### Program Description

**Mission **

The program provides students with the opportunity to study the primary areas of contemporary mathematics, provides physical and social science majors with the necessary mathematical tools for work in their disciplines, and introduces all students to serious and interesting mathematical ideas and their applications.

**
Objectives
**

The program strives to enable students to:

1. Build a foundation of basic knowledge of mathematics.

2. Improve analytical and problem-solving skills.

3. Develop research skills and be aware of the variety problems related to the field of study.

4. Enhance professional thinking.

**
Learning Outcomes
**

The mathematics program enables students, by the time of graduation, to achieve the following learning outcomes:

a. Knowledge and understanding of:

1. The basic theorems and concepts in the different areas of mathematics.

2. The implementation of theories in problem solving.

3. The different areas of research in mathematics.

b. Intellectual abilities:

1. Ability to understand the different math concepts and be able to implement them in our everyday problems.

2. Ability to consider problems that could be solved by implementing concepts from different areas in
mathematics.

3. Ability to identify, formulate, and solve problems.

c. Professional and Practical competencies:

1. Efficient use of computers, laboratories and software to handle problems that are difficult to be solved
manually.

2. Understanding of professional and ethical responsibilities.

3. Efficient use of the techniques, skills and tools of modern mathematics.

d. General and Transferable Skills:

1. Functioning in multi-disciplinary teams.

2. Communicate ideas effectively in graphical, oral, and written media.

3. Recognize and respond to the need for lifelong and self-learning for a successful career.

**
Career Opportunities
**

1. Teaching

2. Consultants to actuaries

3. Management Services & Computing

4. Accountancy

5. Statistical Work

Academic Staff:

Chairperson: Prof. Mohammad N. Abdulrahim

Professors: Prof. Ali El-Zaart

Associate Professors: Dr. Imad Al Ashmawy, Dr. Toufic El Arwadi, Dr. Noura Yassin, Dr. Abdullah al-Chakik

Assistant Professors: Dr. Ahmed Sherif, Dr. Wassim El-Hajj Chehade, Dr. Maher Jneid, Dr. May Itani, Dr. Lama Affara

Mission:

The program provides students with the opportunity to study the primary areas of contemporary mathematics, provides physical and social science majors with the necessary mathematical tools for work in their disciplines, and introduces all students to serious and interesting mathematical ideas and their applications.

Objectives:

The program strives to enable students to:

- Build a foundation of basic knowledge of mathematics.
- Improve analytical and problem-solving skills.
- Develop research skills and be aware of the variety problems related to the field of study.
- Enhance professional thinking.

Learning Outcomes :

The mathematics program enables students, by the time of graduation, to achieve the following learning outcomes:

a- Knowledge and understanding of:

- The basic theorems and concepts in the different areas of mathematics.
- The implementation of theories in problem solving.
- The different areas of research in mathematics.

b- Intellectual abilities:

- Ability to understand the different math concepts and be able to implement them in our everyday problems.
- Ability to consider problems that could be solved by implementing concepts from different areas in mathematics.
- Ability to identify, formulate, and solve problems.

c- Professional and Practical competencies:

- Efficient use of computers, laboratories and software to handle problems that are difficult to be solved manually.
- Understanding of professional and ethical responsibilities.
- Efficient use of the techniques, skills and tools of modern mathematics.

d- General and Transferable Skills:

- Functioning in multi-disciplinary teams.
- Communicate ideas effectively in graphical, oral, and written media.
- Recognize and respond to the need for lifelong and self-learning for a successful career.

Degree Requirements :

To obtain the Bachelor Degree in Mathematics’ Program, students must successfully complete a total of 97 credit hours + IC3, where the standard duration of study is 6 semesters. There is one general semester of study for the students of the Mathematics Program.

Career Opportunities:

Teaching, Consultants to actuaries, Management Services & Computing, Accountancy, Statistical Work.

Program Overview:

** I. University Requirements** |
**Credits** |

* University Mandatory Courses |
5 |

* University Elective Courses |
11 |

**II. Program Requirements** |
**Credits** |

Faculty Core Courses |
19 |

Major Core Courses |
44 |

Departmental Electives |
12 |

**Faculty Electives |
6 |

**Total** |
**97** |

**
*A total of 16 credits is required as University Requirements: **5 credits are selected from the University Mandatory courses list.

At least one course from social sciences and one course from humanities should be selected among the university elective courses.

**** A total of 6 credits is required as faculty electives.**

Students can enroll in any course offered by the Faculty of Science.

Student Enrollment History:

Academic Years |

**2013/2014:** 46 |

**2014/2015:** 56 |

**2015/2016:** 51 |

**2016/2017:** 54 |

**2017/2018:** 37 |

Student Graduation History:

Academic Years |

**2013/2014:** 10 |

**2014/2015:** 11 |

**2015/2016:** 10 |

**2016/2017: **24 |

**2017/2018:** 15 |

Study Plan:

A study of the fundamental concepts of chemistry including matter and measurement, atoms, molecules, ions, moles, nomenclature, atomic and molecular weights. Stoichiometry. Chemical reactions, quantitative calculations. Periodic table, atomic structure, periodic properties of the elements, chemical bonding, molecular structure. The gaseous, liquid, and solid states of matter. Properties of solutions, aqueous reactions and solution stoichiometry. Thermochemistry, chemical thermodynamics, chemical kinetics, chemical equilibrium, acids, bases and ionic equilibria, electrochemistry, nuclear chemistry and coordination chemistry.

Selected experiments illustrate the topics discussed in CHEM 241. Co-req.: CHEM 241.

Introduction to computer hardware and software. Binary system and data representation. The software life-cycle. Flow charts and IPO-charts. Introduction to computer programming and problem solving. Structured high level language programming with an emphasis on procedural abstraction and good programming style. The basic looping and selection constructs arrays, functions, parameter passing and scope of variables.

Multivariable functions, partial derivatives, polar, cylindrical and spherical coordinates, indefinite and definite integrals, methods of integration, multiple integrals, sequences and series, power series, vector field integration.

Physics and measurement: standards of length, mass, and time; Non-viscous fluids, Pascal’s principle, Bernoulli’s equation, Viscous flow of fluids and Poiseuille’s law; Temperature, heat and thermal properties of matter; Heat transfer by conduction, convection and radiation; Reflection, refraction and image formation by the eye and camera; Sound waves; Moduli of Elasticity: Young, shear and bulk and relation among them; Elastic properties of materials; Coulomb's law and the electric field; Electric flux and Gauss’s law, Electric potential and potential energy; Capacitance and dielectrics; Magnetism: magnetic forces, magnetic dipole; Magnetic flux and Gauss law in magnetism.

): Experimental work related to the topics discussed in PHYS 243. Co-req.: PHYS 243.

Basic concepts in statistics (mean, variance and frequency distribution), Random variables, discrete probability, conditional probability, independence, expectation, standard discrete and continuous distributions, central limit theorem, regression and correlation, confidence intervals.

First order ordinary differential equations and applications, linear higher order differential equations, systems of linear differential equations, series solutions of differential equations, Laplace transforms. Pre-req.: MATH 241.

Metric spaces, basic topics in topology of the real line, numerical sequences and series, continuity and uniform continuity of functions, differentiation, the mean-value theorem, Taylor’s theorem, Riemann-Stieljes integral. Pre-req.: MATH 241.

Multivariable functions, partial derivatives, multiple integrals, polar coordinates, vectors and analytic geometry in space. Pre-req.: MATH 241.

A rigorous introduction to linear algebra with emphasis on proof and conceptual reasoning, matrices, determinants, system of linear equations, vector spaces, linear transformations and their matrix representation, linear independence, bases and dimension, rank-nullity, brief discussion on inner product, projections, orthonormal bases, eigenvalues, eigenvectors, diagonalization.

Legendre and Bessel functions, Hermite and Laguerre polynomials, hypergeometric functions, Gamma, Beta and Error functions. Pre-req.: MATH 244.

Logical reasoning and proof, sets, relations and functions, matrices, Boolean Algebra, mathematical induction, counting and simple finite probability theory, analysis of algorithms, truth table, graphs and trees, Euler’s path and Euler’s cycle.

This course provides pedagogical content knowledge and curriculum knowledge for high school teachers in the fields of science. By the end of the course, students should be able to prepare a successful lesson plan and handle different teaching strategies and assessment techniques and they should integrate technology in teaching by the use of useful educational software and perform and interpret a scientific experiment.

Student can enroll in any course offered by BAU faculties, with at least one course outside the department offering the program.

Vector fields, differentiation of vector functions, the derivation as a linear transform, gradient of scalar function, inverse and implicit function theorem, directional derivative, divergence, curl, differential forms, linear integrals, Stoke’s theorem and Green’s Theorem with applications, orthogonal curvilinear coordinate systems, cylindrical, spherical and elliptic coordinate systems. Pre-req.: MATH 241.

Riemann integral, convergence of sequences and series of functions, functions of several variables, limit of integral of a sequence of functions, contraction principle. Pre-req.: MATH 246.

Binary operations, groups, subgroups, normal subgroups, cyclic groups and subgroups, cosets, Lagrange’s theorem, counting theorems, groups of permutations, quotient groups, homomorphisms, isomorphisms, homomorphism theorems. Direct product, fundamental theorem of finite abelian groups. Classification of groups of low order. Pre-req.: MATH 345.

Solutions of nonlinear equations in one variable: Bisection, Newton, Fixed point and Secant methods, interpolation and approximation: Lagrange Polynomial, divided differences, Hermite interpolating polynomial, numerical differentiation and integration (quadrature formulas), direct method for solving linear system, numerical methods for solving nonlinear systems of equations, numerical solutions of ODEs. Pre-req.: MATH 241.

Complex numbers, analytic functions, integration in the complex plane, Cauchy’s integral theorem, Taylor’s series, Laurent series, singularities, residues and contour integration. Pre-req.: MATH 241.

Topological spaces, open sets, closed sets, derived sets, interior and closure, continuous functions, separation axioms, compactness, connectedness, metrizable spaces and finite product spaces. Pre-req.: MATH 246.

Student can enroll in any course offered by BAU faculties, with at least one course outside the department offering the program.

Rings, integral domains, fields, ideals, quotient rings, prime and maximal ideals. Divisibility theory, unique factorization domains, Euclidean domains. Polynomial rings, finite fields. Pre-req.: MATH 346.

A topic in mathematics is chosen under the consent of an academic advisor, where the student has to write about it and submit a written project at the end of the semester.

Uniform and absolute convergence of infinite series and integrals, Gram-Shmidt orthogonalization, orthogonal polynomials, Fourier series, Fourier transform, Parseval and Plancherel theorems, some applications. Pre-req.: MATH 246.

Course Code |
Course Title |
Credits |
Hours Distribution |
Course Type |

First Semester |

CHEM241 |
Principles of Chemistry |
3 |
(3Crs.:3Lec) |
FC |

CHEM241L |
Principles of Chemistry Laboratory |
1 |
(1Cr.:3Lab) |
FC |

CMPS241 |
Introduction to Programming |
3 |
(3Crs.:2 Lec.,2Lab) |
FC |

MATH241 |
Calculus and Analytical Geometry |
3 |
(3Crs.:3Lec) |
FC |

PHYS243 |
General Physics |
3 |
(3Crs.:3Lec) |
FC |

PHYS243L |
General Physics Laboratory |
1 |
(1Cr.:3Lab) |
FC |

------- |
University Requirement |
2 |
(2crs.) |
CUR |

Second Semester |

MATH242 |
Probability and Statistics |
3 |
(3Crs.:2Lec.,2 Lab) |
FC |

MATH244 |
Ordinary Differential Equations |
3 |
(3Crs.:3Lec) |
MJC |

MATH246 |
Real Analysis I |
3 |
(3Crs.:3Lec) |
MJC |

MATH248 |
Multivariable Calculus |
3 |
(3crs.) |
MJC |

------- |
University Requirement |
5 |
(5crs.) |
CUR |

Third Semester |

MATH341 |
Linear Algebra |
3 |
(3Crs.: 3Lec.,1 Lab) |
MJC |

MATH343 |
Special Functions |
3 |
(3Crs.:3Lec) |
MJC |

MATH345 |
Discrete Mathematics |
3 |
(3Crs.:2Lec.,2 Lab) |
MJC |

TSHS341 |
Teaching Science in High School |
2 |
(2crs.: 2lec.) |
FC |

------- |
Departmental Elective |
3 |
(3crs.) |
DE |

------- |
Faculty Elective |
3 |
(3crs.) |
FE |

Fourth Semester |

MATH342 |
Vector Calculus |
3 |
(3Crs.:3Lec) |
MJC |

MATH344 |
Real Analysis II |
3 |
(3Crs.:3Lec) |
MJC |

MATH346 |
Abstract Algebra I |
3 |
(3Crs.:3Lec) |
MJC |

MATH348 |
Numerical Methods |
3 |
(3Crs.:2Lec.,2 Lab) |
MJC |

------- |
University Requirement |
5 |
(5 crs) |
CUR |

Fifth Semester |

MATH441 |
Introduction to Complex Analysis |
3 |
(3Crs.: 3Lec) |
MJC |

MATH443 |
Topology |
3 |
(3Crs.: 3Lec) |
MJC |

------- |
University Requirement |
4 |
(4crs. |
CUR |

------- |
Departmental Elective |
3 |
(3crs.) |
DE |

------- |
Faculty Elective |
3 |
(3crs.) |
FE |

Sixth Semester |

MATH442 |
Abstract Algebra II |
3 |
(3Crs.:3Lec) |
MJC |

MATH444 |
Senior Project |
2 |
(2Crs.:2Lec) |
MJC |

MATH446 |
Fourier Series and Applications |
3 |
(3Crs.:3Lec) |
MJC |

------- |
Departmental Elective |
6 |
(6crs.) |
DE |

### Departmental Elective(DE)

Vectors in Euclidean space, basic rules of vector calculus in Euclidean spaces,theory of curves: arc length, tangent and normal plane, osculating plane, principal normal, curvature, binomial, moving trihedron of a curve, torsion, formulas of Frenet, evolutes and involutes, cylindrical helices, curvature and torsion of involutes and evolutes, surfaces : curves on surfaces, tangent and normal planes, family of surfaces, envelope, edge of regression, Gaussian and mean curvatures, lines and curvature. Pre-req.: MATH 241.

Divisibility, greatest common divisor, prime factorization, congruence, quadratic residues, Legendre symbol, Jacobi symbol, quadratic reciprocity, linear Diophantine equations, binary quadratic forms.

Elementary logic, propositional and predicate calculus, operations on sets and families of sets, ordered sets, countable and uncountable sets, transfinite induction, axiom of choice and equivalent forms, ordinal and cardinal numbers.

Vector algebra, motion of particle in a straight line with variable acceleration, vector motion of a particle, simple harmonic motion with applications, simple pendulum and conical pendulum, motion projectiles, impulse, momentum and impact of elastic bodies, center of mass of rigid bodies, motion of a particle in two dimensions using polar coordinates and intrinsic coordinates, motion of a particle on a rough curve in a vertical plane. Pre-req.: MATH 241.

Topics will include: variation of a functional, the Euler-Lagrange equations, parametric forms, canonical transformations, conservation laws, the Hamilton-Jacobi equation, second variation. Pre-req.: MATH 244.

Normed vector spaces, differentiation, diffeomorphisms, Jacobian matrix (finite dimension case), high order differentiation, Schwarz theorem, critical points and extrema, generalized inverse and implicit function theorems. Pre-req.: MATH 246.

Classifications and characteristics of second order partial differential equations, qualitative behavior of solutions to elliptic equations and evolution equations. First order partial differential equations, eigen function expansion and integral transform, Green’s functions, finite difference method. Pre-req.: MATH 244.

Topics include one and two-sample estimation problems, one and two-sample tests of hypothesis, P value, Analysis of variance (One way ANOVA), Goodness of Fit Test, Chi- Square test, Simple Linear regression and Correlation, Multiple Linear regression, Two Factor Analysis of Variance and some non- parametric tests. Statistical software tools in Microsoft Excel will be used to help in analysis. Pre-req.:Math 242

Modeling linear programming and deriving methods for solving them using algorithms such as: geometrical method, simplex method, dual simplex method, transportation algorithms. Problems without constraint will be also discussed, where various numerical methods apply. Pre-req.: MATH 348.

Hamilton-Cayley theorem, Jordan normal form, adjoints and spectral theory in finite dimensional spaces, primary decomposition, triangularizations, direct sums, canonical forms, orthogonal and unitary transformations. Pre-req.: MATH 341.

This course covers selected topics in mathematics.

Course Code |
Course Title |
Credits |
Hours Distribution |
Course Type |

MATH351 |
Differential Geometry |
3 |
(3Crs.:3Lec) |
DE |

MATH352 |
Number Theory |
3 |
(3Crs.:3Lec.,1Lab) |
DE |

MATH353 |
Set Theory |
3 |
(3Crs.:3Lec) |
DE |

MATH354 |
Introduction to Dynamics |
3 |
(3Crs.:3Lec) |
DE |

MATH355 |
Calculus of Variations |
3 |
(3Crs.:3Lec) |
DE |

MATH451 |
Differential Calculus |
3 |
(3Crs.:3Lec) |
DE |

MATH452 |
Partial Differential Equations |
3 |
(3Crs.:3Lec) |
DE |

MATH453 |
Advanced Probability and Statistics |
3 |
(3Crs.:3Lec,1Lab) |
DE |

MATH454 |
Mathematical Computation |
3 |
(3Crs.:2Lec.,2 Lab) |
DE |

MATH455 |
Topics in Linear Algebra |
3 |
(3Crs.:3Lec.,1Lab) |
DE |

MATH456 |
Topics in Mathematics |
3 |
(3Crs.:3Lec) |
DE |