# MATH Mathematics-Nursing. MATH Remedial Mathematics I-Business & Economics. MATH Remedial Mathematics II-Business and Economics

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1 MATH Mathematics-Nursing MATH Remedial Mathematics I-Business & Economics MATH Remedial Mathematics II-Business and Economics MATH Remedial Mathematics I-Science (3 CH) MATH Remedial Mathematics II-Science MATH Mathematics-Business & Economics MATH Remedial Mathematics II-Business & Economics MATH General Applied Mathematics (3 CH) MATH Calculus I (3 CH) Limits and continuity. Differentiation. Applications of derivatives. Integration. Inverse functions. Applications of the integral. MATH Calculus II (3 CH) Transcendental functions. Techniques of integration. Sequences and infinite series. Parametric equations and polar coordinates MATH General Mathematics I (4 CH) MATH General Mathematics II (2 CH) MATH Mathematics I - Biology (3 CH) MATH Mathematics I-Business and Economics (3 CH) MATH 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 Mathematics and Quantitative Analysis (2 CH) MATH Mathematics I-Engineering (3 CH) MATH Mathematics I-Engineering (3 CH) MATH Mathematics II-Engineering (3 CH)

2 MATH Vector Calculus (3 CH) MATH Advanced Calculus (3 CH) MATH Mathematics II-Biology (3 CH) MATH Calculus III (3 CH) Vectors. Vector calculus. Functions of several variables. Differentials and applications. Double and triple integrals. MATH Calculus IV (3 CH) Line integrals. Surface integrals. Fourier series. Some special functions. Complex numbers. MATH 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 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 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 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 variables. The D Alembert solution of the wave equation. Applications.

3 MATH Mathematics-Physics (3 CH) MATH Foundations of Mathematics (3 CH) Mathematical logic. Sets and families. Relations. Functions. Countable and uncountable sets. MATH 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 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 Linear Algebra (3 CH) of linear equations. Matrices and matrix operations. Determinants. Vector spaces. Linear transformations. Eigenvalues and eigenvectors. MATH Computational & Linear Algebra (3 CH) MATH Abstract Algebra (3 CH) Relations and applications. Binary operations and algebraic systems. Groups. Cosets. Introduction to rings and fields. MATH 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 Mathematics III-Engineering (3 CH) MATH Mathematics IV-Engineering (3 CH) MATH 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 Real Analysis II (3 CH) Euclidean n space Continuous functions Differentiable functions Implicit and inverse function theorems Maxima and minima. MATH Complex Analysis (3 CH) Review on complex numbers. Analytic functions. Elementary functions. Line integrals. Series. MATH Topology (3 CH) Basic concept. Basic topological constructions. Sequential convergence in topological space and derivatives sets. Basic topological properties.

4 MATH Linear Algebra II (3 CH) Linear transformation and matrices Diagonalization Inner. MATH 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 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 Modern Geometry (3 CH) Axiomatic systems. Finite geometries. Euclidean geometry. Neutral geometry. Hyperbolic geometry. MATH Programming and Scientific Computation I MATH 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 Numerical Methods I MATH Operations Research I (3 CH) Overview of operations research. Linear programming. The transportation problem. MATH Graphic Theory & Appllication (3 CH) Introduction to graph. Paths and cycles. Trees. Planarity. Coloring graphs. MATH Advanced Mathematical Methods (3 CH) Some special functions. Method of eigenfunction expansions. Integral transforms. Integral equations. MATH Mathematics-Electrical Engineers MATH 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 Theory of Differential Equations (3 CH) Linear systems of differential equations. Nonlinear systems of differential equations. Stability of linear differential equations. MATH Theory of Distributions (3 CH) Space of test functions Space of distributions Tensor product and convolution Space of tempered distributions.

5 MATH Complex Analysis II (3 CH) Residue theory Mapping by elementary functions Conformal mapping Application of conformal mapping Further theories of functions. MATH Topology II (3 CH) Metric spaces as topological spaces sequential spaces Other topological properties. MATH Functional Analysis (3 CH) Linear spaces. Metric spaces. Normed spaces. Banach spaces. Linear operators and functionals. Inner product spaces. MATH 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 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 Projective Geometry (3 CH) Finite projective geometry Plane projective geometry Projective transformation Projective, affine and Euclidean geometry. MATH Introduction to Differential Geometry (3 CH) Curves. Surfaces. Differentiability structure of regular surfaces. Orientability and isometries of regular surfaces. MATH 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 Numerical Methods II (3 CH) MATH Operations Research II (3 CH) Integer programming. Dynamic programming. Nonlinear programming. MATH Mathematical Modeling (3 CH) Difference equations (Dynamical system 1). Difference systems (Dynamical system 2). Differential equations (Dynamical system 3). Applications. MATH Theory of Elasticity (3 CH) Tensor calculus Analysis of stress Analysis of strain Field equations Elastostatic problems Thermoelasticity Theory of plates. MATH Fluid Dynamics (3 CH) MATH Topics in Principles of Mathematics (2 CH) MATH Independent Study This course aims at providing: depth in some branch of mathematics; skills of independent study and scientific report-

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

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