Bethlehem University - Faculty of Science

The Department of Mathematics offers a Bachelor of Science degree with a major in Mathematics. The department aims to develop within the students skills of analytical thinking, initiative and creativity and prepares the individual for careers not only in teaching but also in firms, banks, governmental and non-governmental organizations, statistics and others. The department also prepares the individuals to pursue post-graduate studies in mathematics and other related fields. The Department of Mathematics also offers service courses to other departments.

A student majoring in Mathematics needs to earn a total of 129 credits distributed as follows.

The Major consists of a total of 70 credits to include all the required courses listed in the tables below and a minimum of 9 credit courses to be selected from the electives list.

MATH 141	Calculus I (4)	MATH 333	Mathematical Statistics (3)
MATH 142	Calculus II (4)	MATH 334	Advanced Calculus I (3)
MATH 241	Calculus III (4)	MATH 335	Advanced Calculus II (3)
MATH 234	Differential Equations (3)	MATH 336	Intro. to Modern Algebra (3)
MATH 235	Intro. to Linear Algebra (3)	MATH 338	Complex Variables (3)
MATH 238	Discrete Mathematics (3)	MATH 389	Senior Seminar (1)
MATH 331	Probability (3)

MATH 332	Theory of Numbers (3)	MATH 362	Topics in Applied Statistics (3)
MATH 337	Topology (3)	MATH 371	Applied Mathematics (3)
MATH 342	Topics in Algebra (3)	MATH 372	Numerical Analysis (3)
MATH 361	Regression Analysis (3)	MATH 399	Special Topics in Math. (3)

CAIT 131	Computer Programming (3)	CHEM 132	General Chemistry II (3)
BIOL 141	Principles of Biology I (4)	PHYS 113	Laboratory Practice (1)
CHEM 113	General Chemistry Lab (1)	PHYS 131	General Physics I (3)
CHEM 131	General Chemistry I (3)	PHYS 132	General Physics II (3)

Students majoring in Mathematics are provided the opportunity to minor in a discipline other than their major field. A student may take any minor offered by the other faculties in the university.

The University requirements for all mathematics students total 34 credits. The mathematics requirement is met by MATH 141 and the science requirement by BIOL 141 or CHEM 131 or PHYS 131.

Students are accepted to major in Mathematics after their third semester provided that they have earned at least 40 credits and that all of the following conditions are met:

In addition to the Major in Mathematics, the Mathematics Department provides the opportunity for all students to join the program towards a minor in mathematics and a minor in computer and information technology.

To earn this minor, students are required to successfully complete 19 credit hours.

MATH 234	Differential Equations	3		MATH 238	Discrete Mathematics	3
MATH 235	Intro. to Linear Algebra	3		MATH 241	Calculus III	4

The minor in Computer and Information Technology requires the successful completion of the following required courses, totaling 9 credits, and 9 credits from the list of electives below.

CAIT 231	Operating Systems	3		CAIT 232	Computer Networks	3
CAIT 233	Sys. Analysis and Design	3

CAIT 234	Internet, Web, and TCP/IP	3	CAIT 326	Multimedia, Graphics, Imag.	3
CAIT 252	Intro. To Data Processing	3	CAIT 421	Object Oriented Program.	3
CAIT 325	Data Base Management Sys.	3	CAIT 429	Special Topics	3

A basic math course for non-science students which covers problem solving techniques, sets, basic probability and statistics, number systems and their structure, linear and quadratic equations, basic consumer mathematics.

The first course in calculus covers functions and their graphs, limits and continuity, tangent lines and derivatives, some theorems on differentiation, applications of derivatives, such as: curve sketching, maxima and minima problems, definite and indefinite integrals, and applications of integrals.

A continuation of Math 141 includes methods of integration and applications. Other topics are: inverse trigonometric, logarithmic and exponential functions, other transcendental functions, conic sections, parameterized curves and polar coordinates, some sequences and series. Prerequisite: MATH 141

Introduction to different types of ordinary differential equations, first and higher order, linear systems of equations, Laplace transform and power series solutions, and some physical applications. Prerequisite: MATH 142

Fields, linear systems over fields, matrices and their arithmetic, determinant of a matrix, linear spaces and subspaces, bases, linear transformations, eigenvalues and eigenvectors, diagonalization and canonical forms are covered. Prerequisite: MATH 142

Introduction to: set theory and logic, Boolean algebra, basic concepts in graph theory, basic combinatorics, equivalence relations and partial ordering, formal languages, finite state mechanics, and cardinality. Prerequisite: MATH 142

This course incorporates further work in calculus and analytic geometry covering vectors and analytic geometry in space, vector functions with their derivatives, multivariable functions, partial differentiation and multiple integration and applications, and some vector analysis. Prerequisite: MATH 142

Introduction to probability, methods of enumeration, conditional probability and independence, random variables of discrete and continuous types, expectation and variance, different kinds of distributions, moment generating function and functions associated with the normal distribution, and the central limit theorem. Prerequisite: MATH 241 (MATH 238 highly recommended)

A study of the integers, divisibility properties, primes, prime factorization, diophantine equations, numerical functions, congruences and their applications, residues, primitive roots, theorems of Euler, Fermat, Lagrange, Wilson and the Chinese Remainder theorem. Prerequisite: MATH 142 (MATH 238 highly recommended)

A continuation of MATH 331 which includes an introduction to sampling theory, the student t and F distributions with random functions associated with them, and the law of large numbers. Estimation theory, which includes unbiased, consistent, efficient, sufficient and maximum likelihood estimators is also included as well as testing hypothesis for means, proportions, variances and some regression. Prerequisite: MATH 331

Formal introduction to the real number system, sequences of real numbers, deeper study of limits, and continuity and differentiability of functions of a real variable. Prerequisite: MATH 241

Continuation of MATH 334 which includes: Riemann integration, series of real numbers, sequences and series of functions, other topics of real analysis. Prerequisite: MATH 334

An introductory course in the elements of modern algebra which includes: groups, homomorphism, Lagrange theorem, quotient groups, isomorphism theorem, symmetric groups and Sylow�s theorems. Rings, ideals, quotient rings and homomorphism, rings of polynomials in integral domains, principal ideal domain and the unique factorization theorem are also included. Prerequisite: MATH 241

Metric spaces, convergence and continuity, completeness and Cauchy�s completion theorem, general topological spaces, separation axioms, metrizability, compactness, and connectedness, compactification theorems, product spaces and Tychonof theorem, the fundamental group and an introduction to homotopy theory are included in the course. Prerequisite: MATH 335

The algebra and geometry of complex numbers, analytic functions, Cauchy-Riemann Equations, complex series, integration of complex functions, and some applications of complex variables to physics are covered in the course. Prerequisite: MATH 335

The Euclidean spaces and elementary topology on them, limits and continuity, differentiability of real and vector valued functions, implicit and inverse function theorems, measure and integrals in Euclidean spaces are covered in the course. Prerequisite: MATH 335

This course is a continuation of MATH 235 and MATH 336 which includes: inner product spaces, orthonormal bases and the Grahm-Schmidt process, linear operators on inner product spaces, unitary and Hermitian operators, the spectral theorem, bilinear and quadratic forms, diagonalization, Sylvester�s and Caley-Hamilton theorems, Jordan forms; extension of fields and an introduction to Galois theory. Prerequisite: MATH 235, MATH 336

The course is a service course. It is intended to provide an introduction to elementary statistical concepts basic to interpretations and applications. The first part of the course is descriptive statistics and the second part is inferential, tests for means proportions, contingency tables, correlation and linear regression are studied. A computer statistical package will be used for data analysis.

Sampling techniques, testing statistical hypothesis, single and multiple linear regression, polynomial and nonlinear regression, model building and statistical inference in regression analysis are covered in the course. A computer statistical package will be used for data analysis. Prerequisite: MATH 333

This course is an introduction to basic methods of experimental design, analysis of variance, contingency tables, nonparametric statistical techniques such as: the sign test, Wilcoxon and other tests. A computer statistical package to utilize these methods will be used. Prerequisite: MATH 361

Fourier series and their applications, orthogonal and periodic functions, Parseval equation, partial differential equations, heat and wave equations are covered in this course. Fourier transforms and some topics in calculus of variation are also covered. Prerequisite: MATH 234 (MATH 235 highly recommended)

Solutions of equations in one variable, polynomial approximation, numerical differentiation and integration, initial value problems for ordinary differential equations, linear systems, iterative technique, and numerical solutions to partial differential equations are covered in the course. Prerequisite: MATH 234 (MATH 235 highly recommended)

Senior mathematics majors are required to conduct an intensive research study of a particular subject in mathematics chosen from a selected list of topics approved by the Mathematics Department. Seminar participants must present their subjects for discussion at seminar meetings with faculty members. Required of and restricted to senior mathematics majors

This is an independent study course open to senior mathematics majors. Topics are selected by the instructor in accordance with the student�s ability and previous study. Prerequisite: Consent of Department

This is a general introduction to historical development, types of computers, computer organization showing memory, processor and peripheral devices, binary numbers and their significance in information presentation, logic and solution formulation, compilers and computer languages, applications in a computer programming language showing control structures, functions, data types and classes, and techniques in programming.

This is an introduction to: operating systems, processes, process states, process management, memory and storage management, processors and scheduling, deadlock and other related topics. Practical work includes examination of DOS and of UNIX as operating systems. Prerequisite: CAIT 131 or BUSA 227

Networking layers, identification of characteristics, requirements and needs for each layer, the concept of a network as a local area network, kinds of channels and connections as hardware elements like hubs, routers and mux�s, drivers and systems utilities for networking, network topologies such as: star, line and bus, the networking software, installation and procedures, network administration and management, resource sharing, security issues and maintenance of networks are covered in the course. Prerequisite: CAIT 231

The course includes analysis of systems, techniques of studying current situation and conducting feasibility studies. Study, planning, development and operation phase structures of the life cycles of a system, planned versus achievement examination and project control, design of a complete system and possibility of implementing a part of it as a project are also covered. Prerequisite: CAIT 131 or BUSA 227

The concept of a network of networks, WANs, MANs, and the Internet are covered. Channels and communications with emphasis on leased lines, microwaves and radio modems, overview of satellite communication, web server installation, configuration and management, web programming, including HTML programming, page design and installation, including data bases on line and how to access them, information transactions on line, technical work of TCP/IP configurations, management and initial trouble shooting skills are also included. Prerequisite: CAIT 232

This is a service course offered to other departments which is an introduction to computers and data processing. The concept of information, and information units, including bytes and bits, data and program files, office automation like sending and receiving email, connecting to the Internet, creating a document and processing it, creating a spread sheet and including formulas and charts in presentations are part of the course. Introduction to statistical data, collecting data and designing a questionnaire sheet, entering data using a spread sheet and producing frequency tables and cross tabulations in addition to averages are also covered.

Data base structures including data fields, records and tables, indexing and access methods, database structures with emphasis on relational data bases are covered. Querying and retrieval techniques, implementation methods and data base management systems, user�s interface, graphic and friendliness, maintenance of data base systems and back up techniques are also included. Practical work includes direct implementation and application of a DBMS such as Delphi or MS Access. Prerequisite: CAIT 233

The use of multimedia techniques, audio processing and integration with images and text, application of different tools of multimedia to generate video files, editing and formatting for publishing, image processing, and techniques such as capturing, filtering, enhancing, and handling of large images, digitization, geographic applications through an introduction to GIS systems are covered in the course. Prerequisite: CAIT 131 or BUSA 227

Object oriented programming with intermediate and advanced techniques in designing and implementing applications are included in the course. Practical work and examination of several software tools will be a main focus in addition to the programming techniques introduced in this course. Prerequisite: CAIT 131

This is a senior year advanced level course in subjects that are the current state-of-the-art topics in information technology and computing sciences and engineering. The topics will be selected and prepared by the teacher, approved by the department, and announced to the students at the time of registration.