, gauss elimination, other direct methods iteration methods, solution
of nonlinear simultaneous equations, least square approximation, eigenvalues
and eigenvectors, solution of partial differential equations, finite elements
method and iteration methods.
Prerequisite: Numerical Analysis I 19333; Elementary
P.D.E. 19204
19340
Discrete Mathematics 4 Cr. Fundamental principles of counting,
relations and functions, languages, finite state machine, principles of
inclusion and exclusion, generating functions, recurrence relations,
introduction to graph theory.
Prerequisite: Foundation of Mathematics 19104; 18101
19402
Number Theory 4 Cr. Solutions of congruencies, congruencies of
higher degree quadratic residues, quadratic reciprocity.
Prerequisite: Foundation of Mathematics 19104
19405
Introductory Algebraic Geometry
4 Cr. Plane conics, cubics and
the group law, curves and their genus, the category of affine varieties,
Affine varieties and the null stellensatz, functions on varieties, projective
and binational geometry, tangent space, tangent cone, singularity, dimension,
lines on a cubic surface, an introduction to spectrum of a ring and structure
sheaf.
Prerequisite: Algebra I 19114
19431 Algebra II 4 Cr. Action of a group on a set, Sylow theorem UFD property, free
modules, modules over PI domains, splitting fields of polynomials, normal
extension galois theorem.
Prerequisite: Algebra I 19114
19438
Algebra III 4 Cr. Torsion modules, invariance theorem,
applications to Abelian groups and linear transformations (rational and
Prerequisite: Algebra II 19431
19440
Introduction to Ordinary Differential Equations
4 Cr. Linear systems,
exponentials of operators, stability. The existence-uniqueness theorem for
systems of ordinary differential equations, dependence on initial conditions
and parameters, the maximal interval of existence, the flow defined by a
differential equations, linearization, stable and unstable manifold theorem,
Hartman-Grobman theorem, stability and Liapunov functions, gradient and
Hamiltonian systems. The Poincare Bendixson theory in R2, Bendixson criteria.
Prerequisite: Mathematical Analysis I
19115; Linear Algebra 19117; Elementary Differential Equation 19201
19441
Topology I 4 Cr. Topological spaces and continuous
functions, connectedness and compactness, countability and separation axioms:
the countability axioms, the separation axioms, the Urysohn lemma, the Urysohn
metrization theorem, the Tychonoff theorem, the Stone-Cech compactification. Prerequisite: Mathematical Analysis I 19115
19443
Mathematical Analysis III 4
Cr. The derivative of functions of
several variables, the Chain Rule, partial derivatives, the inverse function
theorem, the implicit function theorem, the rank theorem, extremum problems
with side conditions, Lagrange's theorem: multiple and iterated integrals for
functions of several variables, Fubini's theorem, change of variables in
multiple intergrals, differential forms and related theorems, simplexes and
chains, Stoke's theorem, closed forms, exact forms and their applications in
vector analysis.
Prerequisite: Mathematical Analysis II 19116
19506
Foundation of Demography 3
Cr. Introduction, source of data on
population, structure of population, factors in population dynamics, population
growth and population policy.
Prerequisite: Sampling Methods 19530
19510
Probability & Statistics 3 Cr. Descriptive statistics, counting rules,
introducing concepts of probability, conditional probability, Bayes theorem,
random variables with emphasis on discrete cases, probability function &
distribution function, conditional probability function, standard discrete
distributions, sum of two independent random variables.
19511
Statistical Methods 3 Cr. An introduction to data analysis, point
estimation, confidence intervals, testing statistical hypotheses, simple linear
regression analysis, one-way analysis of variance, two-way analysis of
variance, contingency tables.
Prerequisite: Probability I 19513
19513
Probability I 3 Cr. Probability models, axioms, theorems and
interpretations related to probability functions, counting techniques,
conditional probability, Bayes' formula, independent events, random variables,
C.D.F. Discrete case, mathematical expectations, and standard discrete
distributions.
Prerequisite: Calculus I 19101; Probability &
Statistics 19510
19514
Probability II 3 Cr. Continuous case, P.D.F., standard
continuous distributions moments, DeMoivre-Laplace theorem, bivariate case,
functions of R.V.'s, conditional distributions, order statistics, M.G.F.,
L.L.N., and C.L.T.
Prerequisite: Calculus II 19102; Probability I 19513
19518
Mathematical Statistics I 3
Cr. Aspects of estimation,
partitions, sufficiency, minimal sufficiency, completeness and bounded
completeness, methods of estimation including method of moments & maximum
likelihood method, unbiased estimation, minimum variance unbiased estimators,
Cramer-Rao inequality, efficiency & consistency, introducing Bayes estimation.
Prerequisite: Statistical Methods 19511; Probability II 19514
19519
Mathematical Statistics II 3
Cr. Aspects of statistical
hypothesis testing, simple vs simple tests, most powerful tests, likelihood
ratio tests, composite vs. composite tests, uniformly most powerful tests,
generalized likelihood ratio test, sequential probability ratio test,
categorical data analysis, contingency tables. Prerequisite: Mathematical Statistics I 19518
19524
Time Series 3Cr. Stationary and weakly stationary
processes, trends, seasonal variation, MA and AR processes, alternative
representations of AR and MA processes, ARMA
processes, Nonstationary time series, Forecasting spectral theory of
time series.
Prerequisite: Mathematical Statistics I 19518
19530 Sampling Methods I 3 Cr. Introduction to
sampling and census; some basic concepts in sampling; random and non-random
sampling; simple random and stratify sampling for mean, proportion's and
ratio's and estimating sample size for above characteristics.
Prerequisite: Mathematical Statistics I 19518
19531 Sampling Methods II 3 Cr. Simple random and
stratify sampling for ratio's in details, regression estimating; cluster
sampling for mean and proportion's, systematic sampling, two stage simple
random-sampling.
Prerequisite: Sampling Methods I 19530
19540 Nonparametric Statistics 3 Cr.
Aspects of nonparametric, p-th quantile estimation and confidence interval,
sign test, McNemar test, Cox and Stewart test, goodness of fit tests,
Mann-Whitney test, Kruscal-Wallis test, Spearman's
Prerequisite: Statistical Methods 19511; Probability II 19514
19544
Statistical Quality Control
3 Cr. Aspects of quality
control, history of quality improvement, TQM, seven magnificent rules, control
charts for variables, control charts for attributes, acceptance sampling.
Prerequisite: Sampling Methods I 19530; Statistical
Methods 19511
19553
Design and Analysis of Experiments I
3 Cr. Aspects of design and analysis of experiments, analysis of
variance and comparison of means. Completely randomized design, complete block
design, incomplete block designs, latin squares, Greeco latin. Youden square,
General Factorial Experiments. Prerequisite: Regression 19562
19554
Design and Analysis of Experiments II
3 Cr. 2k and 3k
factorial experiments, confounding, fractional replications, nested designs,
multifactor experiments with randomization restrictions, split plot designs,
analysis of covariance.
Prerequisite: Design and Analysis of Experiments I 19553
19562
Regression 3 Cr. Aspects of regression analysis,
straight-line regression analysis, sample correlation coefficient and the
straight-line regression analysis, ANOVA table for simple linear regression,
examination of residuals, multiple regression analysis, ANOVA table for
multiple regression analysis, partial & multiple correlation coefficients,
interaction in regression analysis, colinearity, polynomial regression,
lack-of-fit test, orthogonal polynomials.
Prerequisite: Linear Algebra 19117; Mathematical Statistics I 19518
19570
Multivariate Statistical Methods I 3
Cr. Multivariate distribution
theory, sampling from a Multivariate Normal Distribution and maximum likelihood
estimation, Wishart distribution, inferences about a mean vector (generalized
likelihood ratio test), confidence regions of the mean vector, simultaneous
confidence intervals, comparison of several multivariate means, multivariate
linear regression models.
Prerequisite: Mathematical Statistics I 19518
19571
Multivariate Statistical Methods II 4
Cr. Principal component analysis,
factor analysis, canonical correlation analysis, discrimination and
classification, cluster analysis.
Prerequisite: Multivariate Statistical Methods I 19570
19581
Stochastic Processes 3 Cr. Markov Chains, the basic limit theorems,
Random Variables, Branching process, Markov Chains with discrete states in
continuous time including Poisson and Birth and Death processes, Renewal
processes.
Prerequisite: Probability II; Elementary
Differential Equations
GRADUATE PROGRAM
The
Department of Mathematical Sciences offers the degrees of Master of Science (M.Sc.) and the degree of Doctor of Philosophy
(PhD) in Pure Mathematics, Applied Mathematics,
Mathematical Statistics and Applied Statistics. It has more than 200
M.Sc. students and more than 50 Ph.D. students in about 20 fields of study in
Mathematical Sciences.
M.Sc. Program
M.Sc. students
must take 12 credits in their field of study from Table 1, and 8 credits in his or her required courses from
Table 2, Seminar (2 credits) and Thesis (6 credits), totally 28 credits to
obtain M.Sc. degree.
Ph.D. Program
Ph.D.
students according to their field of study should take 16 credits from graduate
courses (at least two courses in their field of study and one course in another
field). After passing the education comprehensive exam, they will take a 20
credits research project and will start their research period. After six
months, they must pass the research comprehensive exam, and then continue their
works to complete their PhD Thesis in Mathematics.
GRADUATE COURSES
Curriculum for the Degree of Master of Science (M.Sc.) in
Mathematics
|
Basic Courses : |
|
|
|
******************* Table I ******************* |
|
|
Pure Mathematics (Analysis): |
|
|
Fourier Analysis |
|
|
Functional Analysis |
|
|
Harmonic Analysis |
|
|
Complex Analysis |
|
|
Operator Theory |
|
|
Real Analysis |
|
|
Topology |
|
|
|
|
|
Pure Mathematics (Algebra): |
|
|
Advanced Algebra |
|
|
Commutative Algebra |
|
|
Group Theory |
|
|
Homological Algebra |
|
|
Module Theory |
|
|
Ring Theory |
|
|
|
|
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Pure Mathematics (Geometry): |
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Algebraic Topology |
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Algebraic Geometry |
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Computational Algebraic Geometry |
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Differential Manifolds |
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Projective Geometry |
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Applied Mathematics (Continuous &
Discrete): |
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Advanced Graph Theory |
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Advanced Numerical Analysis |
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Combinatorial Analysis |
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Dynamical Systems |
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Information Theory |
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Optimization |
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Elective Courses : |
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******************* Table II ******************* |
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Abstract Harmonic Analysis |
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Applied Functional
Analysis |
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Amenability |
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Banach Algebras |
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C*-algebras |
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Representation Theory |
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Several Variable Complex Analysis |
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Topological Groups |
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Theory of Ordinary Differential Equations |
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Partial Differential Equations |
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Coding Theory |
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Special Topics |
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Mathematical Logic |
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Set Theory |
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Fuzzy Set and Fuzzy Logic |
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Model Theory |
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Spectral Graph Theory |
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Algebraic Graph Theory |
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Category Theory |
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Algebraic Number Theory |
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Theory of Finite Groups |
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Infinite Groups |
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Group Representation Theory |
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Vector Boundls |
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Lie Groups and Lie Algebras |
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Topics in Analysis |
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Topics in Dynamical Systems |
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Topics in Operator Theory |
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Topics in K-Algebra |
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…………. |
Curriculum for the Degree of Master of Science (M.Sc.) in
Statistics,
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Basic Courses : |
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******************* Table I ******************* |
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Mathematical
Statistic: |
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Real Analysis |
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Statistical Inference I |
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Statistical Inference II |
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Probability Theory |
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Applied
Statistic: |
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Linear Models |
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Statistical Inference I |
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Statistical Inference II |
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Advanced Multivariate Methods |
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Elective Courses : |
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******************* Table II ******************* |
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Multivariate Statistical Analysis |
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Generalized Linear Models |
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Signal Processing |
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Topics in Fuzzy Probability
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Stochastic Processes |
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Time Series |
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Decision Theory |
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Queuing Theory |
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Sampling Theory |
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Special Topics |
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Sequential Analysis |
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Topics in Fuzzy Statistic |
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Theory of Reliability |
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Advanced Nonparametric Inference |
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………. |