AUL | Bachelor of Science in Mathematics

Bachelor of Science in Mathematics

Overview

Through the different fields of algebra, analysis, geometry, number theory, and applied mathematics, the department aims to provide to students a balance between qualitative and quantitative aspects of mathematics. It will help students master the theory without losing sight of applications. Graduates of the Mathematics Department should be well prepared for graduate work or professional employment in mathematics or related areas.

Educational objectives for mathematics program

pursue professional development by securing acceptance in graduate programs in mathematics and other fields such as the field of quantitative/mathematical finance, mathematical computing, statistics and actuarial science
become contributing members of multidisciplinary teams and successfully apply the fundamentals of their educational background
apply their knowledge in modern industry or teaching

Program Outcome Objectives

At the end of the program, students will be able to

work with abstract mathematical concepts in a general context
apply the mathematical concepts by developing, analyzing, refining and/or resolving mathematical models.
engage complex mathematical reasoning in validating arguments by refining their analytical skills.
define and give good concrete examples of the mathematical structures like vector space, group, ring, etc..
use the appropriate IT resources to tackle mathematical problems and/or to document mathematics.
communicate, verbally and/or written, mathematical principles and ideas with coherence and clarity.
understand professional and ethical responsibility.
adopt effective learning strategies.
function in a multidisciplinary team.

Courses & Requirements

University General Requirements

Code	Name	Credits
ENG203	English for Academic writing English for Academic writing ENG203 This course is a comprehensive rhetoric and sentence structure course. It aims at developing the students’ reading skills to become strategic readers, to expand general vocabulary, and to think critically. Students are expected to be able to comprehend reading by practicing various reading skills such as predicting, scanning for details, skimming for main ideas, guessing meanings from context and making inference. Moreover, students are helped to learn how to appreciate literature. This course emphasizes, however, the interaction of reading and writing skills. Therefore, students are guided to organize and express ideas through writing well-organized and developed essays.	3
ENG204	Advanced Eng. Academic Writing Advanced Eng. Academic Writing ENG204 This course is designed to develop students’ reading, writing, and speaking skills and help them fulfill their academic requirements. They will boost their critical thinking skills through fulfilling various text-analysis tasks, and enrich their vocabulary repertoire. Students will thus improve their sentence structure, paragraph, and essay writing whilst multi-drafting essays of various types. They will have the chance to enrich their fluency and accuracy through preparing and presenting an authentic public talk.	3
ENG206	Business Communication Skills	3
CST201	General Education I	3
CST 202	General Education II	3

Description: Five courses including three English courses and two General Education courses.

Major Electives

Description: 2 major elective courses

Faculty Common Requirements

Code	Name	Credits
MAT211	Discrete Math Discrete Math MAT211 This course introduces students to ideas and techniques from discrete mathematics that are widely used in science and engineering. It teaches the students techniques in how to think logically and mathematically and apply these techniques in solving problems. Students will learn logic and proof, sets, functions, as well as algorithms and mathematical reasoning.	3
MAT220	Linear Algebra Linear Algebra MAT220 This course provides basic knowledge in the following topics: Matrices & systems of linear equations, Gauss-Jordan elimination. Matrix algebra, Matrix operations, Symmetric matrices,The inverse of a matrix. Introduction to determinants, Properties of determinants, Computation of determinants, Matrix inversion & Cramer’s rule. Introduction to vectors, Dot product, norm, angle, Linear transformations, Matrix transformations. Vector spaces, Subspaces, Linear combinations of vectors, Linear dependence and independence, Basis and dimension, Rank of a matrix, Orthonormal projections in Rn. Eigenvalues and eigenvectors, Diagonalization of matrices.	3
CCE210	Logic Design Logic Design CCE210 The course introduces different number systems with various techniques to convert from one number system to another. It covers the representation of the behavior of digital systems through Boolean expressions, logical gates and truth tables and the use of the Karnaugh maps for simplifying Boolean expressions. It focus on the steps for designing combinational (Decoders, Multiplexers, full adders, adder-subtractor) and sequential (Latches, JK & D flipflops, registers, counters) logic circuits.	3
MAT320	Numerical Computing Numerical Computing MAT320 Numerical Computing is the science of understanding computer methods for solving mathematical problems. This course, introduces some of these methods, explains how they work, and discusses how they can fail. It covers the following topics : numerical methods for solving some equations such as bisection, false position, Newton-Raphson and secant methods, Newton and Lagrange interpolation, numerical methods for solving linear equations such as Gauss, elimination, Gauss-Seidel and Jacobi methods and numerical methods for integration and differentiation.	3
MAT208	Probability & Statistics Probability & Statistics MAT208 This course introduces students to a very important branch in mathematics, which is the Probability and Statistics. It shows the students the use of probability and statistics in many fields of science and engineering. This course explains the concept of random variables and its related probability distributions (i.e. Discrete and continuous). It expands the concept of central tendency and dispersion using the mathematical equations of expectation, variance, covariance and correlation. Finally, this course shows students how to use integrals in order to calculate the probability of certain probability distribution, such as the normal distribution.	3
CSC213L	Programing I Lab Programing I Lab CSC213L In the lab, students gain hands on experience on the topics covered in the course CSC213	1
MAT203	Differential Equations Differential Equations MAT203 This course provides techniques of solving some ODE and their applications in Science and engineering. The course covers Definitions & terminology of ODE’s, Initial-value problems. Separable variables, Linear differential equations, Exact equations (Integrating factors), Solution by substitutions (Bernoulli DE). IVP’s and BVP’s, Homogeneous LDE’s, Exact equations ( Integrating factors), Homogeneous LDE’s with constant coefficients, Nonhomogeneous LDE’s, Method of undetermined coefficients, Variation of parameters (method of Lagrange), The Cauchy-Euler LDE. Definition of the Laplace transform, Inverse transforms, Transform of IVP’s, Operational properties, Transforms of generalized functions. Solutions about ordinary points of LDE’s, Solutions about singular points (method of Frobenius).	3
CCE210L	Logic Design Lab Logic Design Lab CCE210L In the lab the students develop their practical design skills through the implementation of boolean functions using logic gates, construct combinational and sequential digital circuits like adders and counters. The Lab also introduce Logisim software, a tool for designing and simulating digital logic circuits.	1
MAT201	Calculus III Calculus III MAT201 This course provides basic knowledge in complex numbers, sequences & series, analytic geometry and multivariate calculus. It covers the following topics: forms of complex numbers and their geometric properties, fundamental concepts in vector calculus, tests of convergence of numerical sequences and series, techniques of double integrations.	3
ENGR202	Introduction to Engineering Introduction to Engineering ENGR202 The course takes the students into the realms of the engineering world and profession, introduce them to various engineering disciplines, engineering ethics and engineering methods in problem solving and critical thinking. In addition the students will learn common software tools they will need throughout their education. The course includes a project where the students will put basic engineering concepts into work as their first applied design.	3
CSC213	Programing I Programing I CSC213 This course introduces the basic principles of algorithmic problem solving and programming using a high level procedural language, namely C/C++. It gets the students acquainted with the language constructs such as variable allocation, data types, input/output instructions, basic control structures, arrays and low-level memory management with pointers. Using functions and procedures, the students use the methods of top down design, stepwise refinement and procedural abstraction. Throughout the course, the students get familiar with the steps of software development process: design, implementation, testing and documentation.	3

Major Requirements

Code	Name	Credits
MAT410	Groups & Rings Theory Groups & Rings Theory MAT410 This course covers the following topics: Complement to Discrete Math; Structure of Groups; Group’s Homomorphism; Rings and Ideals; Fields.	3
MAT411	Integral Calculus Integral Calculus MAT411 This course provides the fudamental concepts of the Riemann integrable functions and a brief introduction to the measure theory.	3
MAT314	Introduction to Complex Analysis Introduction to Complex Analysis MAT314 This course provide an introduction of the Theory and Applications of Functions of Complex Variable. It covers the following topics: Complex Numbers, Analytic Functions, Cauchy-Riemann Equations, Integration in the Complex Plane, Cauchy’s Integral Theorem, Singularities, Residues, Contour Integration.	3
MAT316	Introduction to Real Analysis Introduction to Real Analysis MAT316 The course serves as an introduction to the theory of real analysis. Students should learn from the course the properties of the real number system, the basic definitions and notions for sequences and functions including limits, convergence, continuity uniform continuity, derivatives and their algebraic properties. In this course we look deeply at the concepts you learned in your calculus courses and we will discuss how to prove many of the rules and theorems you have used in the past and have had an intuitive understanding.	3
MAT315	Introduction to Topology Introduction to Topology MAT315 This course provides fundamental concepts in general Topology applied on metric Spaces such as distances and norms, Open and closed sets, interior, exterior, boundary and closure of a set.	3
MAT413	Numbers Theory Numbers Theory MAT413 This course is an introduction to number theory. Topics to be covered include: • Divisibility, Greatest Common Divisor (GCD), Least Common Multiple (LCM), Euclidean Algorithm and the Fundamental Theorem of Arithmetic • Arithmetic Functions, Diophantine Equations • Congruences, Systems of linear Congruences • Residues, Euler’s Totient function, Euler-Fermat Theorem, Primitive Roots Perfect Numbers, Distribution Prime Number.	3
MAT420	Partial Differential Equations + MATLAB Partial Differential Equations + MATLAB MAT420 Partial differential equations (PDEs) are an extremely useful tool on the exact sciences and engineering, and form an important area of pure and applied mathematics. The goal in this course is to achieve an understanding of linear first and second order PDEs, along with the very effective transform methods which make their solution possible in the case of constant coefficients. Building on this understanding, we will also consider briefly some interesting nonlinear problems, where exact or series solutions are almost never available. Techniques and proofs will be brought into the lectures in places where they serve to enhance understanding of the applications of PDEs.	3
MAT430	Analysis on Surfaces Analysis on Surfaces MAT430 This course provides an introduction to differential geometry which is relevant to physics and engineering problems in two or more dimensions. It covers the following topics: local study of curves and surfaces.	3
PHY211	Electricity & Magnetism Electricity & Magnetism PHY211 The course will provide basic understanding of electrostatics (Coulomb's Law, electric field and electric potential resulting from a continuous or discrete distribution of charges, Gauss law) the basic physics behind passive circuit elements (resistors, capacitors and inductors) and circuit variables (current and voltage) the source of magnetic field (Biot-Savart and Ampere's law) and their effect on charged particles (Lorentz force)	3
MAT312	Engineering Mathematics Engineering Mathematics MAT312 This course provides an introduction to complex analysis and vector analysis, which is relevant to physics and engineering problems in two or more dimensions. It covers the following topics: introduction to complex analysis including properties of complex numbers, analytic functions, and special attention to the geometric properties of complex functions and application of differential and integral calculus to vector valued functions, vector field analysis, line and surface integrals, Green, Stokes and Gauss theorem.	3
MCE202	Mechanics I Mechanics I MCE202 This course introduces students to the fundamentals on how solids behave when exposed to forces and deformations which is known as statics and dynamics. Topics covered include: static equilibrium, force resultants, support conditions. The course also introduces Newton’s law of motion applied for one and two dimensions, translational and rotational motion, linear and angular moments.	3
MAT 416	Differential Calculus Differential Calculus MAT 416 This course covers the following topics: 1. Differential Calculus on IR Differential Calculus in Higher Dimensions.	3
MAT499	Senior Project + LATEX	4

Free Electives

Description: 1 free elective course

Department Majors & Programs

Bachelor of Science in Statistics
Credits
Bachelor of Science in Physics
96 Credits
Bachelor of Science in Mathematics
96 Credits
Bachelor of Science in Chemistry
Credits
Bachelor of Science in Biology
Credits
Bachelor of Science in Actuarial Mathematics
Credits

Bachelor of Science in Mathematics

Overview

Educational objectives for mathematics program

Program Outcome Objectives

Courses & Requirements

English for Academic writing

Advanced Eng. Academic Writing

Discrete Math

Linear Algebra

Logic Design

Numerical Computing

Probability & Statistics

Programing I Lab

Differential Equations

Logic Design Lab

Calculus III

Introduction to Engineering

Programing I

Groups & Rings Theory

Integral Calculus

Introduction to Complex Analysis

Introduction to Real Analysis

Introduction to Topology

Numbers Theory

Partial Differential Equations + MATLAB

Analysis on Surfaces

Electricity & Magnetism

Engineering Mathematics

Mechanics I

Differential Calculus

Department Majors & Programs

Bachelor of Science in Statistics

Bachelor of Science in Physics

Bachelor of Science in Mathematics

Bachelor of Science in Chemistry

Bachelor of Science in Biology

Bachelor of Science in Actuarial Mathematics

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