The CIS department offers a minor in Mathematics for RHU students. It is designed to give students a solid foundation in mathematics as well as some experience in the discipline at an advanced level.

The aims of a minor in Mathematics are:

• Provide RHU graduates with a basic proficiency in Mathematics to compete at the university level.

• Support RHU graduates with essential mathematical skills to enhance their knowledge and understanding in their respective majors.

To successfully complete the Minor in Mathematics, a student must

• Declare a Minor in Mathematics by completing the Minor Declaration Form

• Obtain the approval of the dean of the college major and the dean of the College of Business Administration

• Obtain a Minor Cumulative Grade Point Average (MCGPA) of no less than 70 %

• Complete 19 credits of Mathematics coursework as specified below

This minor allows its holders to seek careers in a variety of sectors no matter what a student’s major is. Graduates from this minor can seek jobs related to teaching, banking and finance, computing and statistical works.

Major Courses (13 cr.)

MATH 211 - Calculus III
4

Volumes using cross sections-disc and washer methods, Arc length, Hyperbolic functions, Improper integrals, Infinite sequences and series, Parametric equations and polar coordinates, Partial derivatives, Multiple integrals in rectangular-cylindrical-spherical coordinates, Vector fields.

MATH 311 - Linear Algebra and Applications
3

Linear equations in linear algebra, matrix algebra, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, orthogonality and least squares, symmetric matrices and quadratic forms.
**Prerequisite: **None.

MATH 314 - Ordinary Differential Equations
3

First order linear differential equations, linear differential equations of second and higher order, differential equations with power series solutions, Legendre’s and Bessel’s equations, systems of differential equations, Laplace transforms and their inverses, partial differential equations using separation of variables, heat equations: solutions by Fourier series. **Prerequisite: **MATH 211.

MATH 215 - Advanced Calculus
3

Topics in calculus with emphasis on proof, The (ɛ,ɗ) definition of limit , differentiation rules, the chain rule, Rolle’s theorem, Mean value theorem, Fundamental theorem of calculus, sequence convergence using the (ɛ,L) definition, convergence theorem for power series, The (ɛ,ɗ) definition of limit for a function of two variables, chain rule for a function of two variables, conservative and gradient fields, Green’s theorem, and Stoke’s theorem. Prerequisite: MATH 211.

Elective Courses (6 cr.)

MATH 351 - Probability and Statistics
3

Probability and conditional probability, random variable and distribution, continuous and marginal distributions, expectation, variance- moments-mean-median-covariance and correlation, conditional expectation, the sample mean, special distribution, Bernoulli and binomial distributions, Poisson and Gamma distribution. Prerequisite: MATH 211. Annually.

MATH 421 - Numerical Analysis
3

Error Analysis, solutions of nonlinear equations using fixed point- Newton-Raphson-Muller’s methods, solution of linear system using Gaussian elimination-iterative methods, interpolation and approximation using Taylor series-Lagrange approximation-Newton polynomials, numerical differentiation and integration, numerical optimization, solutions of ordinary and partial differential equations using Euler’s and Heun’s and Rung-Kutta methods. Prerequisite: MATH 314. Annually.

MATH 317 - Partial Differential Equations
3

Ordinary differential equations arising from partial differential equations by means of separation of variables, method of characteristics for first order PDEs, boundary value problems for ODEs, partial differential equation and Fourier analysis and applications, comparative study of heat equation, wave equation and Laplace’s equation by separation of variables and numerical methods, further topics in numerical solution of ODEs. Prerequisite: MATH 314.

MATH 210 - Discrete Mathematics
3

Logic, propositional equivalences, predicates and quantities, methods of proof, sets, set operations, functions, proof strategy, mathematical induction, recursive definitions and structural induction, the basics of counting, permutations and combinations, relations and their properties, representing relations, equivalence relations, introduction to graphs, graph terminology, introduction to trees. Prerequisite: MATH 211.

MATH 316 - Introduction to Analysis
3

Ordered, finite countable and uncountable sets, sequences, subsequences, Cauchy sequences, upper and lower limits, series, limits of sequences of functions, continuity and compactness, connectedness, infinite limits, and limits at infinity, differentiation of vector-valued functions, series of functions, uniform convergence and continuity, functions of several variables, the inverse function and the implicit function theorems, the rank theorem. Prerequisite: MATH 215.

MATH 318 - Vector Calculus
3

Theory of vector-valued functions, divergence, gradient, curl, vector fields, path integrals, surface integrals, constrained extrema and Lagrange multipliers. Implicit function theorem. Green’s and Stokes’ theorems, introduction to differential geometry. Prerequisites: MATH 215 and MATH 311.

MATH 425 - Introduction to Complex Variables
3

Complex numbers and geometric representation, analytic, functions, real line integrals, complex integration, power series, residues, poles, conformal mappings. Prerequisite: MATH 215.

MATH 442 - Introduction to Graph Theory
3

Combinatorics through graph theory .Topics include connectedness, factorization, Hamiltonian graphs, network flows, Ramsey numbers, graph coloring, automorphisms of graphs and Polya’s Enumeration Theorem. Prerequisites: MATH 316 and Math 210.

If you have a query about a specific major or application, please contact the relevant Administrative Assistant.

Administrative Assistant

Tel: +961 5 60 30 90 Ext. 701

E-mail: da_csis@rhu.edu.lb