Bachelor of Mathematics
Department of Mathematics is one of the main departments in the Faculty of Science and Technology since its establishment in 1979. Since its inception, the Department of Mathematics has been considered as a diverse community of competencies devoted to excellence in teaching and scientific research in the Variety fields of mathematics and statistics.One of the most important objectives of the Department of Mathematics at Al-Quds University is to lay down the solid foundation for building a society in which the science and technology play a major role, through the provision of qualified teachers equipped with modern educational methods and a broad base of information and by providing it by qualified experts to work in both private and public sectors.
Department of Mathematics is awarded a bachelor’s degree in mathematics(Full mathematics major, Mathematics major with a minor program, Minor in mathematics, Minor in statistics) and a master’s degree in mathematics as well. In addition, the department offers courses in mathematics and statistics to meet the needs of other programs at AQUUniversity.
The Mathematics Department offers many courses in mathematics and statistics, including real analysis, numerical analysis, complex analysis, abstract and linear algebra, applied mathematics, ordinary differential equations, partial differential equations, integral equations, Euclidean geometry, logic, number theory, numerical methods In differential equations, partial differential equations and integral equations, mathematical statistics, probability, comprehensive survey and sampling, applied and medical statistics, functional analysis and topology, as well as a number of elective courses covering interested topicsin pure mathematics, applied mathematics and statistics.
In addition to teaching, the members of the department council conduct research that contribute to the continuous development processes in the fields of the various mathematical sciences, which adopts the methodology of the survey that promotes the use of mathematics and statistics in various disciplines in engineering, medicine and other fields.
- Qualifying generations of mathematicians to work in various fields of mathematical sciences, both in public sectors (government) or private sectors (self-employment).
- Enhancing the methodology of logical thinking and survey studying as an approach of creativity and excellence depending on theestablished fact that mathematics is thinking and applying.
- Critical thinking
- Analytical thinking
- Quantitative reasoning
- Ability to manipulate precise and intricate ideas
- Construct logical arguments and expose illogical arguments
- Time management
- A Minimum score of % 65 in the Tawjihi
- Meeting the university’s general admissions requirements
The Bachelor of Mathematics program offers graduates the opportunity to work in the following fields:
- Public sector (eg. planning, central department of statistics, education, finance).
- Private sector (eg. banks, insurance, universities).
Department of mathematics offers the following programs:
1. Full mathematics major.
|Requirements for full major||59||27||86|
2. Mathematics major with a minor program.
|Requirements for mathematics major||59||59|
|Minor requirements||according to the other specialization plan||according to the other specialization plan||
3. Minor in mathematics for students majoring in other fields.
4. Minor in statistics for students majoring in mathematics.
5. Minor in statistics for students majoring in other specialization.
1. University Requirements (24 credit hours)
Students should complete the following courses (24 credit hours):
a. Compulsory University Requirements ( 18 credit hours )
|1||Arabic Language Skills||0400101||2|
|2||English Language Skills 1||0400108||2|
|3||English Language Skills 2||0400109||2|
|4||Jerusalem Throughout History||0400120||2|
|5||Palestine: Nature & Environment||0400121||2|
b. Elective University Requirements ( 6 credit hours ) may be chosen from the following list:
|1||Hebrew Language 1 ( Level 1 )||0400111||3|
|2||Hebrew Language 2 ( Level 2 )||0400112||3|
|3||French Language 1 ( Level 1 )||0400113||3||Or|
|4||French Language 2 ( Level 2 )||0400114||3|
|5||German Language 1 ( Level 1 )||0400115||3||Or|
|6||German Language 2 ( Level 2 )||0400116||3|
|7||Spanish Language 1 ( Level 1 )||0400117||3||Or|
|8||Spanish Language 2 ( Level 2 )||0400118||3|
|9||Turkish Language 1 ( Level 1 )||0400119||3||Or|
|10||Turkish Language 2 ( Level 2 )||0400129||3|
|11||Italian Language 1 ( Level 1 )||0400146||3||Or|
|12||Italian Language 2 ( Level 2 )||0400147||3|
|Any foreign language approved by the academic council||6|
Or the following list:
|Course Name||Course Number||Credit hours||Notes|
|1||Science and Life||0300142||3|
|3||Introduction to Music||0400131||3|
|5||Women and Men in Human Societies||0400133||3|
|6||Issues in Modern and Contemporary Arab thought||0400141||3|
|7||Internet for Special Purposes||0303100||3|
|8||Democracy, Human Rights and International Humanitarian Law||0500140||3|
|9||Conflict Resolution by Peaceful Means||0500143||3|
|10||Introduction to Public Health and Environment||0305100||3||Non–Science Students|
|11||Communication Skills||0403131||3||Non–Science Students|
|12||Introduction to Legal Thought||0500145||3||Non-law Students|
|13||History and Philosophy of Science||0409135||3|
2. Faculty Requirements (22 credit hours):
|Course Name||Course Number||Credit hours||Prerequisite|
|1||Introduction to Biology||0305101||3||1||4||—|
|2||Introduction to Physics||0302101||3||–||3||—|
|3||Introduction to Practical Physics||0302111||–||1||1||0302101 Or Altogether|
|4||Introduction to Computer Science||0303101||3||1||4|
|5||Introduction to Chemistry||0304101||3||–||3||—|
|6||Introduction to Practical Chemistry||0304103||–||1||1||0304101 Or Altogether|
|8||Introduction to Environment||0316101||3||–||3||—|
Full major in mathematics:
Total: 86 credit hours distributed as follows:
(I) Student must complete 59 credit hours listed in Table 1.
Table 1: Required Courses for Major in Mathematics (59 credit hours)
|3||Ordinary differential equations I||0306203||3||0306201|
|8||Applied Mathematics I||0306271||3||0306201|
|9||Linear Algebra I||0306281||3||0306102|
|10||Partial Differential Equations I||0306301||3||0306203|
|11||Real Analysis I||0306311||3||0306251|
|12||Complex Analysis I||0306312||3||0306201|
|15||Linear Algebra II||0306381||3||0306281|
|16||Abstract Algebra I||0306382||3||0306251|
|18||Real Analysis II||0306411||3||0306311|
|20||Abstract Algebra II||0306482||3||0306382|
(II) Elective Courses (27 credit hours) distributed as follows:
- 18 credit hours to be chosen from Mathematics courses of 200 level or above from Table 2.
- 3 credit hours to be chosen from courses of 200 level or above from the Computer Science department or the Physics department.
- 6 free courses.
|Course Name||Course Number||Credit hours||Prerequisite|
|7.||Sampling theory I||0306333||2||1||0306231|
|8.||Linear Regression Analysis||0306334||2||1||0306232 0306281|
|9.||Time Series Analysis I||0306335||2||1||0306232|
|10.||Analysis of Variance||0306336||2||1||0306232|
|11.||Statistical Methods for Insurance||0306337||3||0306232|
|12.||History of Mathematics||0306351||3||0306101|
|14.||Applied mathematics II||0306371||3||0306271|
|16.||Partial Differential Equations II||0306401||3||0306301|
|17.||Ordinary Differential Equations II||0306403||3||0306203|
|19.||Calculus of Variations||0306406||3||0306201|
|21.||Complex Analysis II||0306412||3||0306312|
|24.||Numerical Methods for Ordinary Differential Equations||0306421||3||0306203 0306321|
|25.||Numerical Methods for Partial Differential Equations||0306422||3||0306301 0306321|
|28.||Sampling Theory II||0306433||2||1||0306333|
|29.||Nonlinear Regression Analysis||0306434||2||1||0306334|
|30.||Times Series Analysis II||0306435||2||1||0306335|
|32.||Multivariate Statistical Analysis||0306437||2||1||0306232|
|34.||Categorical Data Analysis||0306439||2||1||0306232|
|35.||Foundation of Mathematics||0306451||3||0306251|
|38.||Algebraic Topology||0306464||3||0306382 0306462|
|39.||Numerical Methods in Linear Algebra||0306481||3||0306281|
|40.||Introduction to Galio Theory||0306484||3||0306382|
|41.||Special Topics||0306492||3||Department Content|
Major Mathematics / Minor in Statistics:
- Students must take the 59 credit hours listed above (Table 1) as required courses.
- The required courses for the minor in Statistics (18 credit hours) are given in Table 3
- The elective courses for the minor in Statistics (9 credit hours) are selected from
|Course Number||Credit hours||Prerequisite|
|5.||Sampling Theory I||0306333||2||1||0306231|
|6.||Linear Regression Analysis||0306334||2||1||0306232 0306281|
|Course Number||Credit hours||Prerequisite|
|2.||Time Series Analysis I||0306335||2||1||0306232|
|3.||Analysis of Variance||0306336||2||1||0306232|
|4.||Statistical Methods for Insurance||0306337||3||0306232|
|7.||Sampling Theory II||0306433||2||1||0306333|
|8.||Nonlinear Regression Analysis||0306434||2||1||0306334|
|9.||Time Series Analysis II||0306435||2||1||0306335|
|11.||Multivariate Statistical Analysis||0306437||2||1||0306232|
|13.||Categorical Data Analysis||0306439||2||1||0306232|
Minor in Statistics for Other Departments (27 credits):
(1) Required Courses (21 credits): listed in Table 5
|1.||Mathematic for Statistics||0306200||3||—|
|2.||Descriptive Statistics with Excel||0306206||2||1||0306200|
|3.||Statistical Inference||0306207||2||1||0306200 0306206|
|5.||Statistical Methods I||0306307||2||1||0306207|
|7.||Statistical Methods II||0306407||2||1||0306307|
(2) Elective courses (6 credit hours): selected form elective courses from student’s
major department from level 200 or above.
Minor in Mathematics (27 credit hours) distributed as follows:
(1) The required courses for the minor in Mathematics (18 credit hours) are given in
(2) The elective courses for the minor in Mathematics (9 credit hours) are selected
from Table 7.
|Course Number||Credit hours||Prerequisite|
|1.||Introduction to Statistics||0306131||2||1||0306101|
|3.||Applied Mathematics I||0306271||3||0306201|
|4.||Linear Algebra 1||0306281||3||0306102|
|5.||Complex Analysis I||0306312||3||0306201|
|7.||History of Mathematics||0306351||3||0306101|
|10.||Applied Mathematics II||0306371||3||0306271|
|12.||Linear Algebra II||0306381||3||0306281|
Course Description (Faculty Requirements):
0302101 Introductory Physics 3 credit hours
Measurements, motion, kinematics and dynamics, fluid dynamics, temperature and heat capacitors, current and resistance, direct current, geometrical optics and shadows, microscope, eye and vision.
0302111 Introduction to experimental Physics 1 credit hours
Energy and conservation of energy, linear momentum and collisions, rotation around a fixed axes, angular momentum, electric field, Gauss law, electric potential, magnetic field sources, electromagnetic induction, harmonic oscillatory motion, waves, interference and diffraction.
Prerequisite: 0302101 or Altogether
0303101 Introduction to Computer Science 4 credit hours
The aim of this course is to provide a comprehensive introduction on computer science. Binary numbers and formats, Hexadecimal notation, Conversion between binary and hexadecimal, Memory representation. Computer programming languages, Machine language, Assembly language, High level languages: compilation and interpretation Problem solving before programming. Analyze problems and devise algorithms to produce solutions to problems, a top down approach of Problem analysis .Implementing algorithms in the Java Object Oriented high level computer programming language. Data types, Variables, expressions, Input and output, Control structures, Arrays.
0304101 Introduction to general chemistry 3 credit hours
This course includes topics stoicheometric Determinations, structure of the atom, electronic configuration of the elements, gases, properties of solids, liquids and solutions, thermo-chemistry, and principles of chemical bonding.
0304103 Introduction to general chemistry laboratory 1 credit hours
The laboratory part includes experiments designed to develop skills in the use and handling of laboratory equipments. This course will cover twelve experiments discussed in chemistry 0304101.
Prerequisite: 0304101 or Altogether
0305101 Introduction to Biology 4 credit hours
Introductory topics related to living organisms, plant, animal and human. These topics Include: diversity of life, molecules of life, the cell, energy transformation processes, DNA and genetics, multi cellular organization and reproduction.
The laboratory part is designed to enrich the conceptual understanding of the topics addressed in the theoretical part; the experiments are designed to develop skills in the use and handling laboratory equipments and biological materials, as well as learning related techniques.
0306101 Calculus I 3 credit hours
Limits and continuity: rates of change and limits, limits involving infinity, continuity, tangent lines. Derivatives: the derivative as a function and as a rate of change, derivatives of products, quotients and negative powers, derivatives of trigonometric functions, the chain rule, implicit differentiation and related rates. Application of Derivatives: extreme values of functions, the mean value theorem and differential equations, curve sketching. Integration: Anti-derivatives, integral rules and integration by substitution, Riemann sums and definite integrals, substitution in definite integrals, the mean value and fundamental theorems of calculus. Application of Integrals: volumes by slicing and rotation about an axis, modeling volume using cylindrical shells, lengths of plane curves.
0316101 Introduction to Environmental Sciences 3 credit hours
This course is designed to introduce scientific principles and problem solving techniques used to evaluate the effects of human activities on the Environment. Topics will include the sustainability and stewardship of the natural resources. Natural and anthropogenic environmental hazards such as air and water pollution, waste disposal, the impact of commercial and industrial activities, as well as population and urbanization. Basic chemistry, geology and physics will be introduced throughout the course to explain and expand on these topics.
Course Description (Major/Full Major Mathematics):
0306102 Calculus II 3 credit hours
Transcendental functions and differential equations: logarithms, exponential functions, derivatives of inverse trigonometric functions; integrals, first order separable differential equations and first order linear differential equations. Techniques of integration: Integration by parts, trigonometric substitution, the method of partial fractions, L’Hospital’s rule and improper integrals. Vectors in the Plane and Polar Functions: vectors, dot products, vector-valued functions, polar coordinates and graphs, calculus of polar curves. Infinite series: limits of sequences of numbers, subsequences and bounded sequences, infinite series, tests for convergence, alternating series, absolute and conditional convergence, power series, Taylor and Maclaurin series, application of power series.
0306131 Introduction to Statistics 3 credit hours
Data, qualitative and quantitative variables, steam-leaf and box plot, histogram, measures of location, variation, skewness and kurtosis, random variables, binomial distribution, normal distribution, sampling distribution, central limit theorem, inferences about normal and binomial distributions, simple linear regression and correlation, inferences from small samples.
0306201 Calculus III 3 credit hours
Vectors in space: rectangular coordinates and vectors in space, dot and cross products, lines and planes in space. Vector valued functions, cylinders and quadric surfaces, vector-valued functions and space curves, TNB frame, tangential and normal components of acceleration. Functions of several variables: graphs, level curves and level surfaces, limits, continuity, partial derivatives, the chain rule, the gradient, the directional derivatives, extreme values and LaGrange multipliers. Multiple Integrals: double and triple integrals, double integrals in polar form, triple integrals in cylindrical and spherical coordinates, change of variables in multiple integrals. Integration in Vector Fields: line integrals, vector fields work, circulation and flux, path independence, potential functions and conservative fields, Green’s theorem in the plane, surface area and surface integrals, curl, divergence, Stokes’ Theorem and divergence theorem.
0306203 Ordinary Differential Equations I 3 credit hours
First order differential equations: examples, separable equations, homogeneous and exact equations, integrating factor and Bemoulli’s equation, linear equations, initial value problems, existence and uniqueness theorem. Second order equations: Homogeneous equations with constant coefficients, fundamental solutions, linear independence and the Wronskian, characteristic equations, nonhomogeneous equations: method of undetermined coefficients, variation of parameters. Higher order differential equations. Series solutions near ordinary and near regular singular points. Euler equations. The Laplace transform: definition, solution of initial value problems, step functions, impulse functions, the convolution integral.
0306214 Biostatistics 2 credit hours
Descriptive study of univariate data, scale of measurements, steam-leaf, box plot, histogram, measures of location and variation, random variables, Bernoulli distribution, normal distribution, sampling distribution, inferences about normal and binomial distributions, correlation and regression, use real data sets. Prerequisite: —
0306221 Mathematical Software 1 credit hour
This course introduces students to mathematical simulation software and the use of the software for mathematical applications. Specifically, the course covers matrices, vectors, data input/output, program flow control, functions, two- and three-dimensional graphics. Students will develop the skills to generate readable, compact and verifiably correct MATLAB scripts and functions to obtain numerical solutions to some mathematical problems and to display the results with fully annotated graphics.
0306230 Demographic Statistics 3 credit hours
Data collection, age and sex structure, period fertility, cohort fertility, mortality and life table, migration, marriage and divorce, reproductively, demographic models of age structure, empirical model life tables, relational life tables, models af mortality and fertility, survival analysis, population growth, applications to some real data sets, use of statistical computer packages.
0306231 Probability Theory 3 credit hours
Axioms of probability, conditional probability, random variables, cumulative distribution function, generating functions, jointly distributed random variables, conditional expectation, uniform, normal, gamma, exponential, chi-square, t, F, Poisson, binomial, geometric, negative binomial distributions, bivariate normal and multinomial distributions, distribution of functions of random variables, order statistics, central limit theorem, types of convergence.
0306232 Mathematical Statistics 3 credit hours
Problem of point estimation, likelihood function, MLE, MME, LSE, unbiased ness, consistency, efficiency, CR inequality, CRLB, fisher information, confidence interval, pivotal quantity method, sufficiency and completeness, UMVUE, Nyman- Pearson theorem, random test, likelihood ratio tests.
0306233 Statistical Methods 3 credit hours
Descriptive statistics for univariate and bivariate data, probability, sampling distribution, inferences from large and small samples, comparing two treatments, multiple linear regression analysis, categorical data analysis, analysis of variance, nonparametric statistics. Using statistical packages such as SPSS.
0306234 Statistical Software 3 credit hours
Numerical and graphical representation of data, generating random sample from continuous distributions (exponential, t, chi-square and F), verifying the central limit theorem, point estimation, testing hypothesis, power function, random test, linear and multiple regressions. Using statistical packages such as SAS, SPSS, S-Plus and MINITAB to do statistical analysis.
0306251 Set Theory 3 credit hours
Compound and simple propositions, truth table, quantifiers, propositional calculus, methods of proof, sets and operations on it, Cartesian products, relations ,equivalence relation, order relation, function, images of sets and cardinality.
0306271 Applied Mathematics I 3 credit hours
Algebra and calculus of vectors, dyadics, and tensors. Fourier Analysis: Fourier series. Fourier and Laplace transforms, application to differential equations. Special functions: Gamma, Beta, Bessel and Legendre functions, Calculus of variations: Euler-LaGrange equations, applications. Perturbation method.
0306281 Linear Algebra I 3 credit hours
Systems of linear equations and matrices, determinants, vector and inner product spaces, matrix representations of linear transformations, eigenvalues and eigenvectors. Cayley-Hamilton theorem.
0306301 Partial Differential Equations I 3 credit hours
Definitions and Concepts: general and particular solutions, elimination of arbitrary functions, first order equations (the method of characteristics). Second Order Equations: classifications (hyperbolic, elliptic, parabolic), the normal form. Boundary Value Problems: the heat equation, the wave equation, Laplace equation. Methods of Solutions: separation of variables, the Fourier and Laplace transforms.
0306304 Vector Analysis 3 credit hours
Vector valued functions, scalar and vector fields, gradient, line integral and path independence. Green’s theorem. Divergence and curl of a vector field. Integration over oriented surfaces. Stokes theorem, divergence theorem. Curvilinear coordinates.
0306311 Real Analysis I 3 credit hours
Functions, limits, theorems on limits, continuity, theorems on continuity, nested interval theorem, uniform continuity, extreme value theorem, Bolzano-Weierstrass theorem, Heine-Borel theorem. Differentiation, mean value theorem and L’Hospital’s rule. Darboux integral, lower and upper sums, theorems on integration, the fundamental theorem of calculus and its applications.
0306312 Complex Analysis I 3 credit hours
Complex numbers: properties and representations. Complex functions: limits, continuity, and the derivative. Analytic functions: Cauchy – Riemann equations, harmonic functions, elementary analytic functions. Integration in the complex plan: complex line integrals, Cauchy integral formula; Maximum principle. Liouville’s theorem and the fundamental theorem of algebra.
0306321 Numerical Analysis 3 credit hours
Mathematical preliminaries: Roundoff errors and computer arithmetic, algorithms and convergence. Solution of non-linear equations in one variable: bisection method and fixed-point iteration, Newton’s method, error analysis for iterative methods and accelerating convergence. Interpolation: Lagrange, divided differences, Newton forward, backward and central methods, Hermite interpolation, cubic spline interpolation. Numerical differentiation and integration: Trapezoidal, Simpson’s and Midpoint rules, composite numerical integration, Romberg integration, Gaussian quadrature, multiple and improper integrals. Initial-value problems for ordinary differential equations: Euler’s method, higher-order Taylor methods.
0306331 Stochastic Processes 3 credit hours
The concepts of stochastic processes, birth and death chain, queuing chain, stationary distribution)of Marker chain, pure jump processes, Poisson processes, second order processes, Gaussian and Wiener processes, continuity, integration, and differentiation of second order processes estimation theory.
0306332 Actuarial Statistics 3 credit hours
Mortality, force of mortality, actuarial notation, density function and future lifetime, moments of future lifetime, life table, the select fife table, Compertz and Makeham formula, life table functions, life table as population model, pure endowment, endowment assurance, expected present value, commutation functions, annuities, premiums reserves and alterations.
0306333 Sampling Theory I 3 credit hours
Simple random sampling, sampling proportions and percentages, estimation of sample site, stratified random sampling, quota sampling, ratio and regression estimators, systematic sampling, single-stage clusters of equal and unequal sites, subsampling with units of equal and unequal sites, double sampling.
0306334 Linear Regression Analysis 3 credit hours
Linear regression model with one independent variable, diagnostic and remedial measures, simultaneous inferences in regression analysis, matrix approach to simple linear regression analysis, coefficient of determination, polynomial regression , multiple regression analysis, qualitative independent variable, variable selection and building the regression model, multicolinearity. Use of statistics computer packages.
Prerequisite: 0306232, 0306281
0306335 Time Series Analysis I 3 credit hours
Time series, filtering, differencing, sample autocorrelation function, correlogram, tests of randomness, stochastic processes, autocorrelation function, purely random process, random walk. MA process, AR processes ARIMA processes, Box-Jenkins models, residual analysis, prediction, stationary processes in frequency domain. Use of statistical computer packages.
03063336 Analysis of Variance 3 credit hours
Observational studies, experimental studies, factors, treatments, single-factor analysis of variance, multiple comparison tests, completely randomized design, general linear model approach to ANOVA, analysis of factor level effects, diagnostic and remedial measures, nonparametric tests, random ANOVA model, multifactor ANOVA, analysis of covariance. Use of statistical computer package.
0306337 Statistical Methods for Insurance 3 credit hours
Insurance setting, statistical background, notation and abbreviations, estimation and goodness of fit: exponential distribution, Pareto distribution, Weibull distribution, mixture distribution lognormal distribution, generalizations of Pareto distribution, reinsurance, main result, policy excess, and reinsurance and policy excess.
0306351 History of Mathematics 3 credit hours
A brief historical introduction of ancient: Math. (Indian, Egyptian, Babylonian) through its main mathematical operations. Greek Math. The school of Phythagoras, Euclid and his system of axioms. A brief biography of three to four Greek mathematicians (Phythagoras, Euclid, Archimedes, Ptolemy). Math. Of the world of Islam, its main contributions and salient characteristics. A concise biography of Al-Khowarizmi, Thabit bin. Qurrah, Omar AI-Khayyam, AL- Bayrouni, along with selected topics from their writings. Algebra of Khowarizmi, the determination of Qibla of Bayrouni, Khayyam and his geometric method of solving cubic equations.
0306352 Teaching Mathematics 3 credit hours
The course is designed to assist students in learning the theoretical foundations, skills and strategies to successfully teach school students mathematics with understanding.
0306361 Non-Euclidean Geometry 3 credit hours
Euclid’s postulates and plane geometry. Von-Newman postulates. The parallel postulate. Affine geometry and geometry on the sphere. Projective and hyperbolic geometry. Klein-Beltrami and Poincrse models of the plane. Pappus and Desargues theorems. Transformations: automorphisms, motions, similarities, and congruence.
0306371 Applied Mathematics II 3 credit hours
Introduction to difference equations: elementary, homogeneous and nonhomogeneous, linear and nonlinear. Asymptotic Expansion of Integrals: using integration by parts, Laplace method and Watson’s lemma, method of steepest descent method. Transforms methods: Z-transform and inverse Z-transform, application in signal processing, solutions of difference equations. Functional Differential Equations: delay, neutral and advance.
0306380 Combinatorics 3 credit hours
Permutations and combinations, selections and the binomial coefficients, the principle of inclusion and exclusion, generating functions and recursions – combinatorial problems. Graphs: definitions and examples, paths, circuits and trees, basic properties and theorems on graphs. Block designs-definition, the basic properties and theorems on block designs, Steiner systems. Applications.
0306381 Linear Algebra II 3 credit hours
Addition and multiplication of operators, invertible operators. Similarity of matrices: change of basis, nil potent operators and matrices, diagonalization and triangulization of matrices. Inner product spaces: linear functional, adjoints, normal operators, unitary operators, self-adjoint operators, the spectral theorem. Bilinear and quadratic forms.
0306382 Abstract Algebra I 3 credit hours
Groups: examples, cyclic groups, subgroups, cosets and LaGrange’s theorem, normal subgroups, quotient groups. Group homeomorphisms and isomorphism. Direct products of groups. Symmetric group. Rings: examples, subrings, ideals, quotient rings, integral domains, fields. Ring
homeomorphisms and isomorphism.
0306383 Number Theory 3 credit hours
Divisibility, Euclidean algorithm, prime numbers, the fundamental theorem of arithmetic, the sieve of Eratosthenes. The prime number theorem, irrationality of π, e and π. Congruencies, Chinese remainder theorem, Fermat’s theorem, Wilson’s theorem, Euler’s theorem, and Diophantine equations.
0306401 Partial Differential Equations II 3 credit hours
Linear, quasi linear and non-linear PDE’s. Solutions of first order linear and quasi linear Equations with initial conditions (Cauchy problem). Solution of heat, wave and Laplace equation in infinite domains (two & three dimensions).Systems of first order PDE’s. Cauchy Kowalewski existence theorem. Conditions for the uniqueness theorems for initial-boundary problems. Harmonic functions-Mean-value property, maximum and strong maximum principle, subharmonic and superhanmaic functions. D’A lamberts’ solution.
0306403 Ordinary Differential Equations II 3 credit hours
Proof of existence and uniqueness theorem, continuous dependence on initial conditions. Phase plane for autonomous linear systems and their critical points. Properties of solutions of nth order linear systems, stability of solutions of linear systems.
0306405 Special Functions 3 credit hours
Series solutions of differential equations, method of Frobenius, Bessel Functions: first kind, second kind, modified Bessel functions. Sturm – Liouville equation, properties of solutions of the Sturm – Liouville equation, Legendre polynomials, Laguerre polynomials, Hermite polynomials.
0306406 Calculus of Variations 3 credit hours
Variational problems with fixed boundaries, variational problems with movable boundaries and natural boundary conditions. Variational problems with constraints. Direct methods for variational problems.
0306408 Integral Equations 3 credit hours
Definitions and types of integral equations, integral equations with separable kernels, method of successive approximations, classical Fredholm’s theory, applications to differential equations.
0306411 Real Analysis II 3 credit hours
Functions of bounded variation, total variation functions, continuous functions of bounded variation, Riemann Stieltje’s integral, Euler’s formula, sequences of functions, uniform convergence of power series and of series of functions.
306412 Complex Analysis II 3 credit hours
The Schwartz Lemma; the Phragmen-Lindelof theorem; the arguments Principle and Rouche’s theorm; the reflection principle; the Schwarz-Christoffel formula; Runge’s theorem. infinite products; canonical products and the Weierstrass factorization theorem; The Mitttage-Leffer theorem; elementary properties of elliptic functions; Picard’s theorem; the Riemann Zeta functions. Uniform convergence of analytic functions; normal families; Riemann mapping theorem.
0306413 Functional Analysis 3 credit hours
Vector spaces, norms, Banach spaces, classical Banach spaces, continuous linear operators, dual spaces, Hann-Banach theorem, Hilbert spaces, orthonormal sets, self-adjoint operators and projections.
0306414 Measure Theory 3 credit hours
Lebesgue measure, measurable functions Lebesgue integral, functions of bounded variations, Banach spaces. Hilbert spaces.
0306421 Numerical Methods for Ordinary Differential Equations 3 credit hours
The development, study and implementation of numerical methods for the approximate solution of ordinary differential equation initial and boundary value problems, and related topics.
Prerequisite: 0306203, 0306321
0306423 Numerical Methods for Partial Differential Equations 3 credit hours
The development, study and implementation of numerical methods for the approximate solution of partial differential equation initial and boundary value problems, and related topics.
Prerequisite: 0306301, 0306321
0306430 Applied Statistics 3 credit hours
Multilevel statistical model, longitudinal data analysis, econometrics, item response analysis, biostatistics, structural data analysis, latent variables, use of statistical software for real data.
0306432 Experimental Design 3 credit hours
Completely randomized design, randomized block designs, latin square and related design, completely randomized factorial design with two treatments, nested design and subsampling, repeated measures and related designs. Use of statistical computer package.
0306433 Sampling Theory II 3 credit hours
Sampling weights, double sampling, repeated sampling, sources of errors in surveys, nonresponse design-based approach, mode-based approach model-assisted approach, generalized regression estimators, pseudo likelihood, estimator, calibration. Informative sampling, small area estimation, variances estimation.
0306434 Non-linear Regression Analysis 3 credit hours
Non-linear regression, deviance, generalized linear models, logistic regression, probit model. Use of statistical computer packages.
0306435 Time Series Analysis II 3 credit hours
Structural time series models, Kalman filter, simulation state space models, analysis of time series in frequency domain, spectral analysis. Use of statistical computer packages.
0306436 Non-parametric Statistics 3 credit hours
Examples of nonparametric statistical methods. Statistical inference for one and two samples problems. Nonparametric measures of association. Some nonparametric goodness of fit tests, Kolomogrov and Simimov tests.
0306437 Multivariate Statistical Analysis 3 credit hours
Aspect of multivariate analysis, sample geometry and random sampling, multivariate normal distribution, inferences about a mean vector, multivariate linear regression, principal components, factor analysis, canonical correlation, discrimination and classification, clustering, use of statistical computer packages.
0306438 Bayesian Methods 3 credit hours
Bayes theorem, loss functions decision rules, likelihood principle, convexity, utility, maximum entropy prior, marginal distribution, posterior distribution, conjugate families, Bayesian estimation, credible sets, Bayesian hypothesis testing, empirical Bayes analysis.
0306439 Categorical Data Analysis 3 credit hours
Inferences for multinomial distribution, cross-classifications, contingency tables, chi-squares tests, goodness – of fit tests for discrete and continuous distributions, methods of estimation and testing in cross-classification, measures of association and agreement, model for categorical data, large-sample theory. Use of statistical computer package.
0306451 Foundation of Mathematics 3 credit hours
The axiomatic method, sets and infinite sets, the axiom of choice and equivalent statements, discussion of the paradoxes, Hilbert’s proof.
0306461 Differential Geometry 3 credit hours
Theory of space curves, vector and parametric equations, arc length, curvature and torsion, Frenet Serret formulae and the moving frame. Intrinsic equations, global theory of plane curves. Concept of a surface, representation, tangent surfaces, geodesics, the metric tensor and Gauss- Bonnet theorem, first and second fundamental forms
0306462 Topology 3 credit hours
Topological spaces, bases and sub-bases, subspaces, finite product spaces, continuous maps, homeomorphisms, Hausdorff spaces, metric spaces, compactness and connectedness, separation axioms.
0306463 Graph Theory 3 credit hours
Connectivity, search in graph, minimum spanning trees, shortest paths, maximum flow problem, the minimum cost flow problem, graph coloring, covers, dominating sets and independent sets with applications, planarity and planarity algorithms, Eulerian and Hamiltonian graphs with applications. Programming assignments will be given.
0306464 Algebraic Topology 3 credit hours
Categories, abelian groups and homotopy, complexes, homology of chain complexes, singular homology, applications of the exact homology sequences, homotopy, invariance, and excision.
Prerequisite: 0306382, 0306462
0306481 Numerical Methods in Linear Algebra 3 credit hours
Direct Methods for Solving Linear Systems: Gaussian elimination, LU and Cholesky factorizations. Iterative Techniques in Matrix Algebra: Jacobi, Gauss-Seidel and relaxation iterative methods, ill-conditioned systems. Approximating eigenvalues: the power, Householder’s methods, the QR algorithm. Numerical Solutions of Nonlinear Systems of Equations: fixed point iterations, Newton’s method and steepest descent techniques.
0306482 Abstract Algebra II 3 credit hours
Modules and sub modules, maximal and prime ideals, prime fields, characteristic of a field, field of fractions, unique factorization domains: definitions and properties, Euclidean rings, Gaussian rings, factorization of polynomials, applications in F[x], polynomial rings over Gaussian rings. Field extensions: simple extensions, finite extensions.
0306484 Introduction to Galio Theory 3 credit hours
Algebraic extensions, finite extensions, separable extensions perfect field, finite fields, the existence of GF. Galois Theory, Calois aps over finite field, insolvability of quixotic.
0306491 Seminar 1 credit hour
A literature survey carried by the student under the supervision of the Department. A report should be written and present in a seminar.
Prerequisite: Department Consent
0306492 Special Topics 3 credit hours
Selected topics in mathematics, chosen by the instructor.
Prerequisite: Department Consent
Course Description: Minor in Statistics for Non-Mathematics Major Students
0306200 Mathematics for Statistics 3 credit hours
Sets, union, intersection, functions, quadratic equations, solutions and inequalities, exponential functions, logarithmic functions, sequences, series, limits, continuity, differentiation, integration, partial differentiation, matrix algebra, system of linear equations, determinants, matrix algebra, eigenvalues and eigenvectors.
0306206 Descriptive Statistics with Excel 3 credit hours
Statistics in practice, application in social sciences, univariate data, bivariate data, multivariate data, tabular methods, histograms, graphical methods, exploratory data analysis, measures of location, cross tabulation, measures of variations, detecting outliers, weighted mean, grouped data, index numbers, time series, order statistics, simple linear regression and correlation.
0306207 Statistical Inference 3 credit hours
Introduction to probability, conditional probability, random variables, expectation, covariance, distribution of function of random variable, binomial distribution, multinomial distribution, normal distribution, geometric distribution, Poisson distribution, sampling distribution, central limit theorem, chi-square distribution, student’s t-distribution, F-distribution, point estimation, unbiased estimator, confidence interval, and testing hypotheses.
Prerequisite: 0306200, 0306206
0306208 Demographic Methods 3 credit hours
Introduction basic demographic equation, demographic rates, crude death rate, age-specific death rate, life tables, marriage process, period and cohort analysis of marriage, the average age at marriage, measurement of fertility, analysis of migration, and population projection.
0306307 Statistical Methods I 3 credit hours
Comparing two treatments, analysis of variance, multiple comparisons, completely randomized design, randomized block design, chi-square test, measures of association, odds ratio, crossover design, prospective studies, retrospective studies, case-control design, matched samples, Mantel-Haenszel method, and nonparametric methods. Use SPSS.
0306308 Sampling Methods 3 credit hours
Importance of data collection in the study of statistics, polls, planning and execution of sample surveys, concepts of basic terms of population, sample frame, unit of analysis, auxiliary information, questionnaire design, simple random sampling, systematic sampling, determining sample size, stratified random sampling, and clustering sampling. Use SPSS.
0306407 Statistical Methods II 3 credit hours
Correlation, simple linear regression model, least square method, coefficient of determination, prediction, model assumptions, multiple regression, qualitative independent variable, residual analysis, model building, logistic regression, principal component analysis, factor analysis and cluster analysis. Use SPSS.