MATH 110 Introduction to Differential Calculus (3+1 hours):

Real numbers, inequalities, functions, injective function and its inverse. Limits,  definition, continuity, properties of a continuous function on an interval. Differentiability, techniques of differentiation, critical points, absolute and local extrema, mean value theorem. Intervals of increase and decrease, first derivative and second derivative tests for local extrema, concavity and infection points, asymptote, curve sketching, applied extrema problems, related rates. Conic sections.

MATH 112 Introduction to Integral Calculus (3+1 hours):

Definition of Riemann integral by Riemann sums, properties of the definite integral. Mean value theorem for the integral, the fundamental theorem of calculus, indefinite integral, integration by substitution. Logarithmic and exponential functions, hyperbolic and inverse hyperbolic functions. Techniques of integration: integration by parts, trigonometric substitutions, integrals involving quadratic expressions, partial fractions, miscellaneous substitutions. Numerical integration (the trapezoidal rule). L'Hospital's rule, improper integrals. Evaluation of area, volume of revolution, arc length. Sketching of some elementary curves in polar coordinates, evaluation of area in polar coordinates

MATH 133 Foundations of Mathematics  (3+1 hours):

Introduction to logic, methods of proof, mathematical induction. Sets, operations, on sets, cartesian product, binary relation, partition of a set, equivalence relation, equivalence classes, mappings, equivalence of sets, finite sets, countable sets, cardinal numbers. Binary operations, morphisms. Definition and examples of groups, definition and examples of rings and fields.

MATH 200 Differential and Integral Calculus (3+0 hours):

Cartesian, cylindrical, spherical and curvilinear coordinates. Functions of two and three variables, limits and continuity, partial derivatives, the chain rule, extrema of functions of two variables, Lagrange multipliers. Double integrals, areas and volumes, double integrals in polar coordinates, tripe integral in Cartesian cylindrical and spherical coordinates, surface area, change of variables. Sequences limit of a sequence (definition and theorems), infinite series, geometric series, convergent and divergent series, tests for convergence (integral, comparison and ratio tests), alternating series, absolute convergence, conditional convergence, representation of functions by power series, Taylor and Maclaurin series, the binomial series.

MATH 202 Vector Calculus (3+1 hours):

Vectors in two and three dimensions, scalar and vector products, equations of lines and planes in 3-dimensional space. Surfaces of revolution an their equations in cylindrical and sperical coordinates. Vector valued functions of a real variable, curves in space, curvature. Rates of change in tangent and normal directions, directional derivatives. Gradient of a function, equations of normal and tangent space to a surface at a point. Vector fields, divergence, curl of a vector, line and surface integrals. Green's theorem, Gauss' divergence theorem, Stockers' theorem.

MATH 204 Differential Equations (2+1 hours):

Various types of first order equations and their applications. Linear equations of higher order. Systems of linear equations with constant coefficients, reduction of order. Power series methods for solving second order equations with polynomial coefficients. Fourier series, Fourier series for even and odd functions. Complex Fourier series. The Fourier integral.

MATH 204 Introduction to Ordinary Differential Equations (2+1 hours):

Classification of Differential equations and their origins. Methods of solution of first order differential equations, orthogonal trajectories. Linear equations with constant coefficients and variable coefficients. Linear system of equations, power series solutions of linear differential equation of the second order with polynomial coefficients, Laplace transform and the convolution. Fourier's series

MATH 231 Differential and Integral Calculus (3+0 hours):

Cartesian, cylindrical, spherical and curvilinear coordinates. Functions of two and three variables, limits and continuity, partial derivatives, the chain rule, extrema of functions of two variables, Lagrange multipliers. Double integrals, areas and volumes, double integrals in polar coordinates, tripe integral in Cartesian cylindrical and spherical coordinates, surface area, change of variables. Sequences limit of a sequence (definition and theorems), infinite series, geometric series, convergent and divergent series, tests for convergence (integral, comparison and ratio tests), alternating series, absolute convergence, conditional convergence, representation of functions by power series, Taylor and Maclaurin series, the binomial series.

MATH 233 Introduction to Ordinary Differential Equations (3+1 hours):

Classification of Differential equations and their origins. Methods of solution of first order differential equations, orthogonal trajectories. Linear equations with constant coefficients and variable coefficients. Linear system of equations, power series solutions of linear differential equation of the second order with polynomial coefficients, Laplace transform and the convolution. Fourier's series.

MATH 242  Linear Algebra (3+1 hours):

Matrices and their operations., types of matrices. Elementary transformations. Determinants, elementary properties. Inverse of a matrix. Linear systems of equations. Vector spaces, linear independence, finite dimensional spaces, linear subspaces. Inner product spaces. Linear transformations, kernel and image of a liner transformation. Eigen values and Eigen vectors of a matrix and of a linear operato.

MATH 245 Number Theory (3+1 hours):

First and second principles of Mathematical Induction. Well-ordering principle. Divisibility, Euclidean Algorithm. Prime numbers and their properties. Linear Diphontaine equations. Congruences and their properties, linear Congruences. The Chinese remainder theorem. Fermat's little theorem. Euler's theorem. Wilson's theorem. Arithmetic functions,. Pythagorian triples. Some cases of Fermat's last theorem.

MATH 253 Numberaical Analysis (3+1 hours):

Numerical techniques for solving nonlinear equations including the study of error analysis and rate of convergence. Solving systems of linear equations by direct and interative methods. The error estimate for numerical solutions in matrix algebra. Interpolation and approximation with error analysis. Numerical methods for differentiation and integration with the discussion of the accuracy and error estimate.

MATH 283 Real Analysis (3+1 hours):

Basic properties of the field of real numbers, completeness axiom, countable sets, Sequences and their convergence, monotone sequence, Bolzano-Weierstrass theorem, Cauchy criterion. Basic topological properties of the real numbers. Limit of a function, continuous functions and properties of continuity, uniform continuity, compact sets. The derivative of a function, mean value theorem, L'Hospital rule, Taylor theorem, Riemann Integral: Definition, Darboux's theorem, Riemann sums, fundamental theorem.

MATH 343 Group Theory (3+1 hours):

Definitions and examples, subgroups, Lagrange's theorem, normal subgroups, Factor groups, homomorphisms, isomorphism theorems, automorphisms, Cayley's theorem and its generalization. Simple groups, permutation groups. Class equation. Group action on a set. p-groups, Cauchy's theorem, Sylow theorems. External and internal direct products of groups. Burnside's theorem. Dihedral groups. Quaternions. Groups of automorphisms on finite cyclic subgroups.

MATH 438 Introduction to Graphs and Combinatoriecs (3+1 hours):

Basic concepts. Eulerian graphs. Hamiltonian graphs. Planar graphs. Coloring. Minimal spanning trees. Orientation of graphs. Matching. Ordered sets. Dilworth's theorem. Applications. Permutations and combinations. Inclusion-exclusion. Recurrence relations. Generating functions. Analyzing algorithms and problems. Sorting. Algorithms in graphs and digraphs.

MATH 373 Introduction to Topology (3+1 hours):

Topological spaces, examples, closure of a set, derived set, subspace, topology. Bases, finite product topology, subbases. Metric spaces, examples, metrizability, Rn as a metrizable space. Continuous functions, characterization of continuous functions on topological and metric spaces, homeomorphisms, examples, topological property. Compact spaces, compactness in Rn, limit point and sequentially compact spaces

MATH 444 Rings and Fields (3+1 hours):

Rings, group of units and group of automorphisms of a ring. Ideals and factor rings. Principal ring. Prime and maximal ideals. Field of quotients of integral domain. Characteristic of a ring. Direct sum of rings. Modules. Euclidean rings. Ring of polynomials. Roots of polynomials over a field. Field extensions. Finite and simple extensions of fields. Algebraic closure of a field. Splitting fields. Finite fields.

MATH 456 Introduction to Mathematical Programming (2+1 hours):

The geometric method for solving a linear program. Simplex method. Two-phase method. Degenerate solution. Revised simplex method. Dual linear optimization problems and sensitivity analysis. Applications in transportation and network analysis.

 MATH 475 Introduction to Differential Geometry (3+1 hours):

Theory of curves in R3. Regular curves and reparametrization, Serret-Fernet apparatus and theorem, existence and uniqueness theorems for space curves. Local theory of surfaces: Simple surfaces, coordinate transformations, tangent vectors and tangent spaces, first and second fundamental forms, normal and geodesic curvatures, Weingarten map, principal, Gaussian and mean curvatures. Geodesics, equations of Gauss and Codazzi-Mainardi.

MATH 485 Complex Analysis (3+1 hours):

Complex numbers, Cartesian and polar representation of complex numbers, powers and roots of complex numbers. Limits and continuity of a complex function. Analytic functions, Cauchy-Riemann equations, harmonic functions. Exponential, trigonometric, hyperbolic functions and logarithmic functions. Complex integration, contour integrals, Cauchy's theorem, Cauchy's formula. Bounds on analytic functions. Series representation of analytic functions, Taylor and Laurent series, power series, Zeros and singularities. Residue theory. Applications to real and improper integrals

STAT 101 Elementary Probability and Statistics (2+1 hours):
 
Descriptive Statistics , Measure of central tendency , Measure of variance , Elementary probability (finite case) , Random vectors and their distributions ,Conditional probability , Bayes formula , Random variable and probability distribution , Binomial - Normal distribution.

STAT 104 Elementary Probability and Statistics II (2+1 hours):
Distribution of sample mean , Point and interval estimates and hypothesis testing , Analysis of basic designs (CR.RCB) , Simple linear regression , Gatogorized data , Goodness of fit , Some non-parametric tests.

STAT 111 Elements of Distribution Theory (2+1 hours):

Sample space, Axioms of probability , Counting techniques Bayes theorem , Independence , Discrete random variables and distribution function s- Some discrete probability distribution ,Distributions of functions of a discrete random variable.

STAT 211 Probability (2+1 hours):

Random vectors and their distributions - Marginal and conditional distributions - Distribution of function of random vector - Probability inequalities and sequences of random variables - Weak and strong laws of large numbers - Characteristic functions - Central theorems - order statistics and their properties.

STAT 431 Data Analysis (2+1 hours):

Introduction to data analysis and statistical packages - Data recording - data entry - missing observations and data scrutiny.

 

201  Student’s Research project (2+1 hours).

221  Student’s Research project (2+1 hours).

331  Student’s Research project (2+1 hours).