The Department of Mathematics offers programs leading to the degrees of Bachelor of Science (B.S.) and Bachelor of Arts (B.A.) in Mathematics and in Statistics, and the degree of Bachelor of Science (B.S.) in Computer Science. It also offers programs leading to the degree of Master of Science (M.S.) and Master of Arts (M.A.) in Mathematics and Statistics. A program leading to an M.S. degree in Computer Science is anticipated at a future date.

UNDERGRADUATE PROGRAM

B.A. or B.S. in Mathematics

All prospective mathematics majors are expected to complete Mathematics 201, 210, 211, and 219 in the sophomore year, with a cumulative grade of at least 70. They are also urged to take Mathematics 200 in the sophomore year. Mathematics majors must maintain an average grade of at least 70 in the mathematics courses to qualify for promotion from the junior year to the senior year.

B.S. Degree in Computer Science

All prospective computer science majors are expected to complete Mathematics 200, 201, 202 or 210, 211, and 212 in their sophomore year with a grade of at least 70 in Mathematics 200, and a cumulative average of at least 70 in these courses. They are also urged to take Mathematics 218 or 219 in the sophomore year. Computer science majors are expected to complete Mathematics 255, 256, 257, and 258 in the junior year and maintain an average grade of at least 70 in the computer science courses to qualify for promotion from the junior to the senior year. Students who want to pursue graduate work in computer science are advised to take Mathematics 241.

B.A. OR B.S. DEGREE IN STATISTICS

UNDERGRADUATE COURSES

Mathematics

101 Calculus and Analytic Geometry I.

3.0; 3 cr.; annually. Straight line, differentiation with application to curve plotting, Rolle's Theorem. Integration with application to area, distance, volume and arc length. The fundamental theorem of calculus. Transcendental functions. Members of Department.

 

102 Calculus and Analytic Geometry II.

3.0; 3 cr.; annually. Prerequisite: 101. Methods of integration; improper integrals. The circle, parabola and hyperbola. Hyperbolic functions. Vectors and parametric equations. Vector functions and their derivatives. Members of Department.

 

201 Calculus and Analytic Geometry III.

3.0; 3 cr.; annually. Prerequisite: 102. Polar coordinates, partial differentiation with applications. Multiple integrals with applications. Infinite series. Members of Department.

 

202 Differential Equations.

3.0; 3 cr.; annually. Prerequisite: 201. First order differential equations. Linear differential equations, homogenous and non-homogenous equations with constant coefficients. Power series solutions, Bessel functions, Legendre polynomials, Laplace transforms, initial value problems. Members of Department.

 

203 Mathematics for Social Sciences I.

 3.0; 3 cr.; annually. Not open to holders of Lebanese Bacc. II Exp. Sc. or Math. Elem. or to students with prior credit in Mathematics 101. Sets, relations and functions, rectangular coordinates, the straight lines, the circle, the ellipse, the parabola, the hyperbola; trigonometric, exponential and logarithmic functions. Implicit Differentiation. Members of Department.

 

204 Mathematics for Social Sciences II.

3.0; 3 cr.; annually. Prerequisite: 203 or 102. No credit is given to students who take 201. Sequences and series, power series. Functions of more than one variable; partial differentiation, maxima and minima of functions of two variables. Indefinite and definite integrals. Methods of integration. Multiple integrals, matrix algebra. Members of Department.

 

210 Introduction to Analysis.

3.0; 3 cr.; annually. Prerequisite: 201. Topology of real numbers, bounded sets, compact sets, countable sets; limit points; real sequences and series, convergence, absolute convergence; tests for convergence. Differentiation, the Mean Value Theorem, Taylor's Theorem; Taylor's series, power series. A. Shamsuddin.

 

213 Higher Geometry.

3.0; 3 cr.; annually. Isometry and similarity in Euclidean plane; groups of symmetries, introduction to ordered geometry and affine geometry. H. Abi-Khuzam.

 

216 Topology II.

3.0; 3 cr.; annually. Prerequisite: 214.

 

218 Linear Algebra with Applications.

 3.0; 3 cr.; annually. Prerequisite: 211. No credit will be given for both 218 and 219. Not open to mathematics majors. This course deals with vector spaces over the field of real numbers; System of linear equations and matrices, vector spaces, subspaces, dimension of a vector space, linear transformations and their representation by matrices, eigenvalues and eigenvectors, inner product spaces.

 

219 Linear Algebra I.

 3.0; 3 cr.; annually. Prerequisite: 211. Vector spaces over fields; Definition and examples. Bases and invariance of their cardinality. Linear transformations and matrices. Rank and nullity. Similarity and equivalence of matrices. Systems of linear equations. A. Hanna.

 

220 Linear Algebra II.

3.0; 3 cr.; annually. Prerequisite: 219. Row and column spaces. Determinants, eigenvalue theory. Inner product spaces. Adjoint of a linear transformation. H. Abi-Khuzam.

 

223 Advanced Calculus I.

 3.0; 3 cr.; annually. Prerequisite: 210. Real and complex number systems, metric spaces, compact sets, connected sets, sequences and series, continuity, differentiation, Riemann Stieltjes integrals. H. Abi-Khuzam.

 

224 Advanced Calculus II.

3.0; 3 cr.; annually. Prerequisite: 223. Sequences and series of functions, Stone Weierstrass' theorem, exponential, logarithmic and Gamma functions. Functions of several variables, inverse and implicit function theorem, integration of differentiable forms. H. Abi-Khuzam.

 

225 Introduction to the Theory of Ordinary Differential Equations.

 3.0; 3 cr. Prerequisites: 202, 224. Existence theorems and the method of successive approximations. Linear differential equations. Self-adjoint differential operators. Asymptotic formula for solutions and Liouville's transformation, eigenvalue theory and eigen function expansions.

 

227 Introduction to Complex Variables.

3.0; 3 cr.; annually. Prerequisite: 210. Complex numbers and their elementary properties; analytic functions; continuity and differentiability; Cauchy-Riemann conditions; contour integration; line integrals; Morera's Theorem; the fundamental theorem of algebra; power series; Taylor and Laurent series; residues and poles.

 

241 Topics in Algebra I.

3.0; 3 cr.; annually. Prerequisite: 219. Groups, normal subgroups, isomorphism theorems. Permutation groups and Cayley's Theorem. Automorphism, rings, ideals, and integral domains. Polynomial rings. A. Nahlus.

 

242 Topics in Algebra II.

 3.0; 3 cr.; Prerequisite: 241. Topics chosen from the following: module over a ring, the fundamental theorem on finitely generated modules over a Euclidean ring; algebras over a field, vector spaces, the dual space, linear transformations, characteristic roots, diagonable linear transformations, the triangular form theorem, Jordan and rational canonical forms. Group theory, Galois theory. A. Nahlus.

 

261 Number Theory:

 3.0; 3 cr.; annually. Prerequisite: 219. General introduction to the theory of numbers. Theorems of divisibilty and congruence. The Euclidean algorithm. Quadratic residues and the reciprocity law. Some Diophantine equations. Binary quadratic forms. Simple continued fractions. Some number theoretic functions.

 

271 Set Theory.

3.0; 3 cr.; biannually. Introduction to metric spaces with emphasis on the real line. Baire's category. Cardinality and ordinality. The axiom of choice. Transfinite induction. Well-ordering principle.

293 and 294 Senior Tutorial Courses.

3.0; 3 cr.

Statistics

207 Elementary Statistics for the Social Sciences.

 3.0; 3 cr.; annually. Open only to Arts students. Not open to any major in the Department. Not open to science students nor to those who hold Bacc II Exp. Sc. or Math. Elem. Students cannot receive credit for more than one of the following: Mathematics 207, Economics 213, or Education 227. Designed for students whose mathematical preparation does not allow them to follow Math 208. Includes data organization, frequency distributions, measures of central tendency and dispersion, normal distribution; random sampling and probability, binomial distribution hypothesis testing, Chi-Square tests. J. El-Haddad.

 

208 Elementary Statistics for the Sciences.

 3.0; 3 cr.; annually. Not open to students with prior credit in 233. Students can receive credit for only one of 207 and 208. Populations and samples. Random sampling errors. Types of data. Frequency distributions, empirical definition of probability. Probability distributions. Elements of point and interval estimation and hypothesis testing. Applications, using the binomial, normal, Chi-Square and t distributions. Relationship between categorical variables and between numerical variables (regression). J. El-Haddad.

 

230 Introduction to Random Variables and Statistical Inference with Computing.

 3.0; 3 cr.; annually. Prerequisites: 200 and 201.

 

233 Introduction to Probability and Random Variables.

 3.0; 3 cr.; annually. Prerequisite: 201. Axiomatic definition of probability, random variables, univariate and multivariate p.d.f. and c.d.f. Expectation and moment generating functions. Conditional distributions, Families of discrete and continuous random variables. Distribution of functions of random variables. Stochastic convergence and convergence of distribution functions. The law of large numbers and the central limit theorem. J. El-Haddad.

 

234 Introduction to Statistical Inference.

3.0; 3 cr.; annually. Prerequisite: 233. Sampling distributions. Point estimation, interval estimation. Neuman-Pearson theory of hypothesis testing. Likelihood ratio test. Sequential analysis. Elementary decision theory.

 

235 Topics in Statistics.

 3.0; 3 cr.. Prerequisite: 234. Multivariate distributions. Simple regression models. Nonparametric statistics; order and rank test. Sequential analysis. Elementary decision theory.

 

236 Sampling Techniques.

 (Same as EB 222). 2.2; 3 cr.; annually. Pre- or co-requisite: 234. Simple random, systematic, startified, cluster and two-stage sampling. Estimation of parameters and properties of estimates. Ratio and regression estimates. Problem of non-response.

 

238 Probability Theory.

 3.0; 3 cr.; annually. Prerequisite: 233.

Computer Science

200 Introduction to Programming.

3.3; 4 cr.; annually. Introduces a disciplined approach to computer programming and problem solving, utilizing a block-structured high level language like Pascal. Emphasizes procedural abstraction, and good programming style. Covers the basic repetition and selection constructs; procedures and functions, parameter passing and scope of variables. Members of Department.

 

206 Computers and Programming for the Arts.

2.3; 3 cr.; annually. Open to Arts students only. No credit for this course is given to computer science majors. Introduces computers and illustrates their use through common application packages. Word-processing, spreadsheets and database systems are considered. Programming will be introduced through a commonly used programming language (Basic). The course is meant to be a computer literacy course.

 

209 Computers and Programming for the Sciences.

2.3; 3 cr.; annually. No credit for this course is given to computer science majors. Introduces computers and illustrates their use through common application packages. Word-processing, spreadsheets and database systems are considered. Programming will be introduced through a commonly used programming language. The course is meant to be a computer literacy course.

 

211 Discrete Structures.

3.0; 3 cr.; annually. Introduces logical reasoning, sets, relations and functions; mathematical induction, counting and simple finite probability theory; modular arithmetic and arithmetic in different bases; recurrence relations and difference equations; truth tables; and switching circuits, graphs and trees; strings and languages. W. Jureidini, A. Shamsuddin.

 

212 Intermediate Programming with Data Structure.

3.3; 4 cr.; annually. Prerequisite: 70 or more in 200. Continuation of Math 200. Consolidates algorithm design and programming techniques, emphasizing large programs, giving a detailed study of data structures and data abstraction, and introducing complexity considerations and program verification. A. Nasri.

 

230 Introduction to Random Variables and Statistical Inference with Computing.

 3.0; 3 cr.; annually. Prerequisites: 200, 201. Random variables, mathematical expectations, probability, density functions, moment generating functions. Overview of probability theory. Selected probability distributions: binomial, normal, exponential, T, C2, F-Point and interval estimation. Hypothesis testing and use of computer packages.

 

251 Numerical Computing.

 3.0; 3 cr.; annually. Prerequisites: 200 or 209, 202 or 210. Introduces the classical techniques of numerical analysis: number representations and round-off errors; root finding; approximation of functions; integration; solving initial value problems; Monte-Carlo methods. Implementations and analysis of the algorithms used will be stressed. W. Jureidini.

 

255 Computer Architecture and Assembly Language.

 3.0; 3 cr.; annually. Prerequisite: 212. Gives a structured overview of the architecture of digital computers. Students will be exposed to one or more micro/mini architectures, and will be expected to complete a number of programs in assembly language. G. Jalloul.

 

256 Advanced Algorithms and Data Structures.

3.0; 3 cr.; annually. Prerequisite: 212. Systematic study of algorithms and their complexity. Topics includes advanced searching and sorting algorithms, graph and matrix algorithms, and intractable problems. A. Shamsuddin.

 

257 Theory of Computation.

3.0; 3 cr.; annually. Prerequisite: 211. Covers basic theoretical principles embodied in automata and grammars. Turing machines, and complexity theory. Topics include regular expressions, finite automata, context-free grammars, pushdown automata, closure properties, parsing; Turing enumerability; TIME classes, P and <P problems, P-time reductions and NP-Completeness. W. Jureidini.

 

258 Programming Languages

3.0; 3 cr; annually. Prerequisite: 212. Emphasizes the principles and programming styles that govern the design and implementation of contemporary programming languages. Focuses on functional, object oriented, and rule-based paradigms, using the languages Lisp, Smalltalk, and Prolog. Students are assumed to be familiar with the procedural paradigms. G. Jalloul.

 

272 Operating Systems.

 3.0; 3 or; annually. Prerequisites: 255, 256. Presents an overview of the structure and the different functions of operating systems. Topics include: processes and CPU scheduling, memory management, virtual memory, disk and drum scheduling, file systems, concurrent processing and synchronizations, and general resource allocation. A. Nasri.

 

274 Compiler Construction.

 3.0; 3 cr; annually. Prerequisites: 255, 257. Syntax specifications of programming languages, parsing theory, top-down and bottom-up parsing, parser generators, syntax-directed code generation, symbol table organization and management, dynamic storage allocation, code optimization, dataflow analysis, register allocation. G. Jalloul.

 

277 Database Systems.

 3.0; 3 cr.; annually. Prerequisites: 256 and preferably 272. Presents an overview of the nature and purposes of database systems. Introduces data modeling, file organization and the internal structures of database systems, and issues of query optimization, protection, concurrent operations, and distributed database systems. Students will be exposed to query languages such as SQL or Quel. W. Jureidini.

 

281 Numerical Linear Algebra.

 3.0; 3 cr.; biannually. Prerequisites: 219, 251. Direct and interactive methods for solving general and special systems of linear equations. Covers LU decomposition, Choleski decomposition, nested dissection, marching algorithms; Jacobi, Gauss-Seidel, successive overrelaxation, Alternating directions, and cojugate gradient iterative methods.

 

282 System Design and Analysis.

 3.0; 3 cr.; biannually. Prerequisite: 277. Project management, systems requirements. Data flow concepts, decision tables. Conditions and decision variables. Design of output and input forms. Files and database development. On-line and distributed environments. System documentation. System implementation. G. Jalloul.

 

283 The Logic of Programming.

3.0; 3 cr.; biannually. Prerequisites: 212, Philosophy 211. Presents computer programming as a rigorous mathematical discipline. Topics include: sentential logic; predicate logic; expressions and commands; pre/post-conditions; assignment, alteration, repetition, invariant predicate, function predicate; modules; data structures; concurrency.

 

285 Computer Graphics.

3.0; 3 cr.; annually. Prerequisite: 256. Covers the practice of, and underlying mathematical foundation for, interactive graphics programming. Topics include segmentations, windows and viewports, clipping, hidden, lines, geometric transforms, data structures for memory management, and device independent graphics specifications. A. Nasri.

 

287 Artificial Intelligence.

 3.0; 3 cr.; annually. Prerequisites: 256, 258. Introduces the principles and techniques that enable computers to behave intelligently. Covers basic problem solving methods; knowledge representation; memory organizations and deduction; abduction, reasoning under uncertainty, and expert systems; language processing; learning from samples and from experience. Several projects will be given using Lisp and/or Prolog.

 

297 Selected Topics in Computer Science.

 3.0; 3 cr. Prerequisite: Senior standing. Contents change according to the interests of the instructor. Topics will be chosen from: distributed computer systems, concurrent processing and parallel algorithms, theory of relational databases, and others.

GRADUATE PROGRAM

M.A. or M.S. in Mathematics

M.A. or M.S. in Statistics

GRADUATE COURSES

Mathematics

301 and 302 Graduate Tutorial Courses.

1-3 cr.; Prerequisite: Graduate standing or consent of instructor.

303 Measure and Integration.

3.0; 3 cr.; annually. Prerequisite: 224. Abstract integration, positive Borel measures and Riesz representation theorem. LP spaces, complex measures, Radon-Nikodym theorem, integration product spaces and Fubini's theorem. Derivatives of measures and differentiable transformations.

304 Complex Analysis.

3.0; 3 cr.; annually. Prerequisites: 224, 227. Elementary properties of holomorphic functions, open mapping theorem and applications, Harmonic functions, Poisson integral, the maximum modulus principle, conformal mapping and Rienmann mapping theorem, analytic continuation, monodromy theorem, Picard's theorem.

305 Functional Analysis.

3.0; 3 cr.; annually. Prerequisite: 224. Vector spaces, Hamel basis, Schuder basis, Hahn-Banach theorem, Banach-Steinhaus theorem, open mapping and closed graph theorem with applications.

306 Calculus and Manifolds.

 3.0; 3 cr. Prerequisite: 224.

307 Topics in Analysis.

3.0; 3 cr.

314 Algebraic Topology I.

3.0; 3 cr.; annually. Prerequisites: 214, 241. Categories and functors; homotopy; covering projections and fibrations; simplicity complexes; simplicial and singular homology. J. Nikiel.

315 Algebraic Topology II.

3.0; 3 cr.; annually. Prerequisite: 314. Characteristic functions; types if convergence; limiting properties of distribution and characteristic functions; limit theorems; multivariant functions.

316 Topics in Topology.

3.0; 3 cr.

341 Modules and Rings I.

 3.0; 3 cr.; annually. Prerequisite: 241. Fundamental concepts of modern ring theory; injective and projective modules, generating and congenerators, tensor products and flat modules. Finiteness conditions; Artinian and Neotherian modules and rings, modules with composition series. A. Shamsuddin.

342 Modules and Rings II.

 3.0; 3 cr.; annually. Prerequisite: 341. Topics may include any of the following: ring theory, homological algebra or lattice theory.

343 Field Theory.

3.0; 3 cr.; annually. Prerequisite: 242.

344 Commutative Algebra.

 3.0; 3 cr. Prerequisites: 242, 341.

345 Topics in Algebra.

3.0; 3 cr. A. Hanna.

351 Topics in Applied Mathematics.

 3.0; 3 cr.; annually. Prerequisites: 223 and 251. Topics chosen from approximation theory, numerical methods for ordinary and partial differential equations, numerical linear algebra.

399 M.A. or M.S. Thesis.

Statistics

331 Advanced Probability Theory.

3.0; 3 cr.; annually. Prerequisites: 227, 238, 304. Characteristic functions; types if convergence; limiting properties of distribution and characteristic functions; limit theorems; multivariant functions.

332 Advanced Mathematical Statistics.

 3.0; 3 cr.; annually. Prerequisites: 235, 238. Distribution theory; decision theory; advanced topics in estimation and inference.

333 Multivariate Analysis.

3.0; 3 cr.; annually. Prerequisites: 238. Multivariant distributions; correlation coefficients; classification and discrimination; Hotelling's T2; tests of hypotheses for multivariate distributions; canonical variables.

334 Advanced Topics in Statistics.

3.0; 3 cr.; annually.

335 Selected Topics from Probability and Statistics.

3.0; 3 cr.; annually.

399 M.A. or M.S. Thesis.