**MATH 090 - Mathematics-Nursing **

**MATH 091 - Remedial Mathematics I-Business & Economics **
**MATH 094 - Remedial Mathematics II-Business and Economics **
**MATH 095 - Remedial Mathematics I-Science (3 CH) **

**MATH 096 - Remedial Mathematics II-Science **
**MATH 098 - Mathematics-Business & Economics **

**MATH 099 - Remedial Mathematics II-Business & Economics **
**MATH 100 - General Applied Mathematics (3 CH) **

**MATH 101 - Calculus I (3 CH) **

Limits and continuity. Differentiation. Applications of derivatives. Integration. Inverse functions. Applications of the integral.

**MATH 102 - Calculus II (3 CH) **

Transcendental functions. Techniques of integration. Sequences and infinite series. Parametric equations and polar coordinates

**MATH 103 - General Mathematics I (4 CH) **
**MATH 104 - General Mathematics II (2 CH) **
**MATH 110 - Mathematics I - Biology (3 CH) **

**MATH 118 - Mathematics I-Business and Economics (3 CH) **
**MATH 119 - Business Mathematics I (3 CH) **

Algebra Review. Equations: Linear, fractional, quadratic and radical equations. factorizing higher degree equations. Functions and Graphs: Functions. Domain. Evaluating a function. Combinations and composition of functions. Graphs of functions in rectangular coordinates. Lines, Parabolas and Systems: Equations of lines. Parallel and perpendicular lines. Graphing quadratic functions. Sys-tems of linear equations with at most three variables. Exponential and Logarithmic Functions: Graph of exponential functions. Population growth. Graph of logarithmic functions. Solving logarithmic and exponential equations. Matrices: Transpose of a matrix. Special matrices. Matrix addition, subtraction, scalar multiplica-tion and multiplication. Reduction methods for homogeneous and

nonhomogeneous systems. Differentiation: Derivatives. Tangent lines. Rules of differentiation. Chain rule. Derivatives of loga-rithmic and exponential functions. Implicit differentiation. Integration: Indefinite integrals. Basic integration formulas.

**MATH 177 - Mathematics and Quantitative Analysis (2 CH) **
**MATH 180 - Mathematics I-Engineering (3 CH) **

**MATH 181 - Mathematics I-Engineering (3 CH) **
**MATH 182 - Mathematics II-Engineering (3 CH) **

**MATH 208 - Vector Calculus (3 CH) **
**MATH 209 - Advanced Calculus (3 CH) **
**MATH 210 - Mathematics II-Biology (3 CH) **
**MATH 211 - Calculus III (3 CH) **

Vectors. Vector calculus. Functions of several variables. Differentials and applications. Double and triple integrals.
**MATH 212 - Calculus IV (3 CH) **

Line integrals. Surface integrals. Fourier series. Some special functions. Complex numbers.
**MATH 213 - Differential Equations (3 CH) **

First order differential equations. Second order differential equations. Linear systems of differential equations. Laplace transforms. Differential equations with variables coefficients.

**MATH 215 - Mathematics-Computer Science (3 CH) **

Infinite Series: Sequences of real numbers. Infinite series. Geometric series. The divergence test. The integral test. Comparison theorems. The root test. The ratio test. Alternating series. Ab-solute convergence. Alternating series test. Power series. Taylor and Maclaurin series. Fourier Series. Some Special Functions: Gamma function. Beta function. Error function. Applications. Functions of Several Variables: Elementary examples. Quadratic surfaces. Limits and Continuity. Direction angle. Differentials and Applications: Notion of differentiability. Differentials. Directional

derivatives. Mean value theorem. Chain rules. Maximum and Minimum values. Lagrange’s method. Double and Triple Integrals: Double integrals. Properties. Evaluation by repeated integrals. Polar coordinates. Triple integrals.

Properties. Evaluation by repeated integrals. Cylindrical and spherical coordi-nates. Applications. Differential Equations: Classification by type. Classification by order. Linearity. Solutions. Initial value prob-lem. Separable variables. Homogeneous equations. Exact equations. Linear equations. Integrating factor. Homogeneous equations with constant coefficients.

**MATH 216 - Mathematics-Chemistry (3 CH) **

Logic, Sets and Functions: Logic. Propositional equivalences. Predicates and quantifiers. Sets. Set operations. Functions. Sequences and summations. Mathematical Reasoning: Methods of proof. Mathematical induction. Relations: Relation and their properties. N-ary relations and their applications. Representing rela-tions. Equivalence relations. Partial ordering. Counting: The basics of counting. The pigeonhole principle. Permutations and

combinations. Ge-neralized permutations and combinations. Graphs: Introduction to graphs. Graph Terminology. Representing graphs and graphs isomor-phism. Connectivity. Euler and Hamiltonian paths. Planar

graphsIntroduction.

**MATH 217 - Mathematics-Engineering (3 CH) **

First-Order Differential Equations: Initial-value problem. separable variables. Homogeneous equations. Exact equations. Li-near equations. Integrating factor. Bernoulli equation. Applications. Second-Order Differential Equations: Initial-value and Boundary-value problems. Linear differential operators. Reduction of order. Homogeneous equations with constant coefficients. Nonhomogeneous equations. Method of undetermined coefficients. method of variation of parameters. some nonlinear equations. Ap-plications. Higher order Differential Equations. Laplace Transforms: Definitions. Properties. Inverse Laplace transforms. Solving initial-value problems. Special functions: Heavyside unit step function. Convolution theorem. System of Linear Differential Equations: Definitions. Elimination method. Application of Linear Algebra. Homogeneous linear systems. Nonhomogeneous linear systems. Solving systems by Laplace transforms. Series Solutions: Cauchy-Euler equation method. Solutions about ordinary points. Solutions about singular points. Method of Frobenius. Second Solutions and Logarithm terms. Partial Differential Equations: Some mathematical models. Fourier series solutions. Method of seperation of

**MATH 218 - Mathematics-Physics (3 CH) **
**MATH 220 - Foundations of Mathematics (3 CH) **

Mathematical logic. Sets and families. Relations. Functions. Countable and uncountable sets.
**MATH 221 - Business Mathematics II (3 CH) **

This course covers some economic applications of mathematical concepts such as the linear and non linear

functions, difference equations, partial derivatives, constrained and unconstrained optimization problems, definite and indefinite integration in addition to mathematics of finance.

**MATH 222 - Real Analysis (3 CH) **

Structure of point sets. Real numbers. Real sequences. Limits and continuity. Differentiation and mean value theorem. Riemann integral. Riemann-Stieltjes integral.

**MATH 231 - Linear Algebra (3 CH) **

of linear equations. Matrices and matrix operations. Determinants. Vector spaces. Linear transformations. Eigenvalues and eigenvectors.

**MATH 232 - Computational & Linear Algebra (3 CH) **
**MATH 233 - Abstract Algebra (3 CH) **

Relations and applications. Binary operations and algebraic systems. Groups. Cosets. Introduction to rings and fields.
**MATH 261 - Discrete Mathematics (3 CH) **

General Applied Mathematics Sets, operation on sets, review of numbers (Natural, Integer, Rational, Irrational and Real numbers), prime numbers, divisibility, least common multiple, greatest common divisor. Logic, truth tables, connectives. Functions (polynomial, roots, rational, absolute value, exponential), some applications (profit simple and compound). Equations, inequalities, simple applications of equations, some linear programming problems (feasible solutions, blending model, production model, transportation). Analytic geometry: Cartesian coordinate system, distance between two points, midpoint formula, lines, circles. Matrices operations, determinant (3?3), solutions of systems of linear equations (Cramer’s rules). Statistics: Frequency tables, Mean, Median, Mode, some application (grade point average).

**MATH 283 - Mathematics III-Engineering (3 CH) **
**MATH 284 - Mathematics IV-Engineering (3 CH) **
**MATH 314 - Partial Differential Equations (3 CH) **

First order partial differential equations. Second order partial differential equations. Elliptic partial differential equations. Parabolic partial differential equations. Hyperbolic partial differential equations.

**MATH 322 - Real Analysis II (3 CH) **

Euclidean n space – Continuous functions – Differentiable functions – Implicit and inverse function theorems – Maxima and minima.

**MATH 324 - Complex Analysis (3 CH) **

Review on complex numbers. Analytic functions. Elementary functions. Line integrals. Series.
**MATH 325 - Topology (3 CH) **

Basic concept. Basic topological constructions. Sequential convergence in topological space and derivatives sets. Basic topological properties.

**MATH 331 - Linear Algebra II (3 CH) **

Linear transformation and matrices – Diagonalization – Inner.
**MATH 333 - Abstract Algebra II (3 CH) **

Normal subgroups – Cyclic structure of finite permutation groups – Direct product of groups – Action of groups on sets – Ideals and domains – Euclidean domains – Applications.

**MATH 335 - Number Theory (3 CH) **

ntegers. Greatest common divisor and prime factorization. Congruence. Application and some special congruence. Multiplicative functions. Primitive roots. Introduction to quadratic residues and reciprocity.

**MATH 341 - Modern Geometry (3 CH) **

Axiomatic systems. Finite geometries. Euclidean geometry. Neutral geometry. Hyperbolic geometry.
**MATH 365 - Programming and Scientific Computation I **

**MATH 366 - Numerical Analysis I **

Errors in numerical computation. Solutions of nonlinear equations. Direct methods for solving linear systems. Interpolation and polynomials approximations. Numerical differentiation. Numerical integration.

**MATH 367 - Numerical Methods I **

**MATH 368 - Operations Research I (3 CH) **

Overview of operations research. Linear programming. The transportation problem.
**MATH 369 - Graphic Theory & Appllication (3 CH) **

Introduction to graph. Paths and cycles. Trees. Planarity. Coloring graphs.
**MATH 371 - Advanced Mathematical Methods (3 CH) **

Some special functions. Method of eigenfunction expansions. Integral transforms. Integral equations.
**MATH 384 - Mathematics-Electrical Engineers **

**MATH 385 - Advanced Mathematics (3 CH) **

Mathematics for Electrical Engineers. Complex Numbers and Complex Functions: Algebra of complex numbers. Modulus and argument. Trigonometric form. Exponen-tial form. Roots. De Moivre's theorem. Analytic Functions: Functions of a complex variable. Mappings. Limits. Continuity. Derivatives. Cauchy-Riemann equations. Polar coordinates. Analytic functions. Harmonic functions. Har-monic conjugate. Elementary functions. Complex Integration: Definite integrals. Contours. Line integrals (Real). Line integral (Complex). Cauchy in-tegral theorem. Cauchy integral formulas. Taylor's series and Laurent's series of ana-lytic functions. Residue theorem. Applications. Fourier Transforms: Fourier transforms. Properties. Inverse of the Fourier transform. Convolution theorem. Fourier sine and Fourier Cosine transforms.

**MATH 413 - Theory of Differential Equations (3 CH) **

Linear systems of differential equations. Nonlinear systems of differential equations. Stability of linear differential equations.

**MATH 423 - Theory of Distributions (3 CH) **

**MATH 424 - Complex Analysis II (3 CH) **

Residue theory – Mapping by elementary functions – Conformal mapping – Application of conformal mapping – Further theories of functions.

**MATH 425 - Topology II (3 CH) **

Metric spaces as topological spaces – sequential spaces – Other topological properties.
**MATH 426 - Functional Analysis (3 CH) **

Linear spaces. Metric spaces. Normed spaces. Banach spaces. Linear operators and functionals. Inner product spaces.

**MATH 435 - Number Theory II (3 CH) **

Prime numbers and their distribution – Dirichlet’s series and Euler’s products – Further Diaphantine equations and elliptic curves – Extension of the p-adic field Qp.

**MATH 436 - Applied Algebra (3 CH) **

Boolean algebra and switching circuits – Introduction to formal languages and automata– Polga enumeration – Introduction to algebraic coding – Introduction to cryptography.

**MATH 441 - Projective Geometry (3 CH) **

Finite projective geometry – Plane projective geometry – Projective transformation – Projective, affine and Euclidean geometry.

**MATH 443 - Introduction to Differential Geometry (3 CH) **

Curves. Surfaces. Differentiability structure of regular surfaces. Orientability and isometries of regular surfaces.
**MATH 466 - Numerical Analysis II (3 CH) **

Iterative methods for solving linear systems. Approximation theory. Eigenvalues. Numerical solutions of the initial value problems. Numerical solutions of the boundary value problems. Numerical solutions of partial differential equations.

**MATH 467 - Numerical Methods II (3 CH) **
**MATH 468 - Operations Research II (3 CH) **

Integer programming. Dynamic programming. Nonlinear programming.
**MATH 471 - Mathematical Modeling (3 CH) **

Difference equations (Dynamical system 1). Difference systems (Dynamical system 2). Differential equations (Dynamical system 3). Applications.

**MATH 474 - Theory of Elasticity (3 CH) **

Tensor calculus – Analysis of stress – Analysis of strain – Field equations – Elastostatic problems – Thermoelasticity – Theory of plates.

**MATH 475 - Fluid Dynamics (3 CH) **

**MATH 487 - Topics in Principles of Mathematics (2 CH) **
**MATH 497 - Independent Study **

report-writing, and ability to use research tools and methods by accessing and using the library and data bases through modern information technology.

**MATH 498 - Special Topics (3 CH) **

This course usually aims at either pursuing in more depth the study of a certain discipline, or an opportunity for
learning some advanced coherent topics, or exposure to new material in a currently active field of mathematics.
**MATH 499 - Senior Project (3 CH) **

This course aims at applying the educational experience gained, to study practical problems and issues, associated with realistic field, related to the nature of professional work and its requirements, and putting what a student has learned into practice, in order to reach solutions to problems, and procedural issues, from the perspective of global view.